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Fundamentals of communication systems
Citation preview
Essentials Of Communication Systems
A Presentation By-A S Kurhekar
httpsitesgooglecomsiteanilkurhekar100
Overview of Analog Technology
Areas of ApplicationOld telephone networksMost television broadcasting at presentRadio broadcasting
Analog Signals The Basics
Cycle
Time
Signal
Amplitude
Frequency = CyclesSecond
Amplitude and Cycle
Amplitude Distance above reference line
Cycle One complete wave
Frequency Frequency
Cycles per second Hertz is the unit used for expressing frequency
Frequency spectrum Defines the bandwidth for different analog
communication technologies
Frequency Spectrumand Bandwidth Available range of frequencies for
communication Starts from low frequency communication
such as voice and progresses to high frequency communication such as satellite communication
The spectrum spans the entire bandwidth of communicable frequencies
Frequency Spectrum
Low Frequency High Frequency
Radio Frequency
CoaxialCable
MHz
Voice
KHz
SatelliteTransmission
MicrowaveMHz
Low-endVoice band
MiddleMicrowave
High-endSatellite communication
An Overview of Digital Technology
Areas of Application Computers New telephone networks Phased introduction of digital television technology
Digital Technology Basics Digital signals that could be assigned digital values
Digital computer technology Digital signals Binary representation
Encoded into ones and zeros
Digital Signal And Binary Signals
Digital signals Value limited to a finite set Digital systems more robust Binary Signals Has at most 2 values Used to represent bit values Bit time T needed to send 1 bit Data rate R=1T bits per second
t
x(t)
t
x(t) 1
0 0 0
1 1
0T
Digital Terms
Pulse Pulse duration Pulse amplitude Signal strength
Clock Speed and Execution Speed Pulse duration is inversely proportional to the
clock frequency Faster the clock speed the smaller the pulse
duration Smaller the pulse duration the faster the
execution in general
Performance Metrics
Analog Communication Systems Metric is fidelity Want m(t)m(t)
Digital Communication Systems Metrics are data rate (R bps) and probability of
bit error (Pb=p(bb)) Without noise never make bit errors With noise Pb depends on signal and noise
power data rate and channel characteristics
Data Rate Limits
Data rate R limited by signal power noise power distortion and bit error probability
Without distortion or noise can have infinite data rate with Pb=0
Shannon capacity defines maximum possible data rate for systems with noise and distortion Rate achieved with bit error probability close to zero In white Gaussian noise channels C=B log(1+SNR) Does not show how to design real systems
Shannon obtained C=32 Kbps for phone channels Get higher rates with modemsDSL (use more BW) Nowhere near capacity in wireless systems
Signal Energy and Power The energy in a signal g(t) is
The power in a signal g(t) is
Power is often expression in dBw or dBm [10 log10 P] dBW is dB power relative to Watts [10 log10 (P001)] dBm is dB power relative to mWatts Signal powerenergy determines its resistance to noise
dttgdttgEg )(|)(| 2
T
T
T
T
T
T dttgT
dttgT
P 22 )(2
1lim|)(|
2
1lim
The Communication System
Communication systems modulate analog signals or bits for transmission over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Overview of Analog Technology
Areas of ApplicationOld telephone networksMost television broadcasting at presentRadio broadcasting
Analog Signals The Basics
Cycle
Time
Signal
Amplitude
Frequency = CyclesSecond
Amplitude and Cycle
Amplitude Distance above reference line
Cycle One complete wave
Frequency Frequency
Cycles per second Hertz is the unit used for expressing frequency
Frequency spectrum Defines the bandwidth for different analog
communication technologies
Frequency Spectrumand Bandwidth Available range of frequencies for
communication Starts from low frequency communication
such as voice and progresses to high frequency communication such as satellite communication
The spectrum spans the entire bandwidth of communicable frequencies
Frequency Spectrum
Low Frequency High Frequency
Radio Frequency
CoaxialCable
MHz
Voice
KHz
SatelliteTransmission
MicrowaveMHz
Low-endVoice band
MiddleMicrowave
High-endSatellite communication
An Overview of Digital Technology
Areas of Application Computers New telephone networks Phased introduction of digital television technology
Digital Technology Basics Digital signals that could be assigned digital values
Digital computer technology Digital signals Binary representation
Encoded into ones and zeros
Digital Signal And Binary Signals
Digital signals Value limited to a finite set Digital systems more robust Binary Signals Has at most 2 values Used to represent bit values Bit time T needed to send 1 bit Data rate R=1T bits per second
t
x(t)
t
x(t) 1
0 0 0
1 1
0T
Digital Terms
Pulse Pulse duration Pulse amplitude Signal strength
Clock Speed and Execution Speed Pulse duration is inversely proportional to the
clock frequency Faster the clock speed the smaller the pulse
duration Smaller the pulse duration the faster the
execution in general
Performance Metrics
Analog Communication Systems Metric is fidelity Want m(t)m(t)
Digital Communication Systems Metrics are data rate (R bps) and probability of
bit error (Pb=p(bb)) Without noise never make bit errors With noise Pb depends on signal and noise
power data rate and channel characteristics
Data Rate Limits
Data rate R limited by signal power noise power distortion and bit error probability
Without distortion or noise can have infinite data rate with Pb=0
Shannon capacity defines maximum possible data rate for systems with noise and distortion Rate achieved with bit error probability close to zero In white Gaussian noise channels C=B log(1+SNR) Does not show how to design real systems
Shannon obtained C=32 Kbps for phone channels Get higher rates with modemsDSL (use more BW) Nowhere near capacity in wireless systems
Signal Energy and Power The energy in a signal g(t) is
The power in a signal g(t) is
Power is often expression in dBw or dBm [10 log10 P] dBW is dB power relative to Watts [10 log10 (P001)] dBm is dB power relative to mWatts Signal powerenergy determines its resistance to noise
dttgdttgEg )(|)(| 2
T
T
T
T
T
T dttgT
dttgT
P 22 )(2
1lim|)(|
2
1lim
The Communication System
Communication systems modulate analog signals or bits for transmission over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Analog Signals The Basics
Cycle
Time
Signal
Amplitude
Frequency = CyclesSecond
Amplitude and Cycle
Amplitude Distance above reference line
Cycle One complete wave
Frequency Frequency
Cycles per second Hertz is the unit used for expressing frequency
Frequency spectrum Defines the bandwidth for different analog
communication technologies
Frequency Spectrumand Bandwidth Available range of frequencies for
communication Starts from low frequency communication
such as voice and progresses to high frequency communication such as satellite communication
The spectrum spans the entire bandwidth of communicable frequencies
Frequency Spectrum
Low Frequency High Frequency
Radio Frequency
CoaxialCable
MHz
Voice
KHz
SatelliteTransmission
MicrowaveMHz
Low-endVoice band
MiddleMicrowave
High-endSatellite communication
An Overview of Digital Technology
Areas of Application Computers New telephone networks Phased introduction of digital television technology
Digital Technology Basics Digital signals that could be assigned digital values
Digital computer technology Digital signals Binary representation
Encoded into ones and zeros
Digital Signal And Binary Signals
Digital signals Value limited to a finite set Digital systems more robust Binary Signals Has at most 2 values Used to represent bit values Bit time T needed to send 1 bit Data rate R=1T bits per second
t
x(t)
t
x(t) 1
0 0 0
1 1
0T
Digital Terms
Pulse Pulse duration Pulse amplitude Signal strength
Clock Speed and Execution Speed Pulse duration is inversely proportional to the
clock frequency Faster the clock speed the smaller the pulse
duration Smaller the pulse duration the faster the
execution in general
Performance Metrics
Analog Communication Systems Metric is fidelity Want m(t)m(t)
Digital Communication Systems Metrics are data rate (R bps) and probability of
bit error (Pb=p(bb)) Without noise never make bit errors With noise Pb depends on signal and noise
power data rate and channel characteristics
Data Rate Limits
Data rate R limited by signal power noise power distortion and bit error probability
Without distortion or noise can have infinite data rate with Pb=0
Shannon capacity defines maximum possible data rate for systems with noise and distortion Rate achieved with bit error probability close to zero In white Gaussian noise channels C=B log(1+SNR) Does not show how to design real systems
Shannon obtained C=32 Kbps for phone channels Get higher rates with modemsDSL (use more BW) Nowhere near capacity in wireless systems
Signal Energy and Power The energy in a signal g(t) is
The power in a signal g(t) is
Power is often expression in dBw or dBm [10 log10 P] dBW is dB power relative to Watts [10 log10 (P001)] dBm is dB power relative to mWatts Signal powerenergy determines its resistance to noise
dttgdttgEg )(|)(| 2
T
T
T
T
T
T dttgT
dttgT
P 22 )(2
1lim|)(|
2
1lim
The Communication System
Communication systems modulate analog signals or bits for transmission over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Amplitude and Cycle
Amplitude Distance above reference line
Cycle One complete wave
Frequency Frequency
Cycles per second Hertz is the unit used for expressing frequency
Frequency spectrum Defines the bandwidth for different analog
communication technologies
Frequency Spectrumand Bandwidth Available range of frequencies for
communication Starts from low frequency communication
such as voice and progresses to high frequency communication such as satellite communication
The spectrum spans the entire bandwidth of communicable frequencies
Frequency Spectrum
Low Frequency High Frequency
Radio Frequency
CoaxialCable
MHz
Voice
KHz
SatelliteTransmission
MicrowaveMHz
Low-endVoice band
MiddleMicrowave
High-endSatellite communication
An Overview of Digital Technology
Areas of Application Computers New telephone networks Phased introduction of digital television technology
Digital Technology Basics Digital signals that could be assigned digital values
Digital computer technology Digital signals Binary representation
Encoded into ones and zeros
Digital Signal And Binary Signals
Digital signals Value limited to a finite set Digital systems more robust Binary Signals Has at most 2 values Used to represent bit values Bit time T needed to send 1 bit Data rate R=1T bits per second
t
x(t)
t
x(t) 1
0 0 0
1 1
0T
Digital Terms
Pulse Pulse duration Pulse amplitude Signal strength
Clock Speed and Execution Speed Pulse duration is inversely proportional to the
clock frequency Faster the clock speed the smaller the pulse
duration Smaller the pulse duration the faster the
execution in general
Performance Metrics
Analog Communication Systems Metric is fidelity Want m(t)m(t)
Digital Communication Systems Metrics are data rate (R bps) and probability of
bit error (Pb=p(bb)) Without noise never make bit errors With noise Pb depends on signal and noise
power data rate and channel characteristics
Data Rate Limits
Data rate R limited by signal power noise power distortion and bit error probability
Without distortion or noise can have infinite data rate with Pb=0
Shannon capacity defines maximum possible data rate for systems with noise and distortion Rate achieved with bit error probability close to zero In white Gaussian noise channels C=B log(1+SNR) Does not show how to design real systems
Shannon obtained C=32 Kbps for phone channels Get higher rates with modemsDSL (use more BW) Nowhere near capacity in wireless systems
Signal Energy and Power The energy in a signal g(t) is
The power in a signal g(t) is
Power is often expression in dBw or dBm [10 log10 P] dBW is dB power relative to Watts [10 log10 (P001)] dBm is dB power relative to mWatts Signal powerenergy determines its resistance to noise
dttgdttgEg )(|)(| 2
T
T
T
T
T
T dttgT
dttgT
P 22 )(2
1lim|)(|
2
1lim
The Communication System
Communication systems modulate analog signals or bits for transmission over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Frequency Spectrumand Bandwidth Available range of frequencies for
communication Starts from low frequency communication
such as voice and progresses to high frequency communication such as satellite communication
The spectrum spans the entire bandwidth of communicable frequencies
Frequency Spectrum
Low Frequency High Frequency
Radio Frequency
CoaxialCable
MHz
Voice
KHz
SatelliteTransmission
MicrowaveMHz
Low-endVoice band
MiddleMicrowave
High-endSatellite communication
An Overview of Digital Technology
Areas of Application Computers New telephone networks Phased introduction of digital television technology
Digital Technology Basics Digital signals that could be assigned digital values
Digital computer technology Digital signals Binary representation
Encoded into ones and zeros
Digital Signal And Binary Signals
Digital signals Value limited to a finite set Digital systems more robust Binary Signals Has at most 2 values Used to represent bit values Bit time T needed to send 1 bit Data rate R=1T bits per second
t
x(t)
t
x(t) 1
0 0 0
1 1
0T
Digital Terms
Pulse Pulse duration Pulse amplitude Signal strength
Clock Speed and Execution Speed Pulse duration is inversely proportional to the
clock frequency Faster the clock speed the smaller the pulse
duration Smaller the pulse duration the faster the
execution in general
Performance Metrics
Analog Communication Systems Metric is fidelity Want m(t)m(t)
Digital Communication Systems Metrics are data rate (R bps) and probability of
bit error (Pb=p(bb)) Without noise never make bit errors With noise Pb depends on signal and noise
power data rate and channel characteristics
Data Rate Limits
Data rate R limited by signal power noise power distortion and bit error probability
Without distortion or noise can have infinite data rate with Pb=0
Shannon capacity defines maximum possible data rate for systems with noise and distortion Rate achieved with bit error probability close to zero In white Gaussian noise channels C=B log(1+SNR) Does not show how to design real systems
Shannon obtained C=32 Kbps for phone channels Get higher rates with modemsDSL (use more BW) Nowhere near capacity in wireless systems
Signal Energy and Power The energy in a signal g(t) is
The power in a signal g(t) is
Power is often expression in dBw or dBm [10 log10 P] dBW is dB power relative to Watts [10 log10 (P001)] dBm is dB power relative to mWatts Signal powerenergy determines its resistance to noise
dttgdttgEg )(|)(| 2
T
T
T
T
T
T dttgT
dttgT
P 22 )(2
1lim|)(|
2
1lim
The Communication System
Communication systems modulate analog signals or bits for transmission over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Frequency Spectrum
Low Frequency High Frequency
Radio Frequency
CoaxialCable
MHz
Voice
KHz
SatelliteTransmission
MicrowaveMHz
Low-endVoice band
MiddleMicrowave
High-endSatellite communication
An Overview of Digital Technology
Areas of Application Computers New telephone networks Phased introduction of digital television technology
Digital Technology Basics Digital signals that could be assigned digital values
Digital computer technology Digital signals Binary representation
Encoded into ones and zeros
Digital Signal And Binary Signals
Digital signals Value limited to a finite set Digital systems more robust Binary Signals Has at most 2 values Used to represent bit values Bit time T needed to send 1 bit Data rate R=1T bits per second
t
x(t)
t
x(t) 1
0 0 0
1 1
0T
Digital Terms
Pulse Pulse duration Pulse amplitude Signal strength
Clock Speed and Execution Speed Pulse duration is inversely proportional to the
clock frequency Faster the clock speed the smaller the pulse
duration Smaller the pulse duration the faster the
execution in general
Performance Metrics
Analog Communication Systems Metric is fidelity Want m(t)m(t)
Digital Communication Systems Metrics are data rate (R bps) and probability of
bit error (Pb=p(bb)) Without noise never make bit errors With noise Pb depends on signal and noise
power data rate and channel characteristics
Data Rate Limits
Data rate R limited by signal power noise power distortion and bit error probability
Without distortion or noise can have infinite data rate with Pb=0
Shannon capacity defines maximum possible data rate for systems with noise and distortion Rate achieved with bit error probability close to zero In white Gaussian noise channels C=B log(1+SNR) Does not show how to design real systems
Shannon obtained C=32 Kbps for phone channels Get higher rates with modemsDSL (use more BW) Nowhere near capacity in wireless systems
Signal Energy and Power The energy in a signal g(t) is
The power in a signal g(t) is
Power is often expression in dBw or dBm [10 log10 P] dBW is dB power relative to Watts [10 log10 (P001)] dBm is dB power relative to mWatts Signal powerenergy determines its resistance to noise
dttgdttgEg )(|)(| 2
T
T
T
T
T
T dttgT
dttgT
P 22 )(2
1lim|)(|
2
1lim
The Communication System
Communication systems modulate analog signals or bits for transmission over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
An Overview of Digital Technology
Areas of Application Computers New telephone networks Phased introduction of digital television technology
Digital Technology Basics Digital signals that could be assigned digital values
Digital computer technology Digital signals Binary representation
Encoded into ones and zeros
Digital Signal And Binary Signals
Digital signals Value limited to a finite set Digital systems more robust Binary Signals Has at most 2 values Used to represent bit values Bit time T needed to send 1 bit Data rate R=1T bits per second
t
x(t)
t
x(t) 1
0 0 0
1 1
0T
Digital Terms
Pulse Pulse duration Pulse amplitude Signal strength
Clock Speed and Execution Speed Pulse duration is inversely proportional to the
clock frequency Faster the clock speed the smaller the pulse
duration Smaller the pulse duration the faster the
execution in general
Performance Metrics
Analog Communication Systems Metric is fidelity Want m(t)m(t)
Digital Communication Systems Metrics are data rate (R bps) and probability of
bit error (Pb=p(bb)) Without noise never make bit errors With noise Pb depends on signal and noise
power data rate and channel characteristics
Data Rate Limits
Data rate R limited by signal power noise power distortion and bit error probability
Without distortion or noise can have infinite data rate with Pb=0
Shannon capacity defines maximum possible data rate for systems with noise and distortion Rate achieved with bit error probability close to zero In white Gaussian noise channels C=B log(1+SNR) Does not show how to design real systems
Shannon obtained C=32 Kbps for phone channels Get higher rates with modemsDSL (use more BW) Nowhere near capacity in wireless systems
Signal Energy and Power The energy in a signal g(t) is
The power in a signal g(t) is
Power is often expression in dBw or dBm [10 log10 P] dBW is dB power relative to Watts [10 log10 (P001)] dBm is dB power relative to mWatts Signal powerenergy determines its resistance to noise
dttgdttgEg )(|)(| 2
T
T
T
T
T
T dttgT
dttgT
P 22 )(2
1lim|)(|
2
1lim
The Communication System
Communication systems modulate analog signals or bits for transmission over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Digital Signal And Binary Signals
Digital signals Value limited to a finite set Digital systems more robust Binary Signals Has at most 2 values Used to represent bit values Bit time T needed to send 1 bit Data rate R=1T bits per second
t
x(t)
t
x(t) 1
0 0 0
1 1
0T
Digital Terms
Pulse Pulse duration Pulse amplitude Signal strength
Clock Speed and Execution Speed Pulse duration is inversely proportional to the
clock frequency Faster the clock speed the smaller the pulse
duration Smaller the pulse duration the faster the
execution in general
Performance Metrics
Analog Communication Systems Metric is fidelity Want m(t)m(t)
Digital Communication Systems Metrics are data rate (R bps) and probability of
bit error (Pb=p(bb)) Without noise never make bit errors With noise Pb depends on signal and noise
power data rate and channel characteristics
Data Rate Limits
Data rate R limited by signal power noise power distortion and bit error probability
Without distortion or noise can have infinite data rate with Pb=0
Shannon capacity defines maximum possible data rate for systems with noise and distortion Rate achieved with bit error probability close to zero In white Gaussian noise channels C=B log(1+SNR) Does not show how to design real systems
Shannon obtained C=32 Kbps for phone channels Get higher rates with modemsDSL (use more BW) Nowhere near capacity in wireless systems
Signal Energy and Power The energy in a signal g(t) is
The power in a signal g(t) is
Power is often expression in dBw or dBm [10 log10 P] dBW is dB power relative to Watts [10 log10 (P001)] dBm is dB power relative to mWatts Signal powerenergy determines its resistance to noise
dttgdttgEg )(|)(| 2
T
T
T
T
T
T dttgT
dttgT
P 22 )(2
1lim|)(|
2
1lim
The Communication System
Communication systems modulate analog signals or bits for transmission over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Digital Terms
Pulse Pulse duration Pulse amplitude Signal strength
Clock Speed and Execution Speed Pulse duration is inversely proportional to the
clock frequency Faster the clock speed the smaller the pulse
duration Smaller the pulse duration the faster the
execution in general
Performance Metrics
Analog Communication Systems Metric is fidelity Want m(t)m(t)
Digital Communication Systems Metrics are data rate (R bps) and probability of
bit error (Pb=p(bb)) Without noise never make bit errors With noise Pb depends on signal and noise
power data rate and channel characteristics
Data Rate Limits
Data rate R limited by signal power noise power distortion and bit error probability
Without distortion or noise can have infinite data rate with Pb=0
Shannon capacity defines maximum possible data rate for systems with noise and distortion Rate achieved with bit error probability close to zero In white Gaussian noise channels C=B log(1+SNR) Does not show how to design real systems
Shannon obtained C=32 Kbps for phone channels Get higher rates with modemsDSL (use more BW) Nowhere near capacity in wireless systems
Signal Energy and Power The energy in a signal g(t) is
The power in a signal g(t) is
Power is often expression in dBw or dBm [10 log10 P] dBW is dB power relative to Watts [10 log10 (P001)] dBm is dB power relative to mWatts Signal powerenergy determines its resistance to noise
dttgdttgEg )(|)(| 2
T
T
T
T
T
T dttgT
dttgT
P 22 )(2
1lim|)(|
2
1lim
The Communication System
Communication systems modulate analog signals or bits for transmission over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Performance Metrics
Analog Communication Systems Metric is fidelity Want m(t)m(t)
Digital Communication Systems Metrics are data rate (R bps) and probability of
bit error (Pb=p(bb)) Without noise never make bit errors With noise Pb depends on signal and noise
power data rate and channel characteristics
Data Rate Limits
Data rate R limited by signal power noise power distortion and bit error probability
Without distortion or noise can have infinite data rate with Pb=0
Shannon capacity defines maximum possible data rate for systems with noise and distortion Rate achieved with bit error probability close to zero In white Gaussian noise channels C=B log(1+SNR) Does not show how to design real systems
Shannon obtained C=32 Kbps for phone channels Get higher rates with modemsDSL (use more BW) Nowhere near capacity in wireless systems
Signal Energy and Power The energy in a signal g(t) is
The power in a signal g(t) is
Power is often expression in dBw or dBm [10 log10 P] dBW is dB power relative to Watts [10 log10 (P001)] dBm is dB power relative to mWatts Signal powerenergy determines its resistance to noise
dttgdttgEg )(|)(| 2
T
T
T
T
T
T dttgT
dttgT
P 22 )(2
1lim|)(|
2
1lim
The Communication System
Communication systems modulate analog signals or bits for transmission over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Data Rate Limits
Data rate R limited by signal power noise power distortion and bit error probability
Without distortion or noise can have infinite data rate with Pb=0
Shannon capacity defines maximum possible data rate for systems with noise and distortion Rate achieved with bit error probability close to zero In white Gaussian noise channels C=B log(1+SNR) Does not show how to design real systems
Shannon obtained C=32 Kbps for phone channels Get higher rates with modemsDSL (use more BW) Nowhere near capacity in wireless systems
Signal Energy and Power The energy in a signal g(t) is
The power in a signal g(t) is
Power is often expression in dBw or dBm [10 log10 P] dBW is dB power relative to Watts [10 log10 (P001)] dBm is dB power relative to mWatts Signal powerenergy determines its resistance to noise
dttgdttgEg )(|)(| 2
T
T
T
T
T
T dttgT
dttgT
P 22 )(2
1lim|)(|
2
1lim
The Communication System
Communication systems modulate analog signals or bits for transmission over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Signal Energy and Power The energy in a signal g(t) is
The power in a signal g(t) is
Power is often expression in dBw or dBm [10 log10 P] dBW is dB power relative to Watts [10 log10 (P001)] dBm is dB power relative to mWatts Signal powerenergy determines its resistance to noise
dttgdttgEg )(|)(| 2
T
T
T
T
T
T dttgT
dttgT
P 22 )(2
1lim|)(|
2
1lim
The Communication System
Communication systems modulate analog signals or bits for transmission over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
The Communication System
Communication systems modulate analog signals or bits for transmission over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
The Backdrop Data rates over channels with noise have a fundamental capacity limit
Signal energy and power determine resistance to noise
Communication system shift scale and invert signals
Unit impulse and step functions important for analysis
Fourier series represents periodic signals in terms of exponential or sinusoidal basis functions
Exponentials are eigenfunctions of LTI filters
Fourier transform is the spectral components of a signal
Rectangle in time is sinc in frequency Time-limited signals are not bandlimited and vice versa
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
SourceEncoder
Communication System Block Diagram
SourceDecoderChannel ReceiverTransmitter
TextImagesVideo
)(tx )(ˆ tx)(ˆˆˆ
21
tmbb
)(21
tmbb
Source encoder converts message into message signal or bits
Transmitter converts message signal or bits into format appropriate for channel transmission (analogdigital signal)
Channel introduces distortion noise and interference
Receiver decodes received signal back to message signal
Source decoder decodes message signal back into original message
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Analysis Outline
Channel Distortion and Equalization Ideal Filters Energy Spectral Density and its Properties Power Spectral Density and its Properties Filtering and Modulation based on PSD
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Channel Distortion
Channels introduce linear distortion Electronic components introduce nonlinear
distortion
Simple equalizers invert channel distortion Can enhance noise power
X(f) X(f)+N(f)H(f)H(f) 1H(f)
N(f)
+
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Filters
Low Pass Filter (linear phase)
Band Pass Filter (linear phase)
Most filtering (and other signal processing) is done digitally (AD followed by DSP)
1
-B B
11
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Energy Spectral Density (ESD)
Signal energy
ESD measures signal energy per unit Hz
ESD of a modulation signal
dffGdttgEg22 |)(||)(|
fdffdttgE xg )(|)(| 2
Contains less information than Fourier Transform (no phase)
g(f) 25[g(f-f0)+ g(f+f0)]X
cos(2f0t)
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Autocorrelation
Defined for real signals as g(t)=g(t)g(-t)Measures signal self-similarity at tCan be used for synchronization
ESD and autocorrelation FT pairs g(t) g(f)
Filtering based on ESD
)()()()()()()()()(2 ffGfGfGggdttgtg xg
g(f) |H(f)|2g (f)H(f)
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Power Spectral Density
Similar to ESD but for power signals (P=Et) Distribution of signal power over frequency
2)(
2
1lim)( fG
TfS T
Tg
T
T
T dttgT
P 2|)(|2
1lim
|GT(f)|21
2T
gT(t)
-T T
T=Sg(f)
dffSdttgT
P g
T
T
Tg )(|)(|2
1lim 2
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Filtering and Modulation
Filtering
ModulationWhen Sg(f) has bandwidth Bltf0
Sg(f) |H(f)|2Sg(f)H(f)
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)otherwise
+cross terms
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Modulation and Autocorrelation
Modulation When Sg(f) has bandwidth Bltf0
Autocorrelation
Sg(f) 25[Sg(f-f0)+ Sg(f+f0)]X
cos(2fct)
)()(1
lim)()(2
1lim)(
22
2
fSfGT
dttgtgT
R gTT
T
TT
g
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Probability Theory Mathematically characterizes random
events
Defined on a probability space (SAiP(bull)) Sample space of possible outcomes zi
Sample space has a subset of events Ai
Probability defined for these subsets
SA2
A3
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Probability Measures-I
P(S)=1 0P(A)1 for all events A If (AB)= then P(AUB)=P(A)+P(B)
Conditional Probability P(B|A)=P(A B)P(A) Bayes Rule P(B|A)=P(A|B)P(B)P(A)
Independent Events A and B are independent if P(A B)=P(B)P(A) Independence is a property of P(bull) For independent events P(B|A)=P(B)
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Probability Measure-II
Bernoulli Trials Total Probability Theorem
Let A1A2 hellip An be disjoint with iAi=S Then
Random Variables and their CDF and pdf CDF Fx(x)=P(xx)
pdf px(x)=dFx(x)dx
Means Moments and Variance
knk ppk
ntrialsninsuccesseskp
)1()(
A1A2 A3
S
B
P1
P3
P2
0 1 2 3
x
x
x
S
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Gaussian Random Variables
pdf defined in terms of mean and variance
Gaussian CDF defined by Q function
])[( 22
2
1)(
x
X exp
x
x
N(2) Z~N()Tails decreaseexponentially
dxeyQy
x
22
2
1)(
2erfc5)(1)()( xxQx
QxFxXp X
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Several Random Variables
Let X and Y be defined on (SAiP(bull))
Joint CDF FX Y(x y)=P (x x y y)
Joint pdf
Conditional densities
Independent RVs
ddpyxFyxpy x
)()()( xyxyxy
)()()x|( xxyy xpyxpxyp
)()()( yxxy ypxpyxp
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Sums of Random Variables and the Central Limit Theorem Sums of RVs z=x + y
Pz (z)=py (y) px (x) Mean of sum is sum of means Variance of sum is sum of variances
Central Limit Theorem x1hellipxn iid Let y=ixi z=(y-E[y])sY
As n z becomes Gaussian E[y]=0 sy2=1
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Stationarity Mean Autocorrelation
A random process is (strictly) stationary if time shifts donrsquot change probability P(x(t1)x1x(t2) x2hellipx(tn) xn)=
P(x(t1+T)x1x(t2+T) x2hellipx(tn+T) xn)
True for all T and all sets of sample times Mean of random process E[x(t)]=
Stationary process E[X(t)]= Autocorrelation of a random process
Defined as RX(t1t2)= E[x(t1)x(t2)]] Stationary process Rx(t1t2)=RX(t2-t1) Correlation of process samples over time
x(t)
x
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Wide Sense Stationary (WSS) A process is WSS if
E[x(t)] is constant
RX(t1t2)= E[X(t1)X(t2)]]=RX(t2-t1)= RX (t) Intuitively stationary in 1st and 2nd moments
Ergodic WSS processes Have the property that time averages equal
probabilistic averages Allow probability characteristics to be obtained
from a single sample over time
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Power Spectral Density (PSD)
Defined only for WSS processes FT of autocorrelation function RX (t) SX (f) E[X2(t)]= SX (f) df White Noise Flat PSD
Good approximation in practice
Modulation
5N0() 5N0
Sn(f)Rn()
f
Sn(f) 25[Sn(f-fc)+ Sn(f-fc)]X
cos(2fct+)
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Gaussian Processes
z(t) is a Gaussian process if its samples are jointly Gaussian
Filtering a Gaussian process results in a Gaussian process
Integrating a Gaussian process results in a Gaussian random variable
T
g dttxtgY0
)()(
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Examples of noise in Communication Systems Gaussian processes
Filtering a Gaussian process yields a Gaussian process
Sampling a Gaussian process yields jointly Gaussian RVs
If the autocorrelation at the sample times is zero the RVs are independent
The signal-to-noise power ratio (SNR) is obtained by integrating the PSD of the signal and integrating the PSD of the noise
In digital communications the bit value is obtained by integrating the signal and the probability of error by integrating Gaussian noise
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Introduction to Carrier Modulation
Basic concept is to vary carrier signal relative to information signal or bitsThe carrier frequency is allocated by a
regulatory body like the FCC ndash spectrum is pretty crowded at this point
Analog modulation varies amplitude (AM) frequency (FM) or phase (PM) of carrier
Digital modulation varies amplitude (MAM) phase (PSK) pulse (PAM) or amplitudephase (QAM)
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Double Sideband (Suppressed Carrier) Amplitude Modulation
Modulated signal is s (t)=m(t)cos(2pi fct) Called double-sideband suppressed carrier
(DSBSC) AM
Generation of DSB-SC AM modulation Direct multiplication (impractical) Nonlinear modulators Basic premise is to add
m(t) and the carrier then perform a nonlinear operation
Generates desired signal s(t) plus extra terms that are filtered out
Examples include diodetransistor modulators switch modulators and ring modulators
)]()([5)2cos()()( ccc ffSffStftmts
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Coherent Detection of DSBAM
Detector uses another DSB-SC AM modulator
Demodulated signal macute(t)=5cos(f2-f1)m(t) Phase offset if f2-f1=p2 macute(t)=0
Coherent detection via PLL (f2f1) required Will study at end of AM discussion
m(t)
cos(ct+
DSBSCModulator
s(t) DSBSCModulator LPF
macute(t)
cos(ct+
Channel
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Introduction to Angle Modulation and FM
Information encoded in carrier freqphase Modulated signal is s(t)=Accos(q(t))
q (t)=f (m (t))
Standard FM q (t)=2pfct+2pkfm(t)dt Instantaneous frequency fi=fc + kf m(t) Signal robust to amplitude variations Robust to signal reflections and refractions
Analysis is nonlinear Hard to analyze
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
FM Bandwidth and Carsonrsquos Rule
Frequency Deviation Df=kf max |m (t)| Maximum deviation of wi from wc wi =wc + kf m(t)
Carsonrsquos Rule
Bs depends on maximum deviation from wc AND how fast wi changes
Narrowband FM DfltltBmBs2Bm Wideband FM DfgtgtBm Bs2Df
Bs2f+2Bm
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Spectral Analysis of FM
S (t)= A cos (wc t + kf m (a) da)Very hard to analyze for general m(t)
Let m(t)=cos (wm t) Bandwidth fm
S(f) sequence of d functions at f=fc plusmn nfm
If Df ltltfm Bessel function small for f(fcfm)
If Df gtgtfm significant components up to fcplusmnDf
fcfc+fmfc+2
fm
fc+3fm
fc+ 4fm
fc -4fmfc -3fm
fc -2fm
fc-fm
f
helliphellip5AcJn()
B2f WBFM
5AcJn()
S(f) for m(t)=cos(2fmt)
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Generating FM Signals
NBFM
WBFM Direct Method Modulate a VCO with m(t)
Indirect Method
m(t) ProductModulator
Asin(ct)
s(t)2kf(middot)dt
(t)
-90o LO
+
Accos(ct)+
-
)()()())(22cos()( 1120111 tsatsatsdmktfAts nn
t
c
termsother ))(22cos(011
tdmnktnfA
termsother ))(22(cos)(0112
tnncn dmktfAats
ProductModulator
(k1f1)
m(t) s1(t) NonlinearDevice
s2(t)BPF s(t)
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
FM Detection
Differentiator and Envelope Detector
Zero Crossing Detector Uses rate of zero crossings to estimate wi
Phase Lock Loop (PLL) Uses VCO and feedback to extract m(t)
t
fcfc dmkttmkAts ])(sin[)]([)(
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Introduction to Digital Modulation Most information today is in bits Baseband digital modulation converts bits into analog signals y(t)
(bits encoded in amplitude)
Bandwidth and PSD of y(t) determined by pulse shape p(t) and ak
If pulse duration is bit time Tb modulation called non-return to zero (NRZ) if less than Tb called return to zero (RZ)
)()()()()()( bk
kbk
k kTtatxfortptxkTtpaty
AawithpolarforTfPAfSfPfS kbxy |)(|)(|)(|)( 222
1 0 1 1 0 1 0 1 1 0On-Off Polar
t tTb
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Pulse Shaping
Pulse shaping is the design of pulse p(t) Want pulses that have zero value at sample times nT
Rectangular pulses donrsquot have good BW properties
Nyquist pulses allow tradeoff of bandwidth characteristics and sensitivity to timing errors
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Passband Digital Modulation
Changes amplitude (ASK) phase (PSK) or frequency (FSK) of carrier relative to bits
We use BB digital modulation as the information signal m(t) to encode bits ie m(t) is on-off etc
Passband digital modulation for ASKPSK) is a special case of DSBSC has form
FSK is a special case of FM
)cos()()(
ttmts ck
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
ASK PSK and FSK
Amplitude Shift Keying (ASK)
Phase Shift Keying (PSK)
Frequency Shift Keying
)0(0)(0
)1()()cos()cos()()(
b
bcc nTb
AnTmtAttmts
1 0 1 1
1 0 1 1
1 0 1 1
AM Modulation
AM Modulation
FM Modulation
m(t)
m(t)
)0()()cos(
)1()()cos()cos()()(
AnTmtA
AnTmtAttmts
bc
bcc
AnTmtA
AnTmtAts
b
b
)()cos(
)()cos()(
0
1
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
ASKPSK Demodulation
Similar to AM demodulation but only need to choose between one of two values (need coherent detection)
Decision device determines which of R0 or R1 that R(nTb) is closest to Noise immunity DN is half the distance between R0 and R1
Bit errors occur when noise exceeds this immunity
s(t)
cos(ct+)
bT
dt0
)(
nTb
Decision Device
ldquo1rdquo or ldquo0rdquo r(nTb)
R0
R1
a
r(nTb)
r(nTb)+
Integrator (LPF)
N
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Noise in ASKPSK
Probability of bit error Pb=p (|N ( nTb)|gtDN=5|R1-R0|)
N ( n Tb) is a Gaussian RV N ~ N( m=0s2=25NoTb) For x~N(01) Define Q (z)=p (xgtz)
ASK
PSK
0
)225( NE
bbbbQTENpP
0
2)25( NE
bbbbQTENpP
s(t)
cos(ct)
bT
0
nTb
R(nTb)+N(nTb) ldquo1rdquo or ldquo0rdquo +
N(t)
ChannelN
R1
R0
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
FSK Demodulation
Minimum frequency separation required to differentiate |f1-f2|5nTb (MSK uses minimum separation of n=1) With this separation R1=0 if ldquo0rdquo sent R0=0 if ldquo1rdquo sent
Comparator R1=5ATb if ldquo1rsquo sent R0=5ATb if ldquo0rdquo sent Comparator outputs ldquo1rdquo if (R1+N1)-(R2+N2)gt0 otherwise ldquo0rdquo
Error probability depends on N1-N2
s(t)
cos(21t)
bT
0
R1(nTb)+N1
ldquo1rdquo or ldquo0rdquo
cos(0t)
bT
0
nTb
R0(nTb)+N2
Comparator
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
FSK Error Probability
Analysis similar to ASKPSK
Pb=p(N1-N2gt5ATb)
Distribution of N1-N2 Sum of indep Gaussians is Gaussian (|f1-f2|5nTb ) Mean is sum of means Variance is sum of variances N1N2~N(m=0s2=25NoTb) (Same as in ASKPSK) N1-N2 ~ N(m=0s2=5NoTb)
Pb=p(N1-N2gt5ATb)= Q(5ATb5N0Tb) =Q(5TbA2N0)=Q(EbN0)
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Summary of Digital Modulation
Pulse shaping used in both baseband and passband modulation to determine signal BW and resistance to impairments
Digital passband modulation encodes binary bits into the amplitude phase or frequency of the carrier
ASKPSK special case of AM FSK special case of FM
Noise immunity in receiver dictates how much noise reqd to make an error
White Gaussian noise process causes a Gaussian noise term to be added to the decision device input
Bit error probability with white noise is a function of the symbol energy to noise spectral density ratio
BPSK has lower error probability than ASK for same energy per bit
FSK same error prob as ASK less susceptible to amplitude fluctuations
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Performance Degradation
Phase offset Dq reduces noise immunity by cos (Dq)
If noise is not mean zero causes Pb to increase in one direction
With timing offset integrate over [Dt Tb+Dt] Interference from subsequent bit
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Multilevel Modulation
m bits encoded in pulse of duration Ts (Rb=mTs)
n constant over a symbol time Ts and can take M=2m different values on each pulse
Phase Shift Keying (MPSK)
Similar ideas in MFSK Demodulation similar to binary case
))(cos()( ttAts ncn
Higher data ratemore susceptible to noise
11
10
01
00
)23cos(
)cos(
)2cos(
)cos(
)(
tA
tA
tA
tA
ts
cc
cc
cc
cc
00 10 01 11
Ts
00 10 01 11
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Key Points To Remember PSD and pulse shaping in BB modulation
PSD depends on pulse shape Nyquist pulses avoid ISI p ( n Tb)=0 Raised Cosine pulses trade BW efficiency for timing error
robustness Passband digital modulation for ASKPSK is a special case of
DSBSC
FSK is a special case of FM Demodulation uses a decision device to determine if a ldquo1rsquorsquo
or ldquo0rsquorsquo was sent Noise can cause the decision device to output an erroneous
bit
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
The Interpretations Communication systems modulate analog signals or bits for transmission
over channel
The building blocks of a communication system convert information into an electronic format for transmission then convert it back to its original format after reception
Goal of transmitter (modulator) and receiver (demodulator) is to mitigate distortionnoise from the channel
Digital systems are more robust to noise and interference
Performance metric for analog systems is fidelity for digital it is rate and error probability
Data rates over channels with noise have a fundamental capacity limit
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
What is Telemetry
Telemetry The process of measuring at a distance
Aeronautical telemetry The process of making measurements on an aeronautical vehicle and sending those measurements to a distant location for analysis
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
TELEMETERING APPLICATIONS
The use of telemetry spectrum is common to many different nations and many purposes National defense Commercial aerospace industry Space applications Scientific research
The primary telemetering applications are Range and range support systems
Land mobile Sea ranges Air ranges
Space-based telemetry systems Meteorological telemetry
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Telemetry Use in Precision Agriculture
1048729Differential GPS1048729Mobile phone reporting and control of center pivot irrigation systems1048729Soil moisture sensor networks1048729Climate control for high value crops1048729Real-time monitoring of equipment and people
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Current Band-Allocations
Band (MHz)ITU All
Regions USCommon Europe UK France Italy
Other European Austria Finland
Norway Spain Sweden Australia Canada
4400-4800 X GX - harmonized
military bandG G X Defense All X Defense
G 4460-4540
4800-49404800-4825 4835-4940
G G G Finland SpainG 4900-4940
4940-4990 4940-4950 G G Finland Spain
5850-5925 X X G X DefenseAustria Norway Spain Sweden
X
6875-7125 X NG NG Spain Sweden X
7125-7300 X7145-7235 7250-
7300NG to 7250
Norway Spain Sweden
7125-7250
7900-8025 X
X - harmonized military band - 7900-7975 MHz
in NATO Countries
Austria(7942-8000) Norway Spain Sweden
14500-15300
X147145-151365
X - harmonized military band
14620-15230
G 14500-15250
14620-15350
Austria Norway Spain Sweden
147145-151365
Defense rest open
(secondary)
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Spectrum Encroachments
239
0
235
0
220
0
225
0
230
0
2200-2290 MHz Unmanned 2360-2390 MHz Manned
1435-1525 MHz Manned Vehicle (L Band) Telemetry
2200-2390 MHz Manned and Unmanned Vehicle (S Band) Telemetry
152
5
150
0
143
5
146
0
148
5
One AC can easily use over 20MHz of spectrum
for a single mission
WARC 92
BBA 97
Terrestrial DAB (Canada) CARIBSS MediaStar
WARC 92US Alternative
Thank You
Thank You
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