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Baseband Digital Communications
• Characteristics and Constraints of Wireless Channels
• Baseband Pulse Transmission: Line Signal Codings [NRZ, AMI, Manchester,2B1Q, ...]
• Pulse Amplitude Modulation [PAM]: Transmitter and Receiver pulse shaping
• Intersymbol Interference [ISI]: Eye Pattern
• The Nyquist Criterion:
– Raised Cosine Pulses
– Multipath
– Performance: Mean-Square Error
– Probability of Error
2
Baseband Modulation
• An information bearing-signal must conform to the limits of its channel
• Generally modulation is a two-step process– baseband: shaping the spectrum of input bits to fit in a limited spectrum
– passband: modulating the baseband signal to the system rf carrier
• Most common baseband modulation is Pulse Amplitude Modulation (PAM)– data amplitude modulates a sequence of time translates of basic pulse
– PAM is a linear form of modulation: easy to equalize, BW is pulse BW
– Typically baseband data will modulate in-phase [cos] and quadrature [sine] datastreams to the carrier passband
• Special cases of modulated PAM include– phase shift keying (PSK)
– quadrature amplitude modulation (QAM)
3
Need for Baseband Modulation
• An analog signal has a finite bandwidth.
• A digital stream or signal, with sharp transitions, has an infinitebandwidth.
• Due to the limited available system bandwidth, only the major portion ofa digital signal spectrum can be transmitted and restored. Even if there isno loss or noise in the communication system, the received signal willhave distortion due to the limited channel bandwidth.
To avoid or to reduce this signal distortion, weuse baseband modulation techniques
time
time
Typical Baseband PAM Signals
1 0 0 0 01 1RZ
s(t)g(t)anM
T0NRZ
2
2
2
4
3
01
01
01
00011110
01
01
-11
-11
-3113
0±1
→→→→
→→→→
→→→→
→→→→→→→→
→→→→
BANDLIMITED
4-LEVEL
BIPOLAR/AMI [Alternate Mark Inversion]
T0
T0
T0 2T
T0
an
S(t)
Each technique will have different spectrum (at DC and band edge),ease of timing recovery
S(t) = ΣΣ ang(t-nT)an represents data (M-ary)1/T = symbol (baud) rateBit rate = log2 M=RT
1
n
= a0g(t) + a1g(t-T) + ...
5
State Diagram for AMI Signaling
State “+” State “-”
1/-p(t)
Branch Labels: Input bit (an)/output waveform or symbol [dnp(t)]
1/p(t)
0/0 0/0
The modulator has two states, labeled “+” and “-”. The modulator responds to a source symbol0 with a zero waveform and to a source symbol 1 with the waveform p(t) or -p(t) depending on whether its state is “-” or “+” respectively.
Note that the choice of the states is not obvious. A common mistake is to choose the output levels,0, 1, and -1 as states. But, if you make this choice, it is hard/impossible(?) to capture the memoryof the system.
6
Examples of Baseband Impulse Responses
(1) NRZ (non return to zero)
(2) Raised Cosine
(3) Bipolar (AMI)
(4) Manchester
0 T 2T
0 T t
0
T 2T
0 T
0 1/T f
0 1/T1/2T
0 1/T1/2T
3T
1T
0 2T
E.g Equalized Voiceband,Cellular or MicrowaveLOS Modem
e.g. 1.544/2.048 MbpsT1 /E1 Carrier on Twisted-Pair
e.g. Ethernet on CoaxialCable (3-10 Mbps)
h (t) |H(f)|
7
Examples of Baseband Impulse Responses (continued)
(5) Multipath: Class I Partial Response(Duobinary)
(6) Multipath: Class IV Partial Response
T 2T
0 T 0
• Multipath Nulls at DC and Nyquist frequency
h (t) |H(f)|
(7) Minimum - Bandwidth Nyquist Pulse
12T
0 12T
• Multipath (Cellular)
• Need Powerful Equalizer(DFE, VA)
• Regularly spaced zero crossings• Not Realized in Practice
0 12T
= W
0
sin2ππ Wt2ππ WT
Typical Linear Channel Characteristics
Voiceband Telephone After Demodulation
0
Frequency ResponseH(f)
Impulse Responseh(t)
Twisted Copper Pair with Transformers (DSL)
Radio
Gitlin1_8
f
0 f
0 ff0
h(t)Linear Equalizer
I/Q Equalizer
~DFE
t
t
t
h(t)
h(t)
|H(f)| ang H(f)
|H(f)|
ang H(f)
|H(f)|ang H(f)
~10 ms
Nulls require a non-linearequalizer: DFE or MLSE/VA
9
Pulse Distortion Due to MultiPath
10
Digital Baseband Modulation Techniques
• NR (Non-Return-to-zero)• Bipolar (AMI)• Partial response• Manchester
• Baseband (PAM): Baseband Channels
Typical Power Spectra:
Bipolar, Partial Reponse,or Manchester
Examples: Twisted-Pair and Coaxial Cable Channels
12T
1T
toFreq.0
Freq.0
NRZ
11
Doubling the Data Rate
• Date Rate =
• If SNR limited ----> double the symbol rate [3 dB SNR penalty]
• If bandwidth limited ----> only choice is to double the number of bits/symbolby increasing the number of points
– For example: going from 4-QAM to 16-QAM [from 2 to 4 bits/symbol]
– This has a ~6-7 dB penalty
• So, assuming that the bandwidth is available it is always better to double thesymbol rate
• The above also assumes that the background noise and/or interference is flatwith frequency
NT 2log1 Recall that 1/T is the symbol rate
and N is the number of modulation levels
12
Coded Baseband Digital Modulation Techniques
• Can be combined with any of the above• Performance improvement at the cost of increased receiver delay
and complexity• Allows rate to approach channel capacity• Types: - block coding
- convolutional or trellis coding
• Coded Systems
Signal-to-Noise Ratio
Uncoded System
Coded Systems withIncreasing Complexity
Channel Capacity Limit
ErrorProbability
Examples of Application: - Cellular Phones- Satellite Channels- High Speed Voiceband
Telephone Modems
13
Example of a Baseband PAM System
QuantizeReceive
FilterBasebandChannel
Trans.Filter
0 → → 10 → −→ −1
r(t)
B C
r(nT)
A
an
1/T persec.
Overall Impulse Response = x(t) Sample att = nT + ττ
ân
At A:{an}
T
• Baud = Symbols/sec x(t) ISI
0 T
At C:{r(nt)}
At D:{ân}
At B:r(t)
Timing Margin
T 2T 3T 4T 5T 6T 7T 8T
Margin Against Noise
anx(t-nT)r(t) =n∑∑
PAM
anδδ(t-nT)n∑∑
Intersymbol Interference (ISI) Can Cause Errors Without Noise
14
Band-Limited Signal for No Intersymbol Interference
-3T -2T -T T 2T 3T0-4T 4T t
t
x(t)
• Ideal Pulse
ππWt
sinππWt
• Minimum Bandwidth Pulse
0-W =2T1- W =
2T1
2W1
X(f)
f
1/T Symbols/sec
Don’t Need Time Limited Pulses for “0” ISI
Nyquist (1928)
15
Why Equalization Is Needed
(A)
Transmitted Pulse
(B)
(C)
Amplitude
0 F1Frequency
Amplitude
-3T -2T -T T 2T 3T0
P(t)
P(t) + P(t-T)
Time
-3T -2T -T T 2T 3T0
Time
16
INTERSYMBOL INTERFERENCE: ISI
• Cause of ISI:
• Elimination or reduction of ISI
- filtering
- equalization
17
EQUALIZATION: Pulse Shaping
Ideal pulse shaping [to satisfy the Nyquis tcriterion]:
y(t) = 0 at t = nT [n = 1, 2, 3, . . . ]
18
The Eye Pattern [as a measure of distortion]
0 T 2T 3T 4T 5T 6T 7T 8T
nT)(t (t) : WaveformPAMn
n −∑= xar
mmkk xaxakTr (0) )(0m
∑+=≠
−
Desired Intersymbol Interference = is a random variable(pdf is difficult to compute)
By the Central Limit Theorem the ISI can be approximated by a Gaussian Random Variable of zero mean and variance ∑
∞
≠0
2
nnx
19
Eye Pattern
“Bad” - Closed
Eye Pattern Display
“Good” - Open
ThresholdLevel
Marginfor ErrorDue ToNoise
Marginfor ErrorDue toTiming
Sample Instant
Symbol Timing Wave
Scope TriggerFrom Modem
20
The Raised Cosine Family of Nyquist Pulses
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-3T -2T -T T 2T 3T
0.5
0
αα = 00
0.51
Raised Cosine
(a)
Excess Bandwidth
(b)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
α α = 0
X (ωω)
ππ/T 2ππ/T
Raised Cosine Pulse Shaping: (a) Frequency Response, (b) Time Response
1
==ωω
T
)(X
T2T
sin12T
ππ−−ωω
αα−−
)1(T
0 αα−−ππ
≤≤ωω≤≤
222 T/t4-1t/T cos
T/tT/tsin
)t(xαα
απαπππ
ππ==
1
0.5Fequency
Time
)1(T
)1(T
αα++ππ≤≤ωω≤≤αα−−ππ
,
,
21
Performance of PAM Systems: No ISI/Multipath(Gaussian Noise)
L = 2 4 8 16
1
10-1
10-2
10-3
10-4
10-5
10-6
5 10 15 20 25 30 350
Ps / PN [SNR], dB
Pe
Probability of error Ps for L-level PAM, where Ps / PN is thesignal-to-noise power ratio in the Nyquist bandwidth. Notethat doubling the bit rate requires about 6-7 dB of SNR
For Nyquist Pulse
{{ }}
∫∫∞∞ππ
==
−−==>>ηη
−−==
−−==−−======
−−
==∑∑
x dte 2
1)x(Q
PP
1-L3
Q L1
12dPr L1
1P
31L
Td
1)]d(2i[LT2
IT aPOWER XMITTP
22t
2/1
N
s2e
222
L12
1i
2s
L/2
/ T
22
ΣΣ
Adaptive Equalization
Inputbinarydata
Pulsegenerator
Transmittingfilter Channel Receiving
filterAdaptiveequalizer
Decisiondevice
{a(n)} y(n)
Outputbinarydata
Block diagram of a baseband data transmission system.
Transmitter Noise Receiver
Adaptive equalizer with a decision-directed mode of operation.
Adaptiveequalizer
Decisiondevice
Switch Stored referencegenerator
ΣΣ +
-
Inputsignal
Desired Response = Replica of transmitted signal
Sampler
Error