CS434/534: Topics in Networked (Networking) Systemszoo.cs.yale.edu/classes/cs434/cs434-2017-spring/lectures/09-wireless-bg-mod-demod.pdf17 The information source Typically a low frequency

CS434/534: Topics in Networked (Networking) Systems

Wireless Foundation: Modulation and Demodulation

Yang (Richard) YangComputer Science Department

Yale University208A Watson

Email: [email protected]

http://zoo.cs.yale.edu/classes/cs434/

2

Outline

❒ Admin and recap❒ Wireless background

❍ Frequency domain❍ Basic concepts of modulation

• Amplitude modulation• Amplitude demodulation

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Admin

❒ PS1 deferred to Tuesday❒ Feel free to stop by Chris Leet office at

any time to discuss PS1

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Recap: Fourier Series of Periodic Function

❒ A periodic function g(t) with period T on [a, a+T] can be decomposed as:

❒ For periodic function with period 1 on [0, 1]

g(t) = G[k]ej2π k

Tt

k=−∞

∞

∑

G[k]= 1T

g(t)e− j2π k

Ttdt

a

a+T∫

g(t) = G[k]e j2πk tk=−∞

∞

∑

G[k]= g(t)e− j2πk t dt0

1∫

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Basic Question: Why Not Send Digital Signal in Wireless Communications?

❒ Signals at undesirable frequencies❍ suppose digital frame repeat every T seconds,

then according to Fourier series decomposition, signal decomposes into frequencies at 1/T, 2/T, 3/T, …

❍ let T = 1 ms, generates radio waves at frequencies of 1 KHz, 2 KHz, 3 KHz, …

1

0digital signal

t

6

Frequencies are Assigned and Regulated

Europe USA Japan

CellularPhones

GSM 450 - 457, 479 -486/460 - 467,489 -496, 890 - 915/935 -960,1710 - 1785/1805 -1880UMTS (FDD) 1920 -1980, 2110 - 2190UMTS (TDD) 1900 -1920, 2020 - 2025

AMPS , TDMA , CDMA824- 849, 869-894TDMA , CDMA , GSM1850 - 1910,1930 - 1990

PDC810- 826, 940- 956,1429 - 1465, 1477 - 1513

CordlessPhones

CT1+ 885 - 887, 930 -932CT2864-868DECT 1880 - 1900

PACS 1850 - 1910, 1930 -1990PACS -UB 1910 - 1930

PHS1895 - 1918JCT254-380

Wireless LANs

IEEE 802.112400 - 2483HIPERLAN 25150 - 5350, 5470 -5725

902-928I EEE 802.112400 - 24835150 - 5350, 5725 - 5825

IEEE 802.112471 - 24975150 - 5250

Others RF- Control27, 128, 418, 433,

868

RF- Control315, 915

RF- Control426, 868

US operator: http://wireless.fcc.gov/uls

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Spectrum and Bandwidth: Shannon Channel Capacity❒ The maximum number of bits that can be

transmitted per second by a physical channelis:

where W is the frequency range of the channel, and S/N is the signal noise ratio, assuming Gaussian noise

)1(log2 NSW +

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Why Not Send Digital Signal in Wireless Communications?

voice Transmitter

20-20KHzAntenna:

size ~ wavelength

At 3 KHz, λ =

cf

=3×108

3×103=100km

Antenna too large!Use modulation to transfer

to higher frequency

Recap: Discrete Domain Analysis

❒ FFT: Transforming a sequence of numbers x0, x1, …, xN-1 to another sequence of numbers X0, X1, …, XN-1

❒ Interpretation: consider x0, x1, …, xN-1 as sampled values of a periodical function defined on [0, 1]

ÞXk is the coefficient (scaled by N) for k Hz harmonics if the FFT N samples span one sec

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g(t) = G[k]e j2πk tk=−∞

∞

∑

G[k]= g(t)e− j2πk t dt0

1∫

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FFT Analysis vs Sample Rate

X1

Nfft=Nsample

X2 XNfft/2

1Hz 2Hz Nfft/2 Hz

Nsample

N fft

2Nsample

N fft

Nsample

2

The freq. analysis resolution: Nsample

N fft

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Frequency Domain Analysis Examples Using GNURadio

❒ spectrum_1_realsin_rawfft❍ 1K real cosine wave ❍ 1024 FFT❍ 32000 sample rate

❒ Prediction:❍ Where is the peak of FFT?

❒ Commands❍ ./plot/raw2numf signal.dat signal.show 0 1024❍ ./plot/raw2numfc fft.dat fft.show 0 1024

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❒ spectrum_2_realsin_plus.grc❍ Two signal sources (350 + 440)❍ Audio sink❍ Scope Sink❍ FFT Sink (1024 FFT)

❒ Prediction:❍ What is a good sample rate to see the result?

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❒ spectrum_2_realsin_multiply❍ Multiplication of previous signal by another sine

wave

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Advantage of I/Q representation

❒ Advantages of I/Q representation

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I/Q Multiplication Also Called Quadrature Mixing

spectrum of complexsignal x(t)

spectrum of complexsignal x(t)ej2f0t

spectrum of complexsignal x(t)e-j2f0t

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Outline

❒ Recap❒ Wireless background

❍ Frequency domain❍ Modulation and demodulation

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❒ The information source❍ Typically a low frequency signal❍ Referred to as baseband signal

q Carrierq A higher frequency sinusoidq Example cos(2π10000t)

q Modulated signalq Some parameter of the carrier is varied in accordance with the

baseband signal

Basic Concepts of ModulationBasic Concept of Modulation

  The information source   Typically a low frequency signal   Referred to as the “baseband signal”

  Carrier   A higher frequency sinusoid   Example: cos(2π10000t)

  Modulated Signal   Some parameter of the carrier (amplitude, frequency, phase) is varied in

accordance with the baseband signal

x(t)

t

X(f)

f

Modulator baseband

carrier Modulated signal

7/8/10 5 Flynn/Katz

Basic Concept of Modulation





x(t)

t

X(f)

f

Modulator baseband


7/8/10 5 Flynn/Katz






x(t)

t

X(f)

f

Modulator baseband


7/8/10 5 Flynn/Katz






x(t)

t

X(f)

f

Modulator baseband


7/8/10 5 Flynn/Katz

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Types of Modulation

❒ Analog modulation❍ Amplitude modulation (AM)❍ Frequency modulation (FM)❍ Double and signal sideband: DSB, SSB

❒ Digital modulation❍ Amplitude shift keying (ASK)❍ Frequency shift keying: FSK❍ Phase shift keying: BPSK, QPSK, MSK❍ Quadrature amplitude modulation (QAM)

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Outline



• Basic concepts• Amplitude modulation

Amplitude Modulation (AM)   Block Diagram

  Time Domain

  Frequency Domain

m x +

Ac cos �ct

x(t) xAM(t)=Ac [1+mx(t)]cos �ct

X(f)

f -fm fm

XAM(f)

f -fc fc

Signal information is contained in the sidebands

7/8/10 7 Flynn/Katz 20

Example: Amplitude Modulation (AM)

❒ Block diagram

❒ Time domain

❒ Frequency domain


  Time Domain


m x +

Ac cos �ct


X(f)

f -fm fm

XAM(f)

f -fc fc


7/8/10 7 Flynn/Katz


  Time Domain


m x +

Ac cos �ct


X(f)

f -fm fm

XAM(f)

f -fc fc


7/8/10 7 Flynn/Katz


  Time Domain


m x +

Ac cos �ct


X(f)

f -fm fm

XAM(f)

f -fc fc


7/8/10 7 Flynn/Katz


  Time Domain


m x +

Ac cos �ct


X(f)

f -fm fm

XAM(f)

f -fc fc


7/8/10 7 Flynn/Katz

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Example: am_modulation Example

❒ Setting❍ Audio source (sample 32K)❍ Signal source (300K, sample 800K)❍ Multiply

❒ Two Scopes

❒ FFT Sink

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Example AM Frequency Domain

Note: There is always the negative freq. in the freq. domain.

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Outline



• Basic concepts• Amplitude modulation • Amplitude demodulation

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Problem: How to Demodulate AM Signal?


  Time Domain


m x +

Ac cos �ct


X(f)

f -fm fm

XAM(f)

f -fc fc


7/8/10 7 Flynn/Katz


  Time Domain


m x +

Ac cos �ct


X(f)

f -fm fm

XAM(f)

f -fc fc


7/8/10 7 Flynn/Katz

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Design Option 1

❒ Step 1: Multiply signal by e-j2πfct

❍ Implication: Need to do complex multiple multiplication

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Design Option 1 (After Step 1)

-2fc

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Design Option 1 (Step 2)

❒ Apply a Low Pass Filter to remove the extra frequencies at -2fc

-2fc

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Design Option 2: Quadrature Sampling

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Quadrature Sampling: Upper Path (cos)

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31


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Quadrature Sampling: Lower Path (sin)

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34


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Quarature Sampling: Putting Together

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Summary: Demod of AM

❒ Design option 1: multiply modulated signal by e-jfct, and then LPF

❒ Design option 2: quadrature sampling

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Remaining Hole: How to Design LPF

❒ Frequency domain view

freqB-B

freqB-B

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Design Option 1

freqB-B

freqB-B

compute freq

zeroing outoutband freqcompute lower-pass

time signal

This is essentially how image compression works.Problem(s) of Design Option 1?

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Design Option 2: Impulse Response Filters

❒ GNU software radio implements filtering using❍ Finite Impulse Response (FIR) filters❍ Infinite Impulse Response (IIR) Filters❍ FIR filters are more commonly used

❒ FIR/IIR is essentially online, streaming algorithms

❒ They are used in networks/communications/vision/robotics…

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FIR Filter

❒ An N-th order FIR filter h is defined by an array of N+1 numbers:

❒ They are often stored backward (flipped)

❒ Assume input data stream is x0, x1, …,

h = [h0,h2,...,hN ]

h0h1h2hN…

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FIR Filter

xnxn-1xn-2xn-3

h0h1h2h3

****

xn+1

compute y[n]: yn = xnh0 + xn−1h1 +...+ xn−NhN

= xn−ihii=0

N

∑

3rd-OrderFilter

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FIR Filter

xnxn-1xn-2xn-3

h0h1h2h3

****

xn+1

compute y[n+1]

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FIR Filter

is also called convolution between x (as a vector) and h (as a vector), denoted as

yn = xnh0 + xn−1h1 +...+ xn−NhN

yn = xn *hn

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Key Question Using h to Implement LPF

❒ Q: ❍ How to determine h?

❒ Approach:❍ Understand the effects of y=g*h in the

frequency domain

Backup Slides

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GNURadio: Design Objective

❒ A software development toolkit that provides signal processing blocks to implement software-defined radio systems.

GNURadio Hardware Arch

Hardware Frontend Host Computer

RF Frontend(Daugtherboard)

ADC/DAC andDigital Frontend

(USRP)

http://mobiledevices.kom.aau.dk/fileadmin/mobiledevices/teaching/software_testing/Gnu_radio_lecture.pdf

GNU RadioSoftware

Basic Software ConceptsrBlock

rFlow graph

Basic Software Conceptsrhttp://gnuradio.org/doc/doxygen/classgr

__block.html

rgr_basic_block (name, in/out signature, msg queue)r gr_block (Leaf block; key functions

forecast/general_work)r Example:

http://www.gnu.org/software/gnuradio/doc/howto-write-a-block.html

r gr_hier_block2 (container block; key functions: connect/disconnect/lock/unlock)r gr_top_block (flow graph; start/stop/wait)

Software/Execution Model

Python

Application developmentFlow graph construction

C++

Signal processing blocks

r Software modelr Python

m Application management (e.g., GUI)

m Flow graph constructionm Non-streaming code (e.g.,

MAC-layer)r C++

m Signal processing blocksm Certain routines also coded in

assembly

q Execution modelq Python thread for each

top_block

Discussion: benefits/issues of the hybrid software structure?

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Summary: GNURadio

❒ Interesting/key software design techniques you learned from GNURadio?

Documents

CS434/534: Topics in Networked (Networking) Systemszoo.cs.yale.edu/classes/cs434/cs434-2017-spring/lectures/09-wireless-bg-mod-demod.pdf17 The information source Typically a low frequency