CS434/534: Topics in Networked (Networking) Systems

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1 CS434/534: Topics in Networked (Networking) Systems Wireless Foundation: Modulation and Demodulation Yang (Richard) Yang Computer Science Department Yale University 208A Watson

2 Outline Admin and recap Wireless background Frequency domain Basic concepts of modulation Amplitude modulation Amplitude demodulation 2

3 Admin PS1 deferred to Tuesday Feel free to stop by Chris Leet office at any time to discuss PS1 3

4 Recap: Fourier Series of Periodic Function A periodic function g(t) with period T on [a, a+t] can be decomposed as: g(t) = k= G[k] = 1 T G[k]e j2π k T t a a+t g(t)e j2π k T t dt For periodic function with period 1 on [0, 1] g(t) = G[k] = G[k]e j2πk t k= 1 0 g(t)e j2πk t dt 4

5 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 digital signal 0 t 5

6 Frequencies are Assigned and Regulated Europe USA Japan Cellular Phones Cordless Phones Wireless LANs Others GSM , / , , / , / UMTS (FDD) , UMTS (TDD) , CT , CT DECT IEEE HIPERLAN , RF- Control 27, 128, 418, 433, 868 AMPS, TDMA, CDMA , TDMA, CDMA, GSM , PACS , PACS -UB I EEE , RF- Control 315, 915 PDC , , , PHS JCT IEEE RF- Control 426, 868 US operator: 6

7 Spectrum and Bandwidth: Shannon Channel Capacity The maximum number of bits that can be transmitted per second by a physical channel is: W log (1 + 2 S N ) where W is the frequency range of the channel, and S/N is the signal noise ratio, assuming Gaussian noise 7

At 3 KHz, λ = c f = 3 108 3 10 3 =100km Antenna too

8 Why Not Send Digital Signal in Wireless Communications? voice Transmitter 20-20KHz Antenna: size ~ wavelength At 3 KHz, λ = c f = =100km Antenna too large! Use modulation to transfer to higher frequency 8

9 Recap: Discrete Domain Analysis g(t) = G[k] = k= 1 0 G[k]e j2πk t g(t)e j2πk t dt FFT: Transforming a sequence of numbers x 0, x 1,, x N-1 to another sequence of numbers X 0, X 1,, X N-1 Interpretation: consider x 0, x 1,, x N-1 as sampled values of a periodical function defined on [0, 1] Þ X k is the coefficient (scaled by N) for k Hz harmonics if the FFT N samples span one sec 9

10 FFT Analysis vs Sample Rate X 1 X 2 X Nfft/2 Nfft=Nsample 1Hz 2Hz Nfft/2 Hz N sample N fft 2N sample N fft N sample 2 The freq. analysis resolution: N sample N fft 10

11 Frequency Domain Analysis Examples Using GNURadio spectrum_1_realsin_rawfft 1K real cosine wave 1024 FFT sample rate Prediction: Where is the peak of FFT? Commands./plot/raw2numf signal.dat signal.show /plot/raw2numfc fft.dat fft.show

12 Frequency Domain Analysis Examples Using GNURadio spectrum_2_realsin_plus.grc Two signal sources ( ) Audio sink Scope Sink FFT Sink (1024 FFT) Prediction: What is a good sample rate to see the result? 12

13 Frequency Domain Analysis Examples Using GNURadio spectrum_2_realsin_multiply Multiplication of previous signal by another sine wave 13

14 Advantage of I/Q representation Advantages of I/Q representation 14

15 I/Q Multiplication Also Called Quadrature Mixing spectrum of complex signal x(t) spectrum of complex signal x(t)e j2f0t spectrum of complex signal x(t)e -j2f0t 15

16 Outline Recap Wireless background Frequency domain Modulation and demodulation 16

17 Basic Concepts of Modulation The information source Typically a low frequency signal Referred to to as as the baseband baseba signal x(t) X(f) q Carrier er q A higher frequency sinusoid q Example cos(2π10000t) t baseband carrier Modulator f Modulated signal q Modulated signal q Some parameter of the carrier is varied in accordance with the baseband signal 17

18 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) 18

19 Outline Recap Wireless background Frequency domain Modulation and demodulation Basic concepts Amplitude modulation 19

20 Example: Amplitude Modulation (AM) Block diagram x(t) m x + x AM (t)=a c [1+mx(t)]cos c t Time domain me Domain A c cos c t Frequency Domain domain X(f) X AM (f) sideba -f m f m f -f c f c f 20

21 Example: am_modulation Example Setting Audio source (sample 32K) Signal source (300K, sample 800K) Multiply Two Scopes FFT Sink 21

22 Example AM Frequency Domain Note: There is always the negative freq. in the freq. domain. 22

23 Outline Recap Wireless background Frequency domain Modulation and demodulation Basic concepts Amplitude modulation Amplitude demodulation 23

24 Problem: How to Demodulate AM Signal? X(f) X AM (f) sideba -f m f m f -f c f c f 24

25 Design Option 1 Step 1: Multiply signal by e -j2πfct Implication: Need to do complex multiple multiplication 25

26 Design Option 1 (After Step 1) -2f c 26

27 Design Option 1 (Step 2) Apply a Low Pass Filter to remove the extra frequencies at -2f c -2f c 27

28 Design Option 2: Quadrature Sampling 28

29 Quadrature Sampling: Upper Path (cos) 29

30 Quadrature Sampling: Upper Path (cos) 30

31 Quadrature Sampling: Upper Path (cos) 31

32 Quadrature Sampling: Lower Path (sin) 32

33 Quadrature Sampling: Lower Path (sin) 33

34 Quadrature Sampling: Lower Path (sin) 34

35 Quarature Sampling: Putting Together 35

36 Summary: Demod of AM Design option 1: multiply modulated signal by e -jfct, and then LPF Design option 2: quadrature sampling 36

37 Remaining Hole: How to Design LPF Frequency domain view -B B freq -B B freq 37

38 Design Option 1 compute freq -B B freq compute lower-pass time signal zeroing out outband freq This is essentially how image compression works. -B B freq Problem(s) of Design Option 1? 38

39 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 39

40 FIR Filter An N-th order FIR filter h is defined by an array of N+1 numbers: h = [h 0, h 2,..., h N ] They are often stored backward (flipped) h N h 2 h 1 h 0 Assume input data stream is x0, x1,, 40

41 FIR Filter x n-3 x n-2 x n-1 x n x n+1 3 rd -Order Filter * * * * h 3 h 2 h 1 h 0 compute y[n]: y n = x n h 0 + x n 1 h x n N h N N = x n i h i 41

42 FIR Filter x n-3 x n-2 x n-1 x n x n+1 * * * * h 3 h 2 h 1 h 0 compute y[n+1] 42

43 FIR Filter y n = x n h 0 + x n 1 h x n N h N is also called convolution between x (as a vector) and h (as a vector), denoted as y n = x n * h n 43

44 Key Question Using h to Implement LPF Q: How to determine h? Approach: Understand the effects of y=g*h in the frequency domain 44

45 Backup Slides 45

46 GNURadio: Design Objective A software development toolkit that provides signal processing blocks to implement software-defined radio systems. 46

47 GNURadio Hardware Arch Hardware Frontend Host Computer RF Frontend (Daugtherboard) ADC/DAC and Digital Frontend (USRP) GNU Radio Software

48 Basic Software Concepts rblock rflow graph

49 Basic Software Concepts r block.html rgr_basic_block (name, in/out signature, msg queue) r gr_block (Leaf block; key functions forecast/general_work) r Example: r gr_hier_block2 (container block; key functions: connect/disconnect/lock/unlock) r gr_top_block (flow graph; start/stop/wait)

50 Software/Execution Model r Software model q r r Python m m m C++ m m Application management (e.g., GUI) Flow graph construction Non-streaming code (e.g., MAC-layer) Signal processing blocks Certain routines also coded in assembly Execution model q Python thread for each top_block Python Application development Flow graph construction C++ Signal processing blocks Discussion: benefits/issues of the hybrid software structure?

51 Summary: GNURadio Interesting/key software design techniques you learned from GNURadio? 51

Wireless PHY: Modulation and Demodulation

Wireless PHY: Modulation and Demodulation Y. Richard Yang 09/6/2012 Outline Admin and recap Frequency domain examples Basic concepts of modulation Amplitude modulation Amplitude demodulation frequency