1. Wireless PHY: Modulation and Demodulation Y. Richard Yang 09/6/2012

2. 2 Outline r Admin and recap r Frequency domain examples r Basic concepts of modulation r Amplitude modulation r Amplitude demodulation m frequency shifting

3. 3 Admin r First assignment to be posted by this weekend r Any feedback on pace and coverage

4. 4 Recap: Fourier Series of Periodic Function r A periodic function g(t) with period T on [a, a+T] can be decomposed as: r For periodic function with period 1 on [0, 1]

5. 5 Fourier Transform r For those who are curious, we do not need it formally r Problem: Fourier series for periodic function g(t), what if g(t) is not periodical? r Approach: m Truncate g(t) beyond [-L/2, L/2] (i.e., set = 0) and then repeat to define g L (t)

6. 6 Fourier Transform Define Let L grow to infinity, we derive Fourier Transform:

7. Fourier Series vs Fourier Transform r Fourier series m For periodical functions, e.g., [0, 1] r Fourier transform m For non periodical functions 7 http://www.differencebetween.com/difference-between-fourier-series-and-vs-fourier-transform/

8. Recap: Discrete Domain Analysis r 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 r Note 8

9. Recap: Discrete Domain Analysis r 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 r Interpretation: consider x 0, x 1, …, x N-1 as sampled values of a periodical function defined on [0, 1]  X k is the coefficient (scaled by N) for k Hz harmonics if the FFT N samples span one sec 9

10. 10 FFT Analysis vs Sample Rate X1X1 Nfft=Nsample X2X2 X Nfft/2 1Hz2HzNfft/2 Hz The freq. analysis resolution:

11. 11 Frequency Domain Analysis Examples Using GNURadio r spectrum_2sin_plus m Audio m FFT Sink m Scope Sink m Noise

12. 12 Frequency Domain Analysis Examples Using GNURadio r spectrum_1sin_rawfft m Raw FFT

13. 13 Frequency Domain Analysis Examples Using GNURadio r spectrum_2sin_multiply_complex m Multiplication of a sine first by a real sine and then by a complex sine to observe spectrum

14. 14 Takeaway from the Example r Advantages of I/Q representation

15. 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

16. 16 Basic Question: Why Not Send Digital Signal in Wireless Communications? r Signals at undesirable frequencies m suppose digital frame repeat every T seconds, then according to Fourier series decomposition, signal decomposes into frequencies at 1/T, 2/T, 3/T, … m let T = 1 ms, generates radio waves at frequencies of 1 KHz, 2 KHz, 3 KHz, … 1 0 digital signal t

17. 17 Frequencies are Assigned and Regulated US operator: http://wireless.fcc.gov/uls

18. 18 Spectrum and Bandwidth: Shannon Channel Capacity r The maximum number of bits that can be transmitted per second by a physical channel is: where W is the frequency range of the channel, and S/N is the signal noise ratio, assuming Gaussian noise

19. 19 Frequencies for Communications VLF = Very Low FrequencyUHF = Ultra High Frequency LF = Low Frequency SHF = Super High Frequency MF = Medium Frequency EHF = Extra High Frequency HF = High Frequency UV = Ultraviolet Light VHF = Very High Frequency Frequency and wave length:  = c/f wave length, speed of light c  3x10 8 m/s, frequency f 1 Mm 300 Hz 10 km 30 kHz 100 m 3 MHz 1 m 300 MHz 10 mm 30 GHz 100  m 3 THz 1  m 300 THz visible light VLFLFMFHFVHFUHFSHFEHFinfraredUV optical transmission coax cabletwisted pair

20. 20 Why Not Send Digital Signal in Wireless Communications? voice Transmitter 20-20KHz Antenna: size ~ wavelength At 3 KHz, Antenna too large! Use modulation to transfer to higher frequency

21. 21 Outline r Recap r Frequency domain examples r Basic concepts of modulation

22. 22 r The information source m Typically a low frequency signal m Referred to as 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 Basic Concepts of Modulation

23. 23 Types of Modulation r Analog modulation m Amplitude modulation (AM) m Frequency modulation (FM) m Double and signal sideband: DSB, SSB r Digital modulation m Amplitude shift keying (ASK) m Frequency shift keying: FSK m Phase shift keying: BPSK, QPSK, MSK m Quadrature amplitude modulation (QAM)

24. 24 Outline r Recap r Frequency domain examples r Basic concepts of modulation r Amplitude modulation

25. 25 Example: Amplitude Modulation (AM) r Block diagram r Time domain r Frequency domain

26. 26 Example: am_modulation Example r Setting m Audio source (sample 32K) m Signal source (300K, sample 800K) m Multiply r Two Scopes r FFT Sink

27. 27 Example AM Frequency Domain Note: There is always the negative freq. in the freq. domain.

28. 28 Problem: How to Demodulate AM Signal?

29. 29 Outline r Admin and recap r Frequency domain examples r Basic concepts of modulation r Amplitude modulation r Amplitude demodulation m frequency shifting

30. 30 Design Option 1 r Step 1: Multiply signal by e -j2πfct m Implication: Need to do complex multiple multiplication

31. 31 Design Option 1 (After Step 1) -2f c

32. 32 Design Option 1 (Step 2) r Apply a Low Pass Filter to remove the extra frequencies at -2f c -2f c

33. 33 Design Option 1 (Step 1 Analysis) r How many complex multiplications do we need for Step 1 (Multiply by e -j2πfct )?

34. 34 Design Option 2: Quadrature Sampling

35. 35 Quadrature Sampling: Upper Path (cos)

36. 36 Quadrature Sampling: Upper Path (cos)

37. 37 Quadrature Sampling: Upper Path (cos)

38. 38 Quadrature Sampling: Lower Path (sin)

39. 39 Quadrature Sampling: Lower Path (sin)

40. 40 Quadrature Sampling: Lower Path (sin)

41. 41 Quarature Sampling: Putting Together

42. 42 Exercise: SpyWork r Setting: a scanner scans 128KHz blocks of AM radio and saves each block to a file. r SpyWork: Scan the block in a saved file to find radio stations and tune to each station (each AM station has 10 KHz)