Wireless PHY: Modulation and Demodulation

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

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

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

4. 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]

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

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

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

8. Recap: Discrete Domain Analysis • FFT: Transforming a sequence of numbers x0, x1, …, xN-1 to another sequence of numbers X0, X1, …, XN-1 • Note

9. 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] • Xk is the coefficient (scaled by N) for k Hz harmonics if the FFT N samples span one sec

10. FFT Analysis vs Sample Rate X1 X2 XNfft/2 1Hz 2Hz Nfft/2 Hz Nfft=Nsample The freq. analysis resolution:

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

12. Frequency Domain Analysis Examples Using GNURadio • spectrum_1sin_rawfft • Raw FFT

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

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

15. 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

16. 1 digital signal 0 t 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, …

17. Europe USA Japan Cellular GSM AMPS TDMA CDMA PDC 450 - 457, 479 - , , Phones 486/460 - 467,489 - 824 - 849, 810 - 826, 496, 890 - 915/935 - 869 - 894 940 - 956, TDMA CDMA GSM 960, , , 1429 - 1465, 1710 - 1785/1805 - 1850 - 1910, 1477 - 1513 1880 1930 - 1990 UMTS (FDD) 1920 - 1980, 2110 - 2190 UMTS (TDD) 1900 - 1920, 2020 - 2025 Cordless CT1+ PACS PHS 885 - 887, 930 - 1850 - 1910, 1930 - Phones 932 1990 1895 - 1918 CT2 PACS - UB JCT 1910 - 1930 864 - 868 254 - 380 DECT 1880 - 1900 Wireless IEEE 802.11 IEEE 802.11 902 - 928 LANs I EEE 802.11 2400 - 2483 2471 - 2497 HIPERLAN 2 2400 - 2483 5150 - 5250 5150 - 5350, 5470 - 5150 - 5350, 5725 - 5825 5725 Others RF - Control RF - Control RF - Control 27, 128, 418, 433, 315, 915 426, 868 868 Frequencies are Assigned and Regulated US operator: http://wireless.fcc.gov/uls

18. Spectrum and Bandwidth: Shannon Channel Capacity • 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. Frequencies for Communications twisted pair coax cable optical transmission 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 VLF LF MF HF VHF UHF SHF EHF infrared UV VLF = Very Low Frequency UHF = 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  3x108m/s, frequency f

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

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

22. Basic Concepts of Modulation • The information source • Typically a low frequency signal • 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

23. 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)

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

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

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

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

28. Problem: How to Demodulate AM Signal?

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

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

31. Design Option 1 (After Step 1) -2fc

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

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

34. Design Option 2: Quadrature Sampling

35. Quadrature Sampling: Upper Path (cos)

36. Quadrature Sampling: Upper Path (cos)

37. Quadrature Sampling: Upper Path (cos)

38. Quadrature Sampling: Lower Path (sin)

39. Quadrature Sampling: Lower Path (sin)

40. Quadrature Sampling: Lower Path (sin)

41. Quarature Sampling: Putting Together

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