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Outline

Outline. Transmitters (Chapters 3 and 4, Source Coding and Modulation) (week 1 and 2) Receivers (Chapter 5) (week 3 and 4) Received Signal Synchronization (Chapter 6) (week 5) Channel Capacity (Chapter 7) (week 6) Error Correction Codes (Chapter 8) (week 7 and 8)

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Outline

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  1. Outline • Transmitters (Chapters 3 and 4, Source Coding and Modulation) (week 1 and 2) • Receivers (Chapter 5) (week 3 and 4) • Received Signal Synchronization (Chapter 6) (week 5) • Channel Capacity (Chapter 7) (week 6) • Error Correction Codes (Chapter 8) (week 7 and 8) • Equalization (Bandwidth Constrained Channels) (Chapter 10) (week 9) • Adaptive Equalization (Chapter 11) (week 10 and 11) • Spread Spectrum (Chapter 13) (week 12) • Fading and multi path (Chapter 14) (week 12)

  2. Digital Communication System: Transmitter Receiver

  3. Receivers (Chapter 5) (week 3 and 4) • Optimal Receivers • Probability of Error

  4. Optimal Receivers • Demodulators • Optimum Detection

  5. Demodulators • Correlation Demodulator • Matched filter

  6. Correlation Demodulator • Decomposes the signal into orthonormal basis vector correlation terms • These are strongly correlated to the signal vector coefficients sm

  7. Correlation Demodulator • Received Signal model • Additive White Gaussian Noise (AWGN) • Distortion • Pattern dependant noise • Attenuation • Inter symbol Interference • Crosstalk • Feedback

  8. Additive White Gaussian Noise (AWGN) i.e., the noise is flat in Frequency domain

  9. Correlation Demodulator • Consider each demodulator output

  10. Correlation Demodulator • Noise components {nk} are uncorrelated Gaussian random variables

  11. Correlation Demodulator • Correlator outputs Have mean = signal For each of the M codes Number of basis functions (=2 for QAM)

  12. Matched filter Demodulator • Use filters whose impulse response is the orthonormal basis of signal • Can show this is exactly equivalent to the correlation demodulator

  13. Matched filter Demodulator • We find that this Demodulator Maximizes the SNR • Essentially show that any other function than f1() decreases SNR as is not as well correlated to components of r(t)

  14. The optimal Detector • Maximum Likelihood (ML):

  15. The optimal Detector • Maximum Likelihood (ML):

  16. Optimal Detector • Can show that so

  17. Optimal Detector • Thus get new type of correlation demodulator using symbols not the basis functions:

  18. Alternate Optimal rectangular QAM Detector • M level QAM = 2 x level PAM signals • PAM = Pulse Amplitude Modulation

  19. The optimal PAM Detector For PAM

  20. The optimal PAM Detector

  21. Select si for which Select si for which Optimal rectangular QAM Demodulator • d = spacing of rectangular grid

  22. Probability of Error for rectangular M-ary QAM • Related to error probability of PAM Accounts for ends

  23. Probability of Error for rec. QAM • Assume Gaussian noise 0

  24. Probability of Error for rectangular M-ary QAM • Error probability of PAM

  25. SNR for M-ary QAM • Related to PAM • For PAM find average energy in equally probable signals

  26. SNR for M-ary QAM • Related to PAM Find average Power

  27. SNR for M-ary QAM • Related to PAM Find SNR (ratio of powers) Then SNR per bit

  28. SNR for M-ary QAM • Related to PAM

  29. SNR for M-ary QAM • Related to PAM • Now need to get M-ary QAM from PAM M½=16 M½=8 M½=4 M½=2

  30. SNR for M-ary QAM • Related to PAM (1- probability of no QAM error) (Assume ½ power in each PAM)

  31. SNR for M-ary QAM • Related to PAM M=

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