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Digital Communications

Digital Communications. Chapeter 3. Baseband Demodulation/Detection Signal Processing Lab. Block Diagram of a DCS. Demodulation and Detection. Modeling the received signal. Major Sources of Errors. Inter-Symbol Interference (ISI)

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Digital Communications

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  1. Digital Communications Chapeter 3. Baseband Demodulation/Detection Signal Processing Lab

  2. Block Diagram of a DCS Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  3. Demodulation and Detection • Modeling the received signal Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  4. Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  5. Major Sources of Errors • Inter-Symbol Interference (ISI) • Due to the filtering effect of transmitter and receiver, symbols are “smeared”. • Thermal noise (AWGN) • Disturbs the signal in an additive fashion (Additive) • Has flat spectral density for all frequencies interest (White) • Modeled by Gaussian random process (Gaussian Noise) Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  6. Demodulation and Detection (cont´d) • Demodulation and Sampling : • Waveform recovery and preparing the received signal for detection • Improving SNR using matched filter • Reducing ISI using equalizer • Sampling the recovered waveform • Detection : • Estimate the transmitted symbol based on the received sample Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  7. Baseband and Bandpass • Bandpass model of detection process is equivalent to baseband model because: • The received bandpass waveform is first transformed to a baseband waveform. • Equivalence theorem: • Performing bandpass linear signal processing followed by heterodying the signal to the baseband yields the same results as heterodying the bandpass signal to the baseband followed by a baseband linear signal processing. Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  8. Likelihood Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  9. Signal Space • Inner (scalar) product • Properties of inner product : Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  10. Signal Space (cont´d) • Norm properties : • Euclidean distance between two signals : Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  11. Signal Space (cont´d) • N-dimensional orthogonal signal space is characterized by N linearly independent functions called basis functions. The basis functions must satisfy the orthogonality condition • If all Ki=1, the signal space is orthonormal Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  12. Signal Space (cont´d) • Any arbitrary finite set of waveforms where each member of the set is of duration T, can be expressed as a linear combination of N orthonormal waveforms where N≤M Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  13. Vectorial Representation Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  14. Signals and Noise Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  15. White Noise in Orthonormal Signal Space • AWGN n(t) can be expressed as Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  16. Eb/No: Figure of Merit in Digital Communications • SNR or S/N is the average signal power to the average noise power. SNR should be modified in terms of bit-energy in DCS because : • Signals are transmitted within a symbol duration and hence, are energy signal (zero power) • A merit at bit-level facilitates comparison of different DCSs transmitting different number of bits per symbol. Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  17. Bit Error Probability vs Eb/No Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  18. Decision Theory Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  19. MAP and ML Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  20. Signal Detection Example Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  21. Probability of Bit Error Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  22. Matched Filter Receiver • Problem • Design the receiver filter h(t) such that the SNR (signal power to average noise power) is maximized at the sampling time. • Solution • The optimum filter is the Matched filter, given by which is the time-reversed and delayed version of the conjugate of the transmitted signal Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  23. Matched Filter (cont´d) • The output SNR of a matched filter depends only on the ratio of the signal energy to the PSD of the white noise at the filter input Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  24. Correlator Receiver • The matched filter output at the sampling time can be realized as the correlator output. Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  25. Matched Filter and Correlator Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  26. Implementation of Matched Filter Receiver Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  27. Implementation of correlatorreceiver Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  28. Statistics of The Vector Signals • AWGN channel model : r = si + n • Signal vector si=(si1, si2, … siN) is deterministic. • Elements of noise vector n=(n1, n2, …, nN) are i, i.d Gaussian random variables with zero-mean and variance N0/2. The noise vector pdf is • The elements of observed vector r=(r1, r2,….rN) are independent Gaussian random variables. Its pdf is Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  29. Graphical Example of ML Detection Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  30. Average Probability of Symbol Error • Erroneous decision : For the transmitted symbol mi or equivalently signal vector si, an error in decision occurs if the observation vector r does not fall inside region Zi. • Probability of erroneous decision for a transmitted symbol • Probability of correct decision for a transmitted symbol Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  31. Avg. Prob.of Symbol Error (cont´d) • Average probability of symbol error : • For equally probable symbols : Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  32. BER (Bit Error Rate) • Received signal in Additive White Gaussian Noise Channel • After Matched Filtering & Sampling • where , Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  33. Bit Error Probability Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  34. Maximum Likelihood Decision Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  35. BER versus Eb/No Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  36. Inter-Symbol Interference (ISI) Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  37. Inter-Symbol Interference (ISI) • ISI in the detection process due to the filtering effects of the system • Overall equivalent system transfer function • creates echoes and hence time dispersion • causes ISI at sampling time Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  38. Inter-Symbol Interference (ISI) (cont’d) • Nyquist pulses: No ISI at the sampling time • Ideal Nyquist pulse: Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  39. Inter-Symbol Interference (ISI) (cont’d) • Nyquist bandwidth constraint • Ideal Nyquist filter is not realizable. • Goals and trade-off in pulse-shaping • Reduce ISI • Efficient bandwidth utilization • Robustness to timing error (small side lobes) Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  40. Inter-Symbol Interference (ISI) (cont’d) • Raised-Cosine Filter • A Nyquist pulse (No ISI at the sampling time) Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  41. Inter-Symbol Interference (ISI) (cont’d) Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  42. 3.3.2 Error-Performance Degradation Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  43. Inter-Symbol Interference (ISI) (cont’d) • Square-Root Raised Cosine (SRRC) filter and Equalizer Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  44. Types of Equalizers • Transversal filtering : • Zero-forcing equalizer: Neglect the effect of noise • Minimum mean square error (MSE) equalizer • The basic limitation of a transversal equalizer is that it performs poorly on channels having spectral nulls. • Decision feedback • Using the past decisions to remove the ISI contributed by them Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  45. Transversal Equalizer Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

  46. Decision Feedback Equalizer Signal Processing Lab., http://signal.korea.ac.kr Dept. of Elec. and Info. Engr., Korea Univ.

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