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course_reader_caire - EE 564 Course Reader G. Caire May 9,...

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Unformatted text preview: EE 564 Course Reader G. Caire May 9, 2008 1 USC EE 564 Communications Theory Spring 2008 Course Reader WARNING: This course reader contain a summary of the material covered during the lectures. This is intended as a useful reminder in order to review the course subjects. It is not intended, by any means, to replace neither the course lecture notes nor the course textbook. There may be topics in the course that are not contained in this reader. This does not constitute an excuse for not studying them, and these topics may come up in exam problems. Author: Giuseppe Caire, EE Department, USC 2 Contents 1 Signals and systems 5 1.1 Space L 2 : finite-energy deterministic signals . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Random processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Complex baseband channel model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Basic AWGN channel model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2 MAP decoding 23 2.1 Bayesian hypothesis testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 Upper and lower bounds to P e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3 Sufficient statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3 Signal sets and their performance 33 3.1 Coherent detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.1.1 Minimum distance and asymptotic gain . . . . . . . . . . . . . . . . . . . . . 34 3.2 Signal sets for coherent detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2.1 Pulse-Amplitude Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.2.2 Quadrature-Amplitude Modulation . . . . . . . . . . . . . . . . . . . . . . . . 36 3.2.3 Phase-Shift Keying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.4 Orthogonal signal sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.3 Bit-error probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.4 Non-coherent detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.5 Performance of non-coherent detection . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.5.1 M-ary orthogonal signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.6 Differential PSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.7 Appendix: the characteristic function of HQF-GRV . . . . . . . . . . . . . . . . . . . 49 3.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4 Digitally modulated signals 55 4.1 Signal sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554....
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course_reader_caire - EE 564 Course Reader G. Caire May 9,...

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