| Aims |
At the end of this lecture, the students will be able to - use and understand, for a signal correpted by additive white noise gaussian, the link between the signal, its analytical version, its complex envelope and the Rice components, - use MATLAB to implement a filter in the previous formalism, - expand a digitally modulated signal onto basis functions, - derive the decision rule of an optimal receiver according to the Bayes criterion, for a digital modulation, - establish and compute the bit error rate characterizing the coherent or noncoherent demodulation of a digital transmission corrupted by AWGN, - explain "a priory" and "a posteriory" entropy, - compute the entropy of a source and the Shannon channel capacity, - from the maximum likelihood criterion, derive a Viterby equalizer, - for a Wiener criterion, derive the equations to be fulfilled by a linear or decision feedback equalizer, and solve these equations, - show the relevance of the matched filter by means of a fractionally spaced equalizer and apply this result to other systems, - implement in MATLAB, Viterbi, linear and DF equalizers, - explain from the ML criterion DA or NDA type phase estimators, and understand the tools to characterize the performance of these estimators, - explain from the ML criterion, estimators for the sampling instant (timing recovery) of the DA and NDA types and explain their performance, - understand and provide a mathematical description of multicarrier modulations, cyclic extension and explain the motivation for MC modulation.
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