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EE_564_F09_HW7

# EE_564_F09_HW7 - EE-564 Fall 2009 Homework#7 Due Wednesday...

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EE-564 Fall 2009 Homework #7 Due Wednesday, November 18, 2009 1. “Digital Communications”, 5 th Edition, Proakis & Salehi, Problem 10.2 2. (Course Reader Problem 51) Consider an ISI channel, where the sequence of sampled matched filter outputs is given by ࢟ = ࡳ࢞ + ࢠ Where ࢟ = (ݕ , ݕ , … , ݕ ௡ିଵ ) , is a Hermitian symmetric Toeplitz matrix with (݅, ݆) element [ࡳ] ௜,௝ = ݃ ௜ି௝ , and where denotes the noise contribution to the output of the matched filter. Assume there exists a lower triangular matrix such that ࡳ = ࡸ . This decomposition is called Cholesky factorization and is referred to as the Cholesky factor of G . L = ۉ ۈ ۈ ۈ ۈ ۇ L 0 L L 0 0 0 0 L L 0 L L 0 L L 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 L L 0 L 0 0 0 0 0 0 0 0 L 0 L L 0 0 0 0 L L 0 L L 0 L L ی ۋ ۋ ۋ ۋ ۊ In which L = 1 , L = −1/2 , and L = 1/4 . Input signal set is {-1, 1} and the output sequence is y=(1.5, −1, 2.5, −2, −2.5 , 0, 1, 0) . Assume that the initial state is x ିଵ = x ିଶ = 0 . Find the optimum MAP decoded sequence.

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