EE_564_F09_HW7

EE_564_F09_HW7 - EE-564 Fall 2009 Homework#7 Due Wednesday 1 Digital Communications 5th Edition Proakis Salehi Problem 10.2 2(Course Reader Problem

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E E - 5 6 4 F a l l 2 0 0 9 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 ௡ିଵ ² , is a Hermitian symmetric Toeplitz matrix with ±݅,݆² 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 00 L L 0L L 0 L L 0 0 0 0 0 0 0 0 0 0 0 0 0 L L L 0 L L L 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 ,0,1,0² . Assume that the initial state is x ିଵ =x
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This note was uploaded on 04/03/2010 for the course EE 564 at USC.

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EE_564_F09_HW7 - EE-564 Fall 2009 Homework#7 Due Wednesday 1 Digital Communications 5th Edition Proakis Salehi Problem 10.2 2(Course Reader Problem

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