Hw7SolnBinder - ECE 5670 : Digital Communications ECE...

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Unformatted text preview: ECE 5670 : Digital Communications ECE department, Cornell University, Spring 2011 Homework 7 Solutions Instructor: Salman Avestimehr Office 325 Rhodes Hall 1. 2. 3. See the end. 4. The ISI channel, with a focus on x [1] can be represented in vector notation as y = h x [1] + z , (1) where y is the vector of the three received values, and h = 1 1 3 1 6 , (2) and z = w [1] x [2] + w [2] 1 3 x [2] + x [3] + w [3] . (3) The goal is to make the elements of z uncorrelated and equal variance. At that point, we can use a regular matched filter. The important step is to decorrelate; once that is done, we can normalize them all so as to be of the same variance. Observe the following. z [1] is uncorrelated (even independent) of z [2] , z [3] . The correlation between z [2] and z [3] is E [ z [2] z [3]] = E 3 . (4) So, defining def = E [ z [2] z [3]] E ( z [2]) 2 (5) = E 3 ( E + 2 ) (6) we see that z [3]- z [2] and z [2] are uncorrelated . (7) So, we create the filtered received signal...
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Hw7SolnBinder - ECE 5670 : Digital Communications ECE...

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