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Unformatted text preview: University of Illinois Spring 2011 ECE 361: Problem Set 2 Matched and Unmatched Filtering, and Signal Design Due: Thursday February 3 at 9:30 a.m. Reading: Lecture Notes: Lectures 25 Throughout this Problem Set, assume that the bits being transmitted are equally likely to be 0 or 1. 1. [Matched Filtering] A communication system uses signals s ( t ) and s 1 ( t ) to communicate over a white Gaussian noise channel with twosided power spectral density N / 2. The receiver is an optimum receiver (matched filter) for the signal set, and the maximumlikelihood decision rule is used. For the three sets of signals given below, compute the signal energies E and E 1 , the value of h s ,s 1 i , and the error probability achieved by the optimum receiver. Note: You are not asked for the impulse response of the matched filter, or the sampling time T , or the values of s ( T ) and s 1 ( T ), or the variance of the noise at the receiver filter output, and you should not need any of these to find the answers to the question asked....
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 Spring '09

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