# Exam1 - University of Illinois Spring 2011 ECE 361 First...

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Unformatted text preview: University of Illinois Spring 2011 ECE 361: First MidSemester Exam 1. Consider a binary digital communication system operating over an AWGN channel using signals s ( t ) = ( A, ≤ t < T, , otherwise, and s 1 ( t ) = ( √ 2 A cos( πt/T ) , ≤ t < T, , otherwise. The receiver consists of a linear time-invariant filter whose output is sampled at T = T and is compared to the maximum-likelihood threshold. (a) Suppose that the receiver filter has impulse response h ( t ) = s ( t ). What is the error probability P e achieved by this receiver? (b) Find the error probability P * e achieved by the optimum (matched-filter) receiver for these signals and show that it is smaller than the P e you found in part (a). 2. Suppose that τ is some number in the interval [0 ,T ], and consider a binary digital communication system operating over an AWGN channel using signals s ( t ) = ( A, ≤ t ≤ τ, , otherwise, and s 1 ( t ) = ( A, T- τ ≤ t ≤ T, , otherwise....
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