PS08 - University of Illinois Spring 2011 ECE 361 Problem...

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Unformatted text preview: University of Illinois Spring 2011 ECE 361: Problem Set 8 Equalizers in Band-Limited Communications Due: Thursday April 7 at 9:30 a.m. Reading: Lecture Notes: Lectures 15-18 1. [Zero-forcing transversal filter] The discrete-time model for a band-limited channel has as channel response the sequence- . 05 , . 2 , 1 . , . 3 ,- . 07 Design a two-stage three-tap equalizer for this channel. The symbol X [ m ] will appear in ˆ Y [ m ] (where it is the desired symbol) but not in the ISI affecting ˆ Y [ m + 1] and ˆ Y [ m- 1] where it is forced to zero. However, X [ m ] might appear in the ISI affecting other symbols. What is the coefficient of X [ m ] in the ISI affecting ˆ Y [ m + 2] and ˆ Y [ m- 2]? How does this compare with how much X [ m ] affects Y [ m + 2] and Y [ m- 2]? Has zero-forcing helped or hurt these symbols farther away? 2. [Comparison of equalizers] The received signal in a communication system operating over a band-limited channel is Y [ m ] = X [ m ] + 0 . 5 X [ m- 1] +...
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