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Unformatted text preview: UCSB Spring 2010 ECE 146B: Problem Set 5 Assigned: May 17 Due: May 24 (by noon, in course homework box) Reading: Classnotes, Chapter 7 Topics: ML reception and its performance Problem 1: Three 8-ary signal constellations are shown in Figure 1. (a) Express R and d (2) min in terms of d (1) min so that all three constellations have the same E b . QAM1 QAM2 R 8-PSK Figure 1: Signal constellations for Problem 1 (b) For a given E b /N , which constellation do you expect to have the smallest bit error probability over a high SNR AWGN channel? (c) For each constellation, determine whether you can label signal points using 3 bits so that the label for nearest neighbors differs by at most one bit. If so, find such a labeling. If not, say why not and find some “good” labeling. (d) For the labelings found in part (c), compute nearest neighbors approximations for the average bit error probability as a function of E b /N for each constellation. Evaluate these approximations for E b /N = 15 dB .....
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This note was uploaded on 12/28/2011 for the course ECE 146b taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08