HW5Solutions

# HW5Solutions - ECEN 661 - Modulation Theory - Spring 2008...

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ECEN 661 - Modulation Theory - Spring 2008 Homework #5 Solutions 1. The decision statistic will be of the form where and is a zero-mean Gaussian random variable with variance of . (a) The decision threshold needs to be . (b) The probability of error is . This is 3dB worse than antioodal signalling. 2. (a) . (b) For any binary signalling format, the probability of error is . In this case, the distance between the two waveforms is . Hence the probability of error is: . 3. Start with the general form of the Union Bound for the th signal in the constellation: . For the -ary bi-orthogonal constellation, each point has nearest neighbors at a distance of and one other point at a distance . Hence the union bound for the biorthogonal sig- nal constellation will be z zs n + = s 0 AT , {} n σ 2 N o T 2 = 2 P e Q 2 σ ------   Q A 2 T 2 N o --------- Q E b N o -----  == = E b 1 2 -- st () 2 t d 0 T A 2 T 2 P e Q d 2 2 N o = d 2 1 2 s 1 t s 2 t 2 t d 0 T A 2 T 2 P e Q A 2 T 4 N o Q E b 2 N o i P ei , Q d ij , 2 2 N o ji M M 2 2 E s 2 E s

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## This note was uploaded on 02/21/2012 for the course ECEN 611 taught by Professor Miller during the Spring '08 term at Texas A&M.

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HW5Solutions - ECEN 661 - Modulation Theory - Spring 2008...

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