EE_564_F09_HW2

EE_564_F09_HW2 - EE564 Fall2009 Homework#2...

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E E 5 6 4 F a l l 2 0 0 9 Homework #2 Due Wednesday, September 9, 2009 1. Consider the following binary hypothesis testing problem: ܪ : ݌ ሺݕሻ ൌ 2 3 ሺݕ൅1ሻ ݕ א ሾ0,1ሿ ܪ : ݌ ሺݕሻ ൌ 1 ݕ א ሾ0,1ሿ a) For equal priors and uniform costs, determine the Bayes optimal rule and the associated risk. b) For ߙ א ሺ0,1ሻ, determine the Neyman‐Pearson rule(s) and the associated probability of detection. Plot the receiver operating characteristic. 2. Consider the following binary hypothesis testing problem: ܪ : ࢅ ൌ െܣ ൅ ࡺ ܪ : ࢅ ൌ ܣ ൅ ࡺ Where ܰ~ࣝࣨሺ0, ߪ ሻ, ܣ א ԧ. Thus, the observations, the noise are complex. a) Determine the maximum likelihood detector. To determine the optimal detector, you will need to keep track of complex conjugation, etc. b) For fixed ܣ א ԧ, what is the Bayes risk, assuming equal priors and uniform costs? c)
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This note was uploaded on 04/03/2010 for the course EE 564 at USC.

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EE_564_F09_HW2 - EE564 Fall2009 Homework#2...

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