PracticeExam2 - ECEN 661 -Modulation Theory Spring 2006...

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ECEN 661 -Modulation Theory Spring 2006 Practice Midterm Exam #2 Problem 1. (a) For a full response CPFSK modulation format with a modulation index, , prove that the asymptotic relative power efficiency is bounded by . (b) Since optimizes the above expression, suppose we choose as our modu- lation index (since it is a simple rational number close to the optimal value). Prove that for this case, the upper bound in (a) is tight, that is, for , . Problem 2. Consider a binary signalling format where the two possible transmitted signals, whose complex envelopes are and , satisfy: (i) , and (ii) . The signal is transmitted over a channel the adds white Gaussian noise and also exhibits Rayleigh fading so that the complex envelope of the received signal, , is given by , where is complex white Gaussian noise with , is a Ray- leigh random variable with PDF, , and is a Random variable uni- formly distributed over . Derive the probability of error of the optimum non-coherent detector for this signalling scheme over this channel.
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This note was uploaded on 02/21/2012 for the course ECEN 661 taught by Professor Miller during the Fall '11 term at Texas A&M.

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PracticeExam2 - ECEN 661 -Modulation Theory Spring 2006...

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