PracticeExam1

PracticeExam1 - ECEN 661 -Modulation Theory Spring 2006...

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ECEN 661 -Modulation Theory Spring 2006 Practice Midterm Exam #1 Problem 1. The signal constellation shown is known as the 32-point cross (32-CR) constellation. In all parts of this question, assume that all 32 points in the constellation are equally likely. (a) On the plot of the signal constellation given, carefully sketch the boundaries of the decision region for the ML receiver. (b) Find the relationship between the mini- mum squared Euclidean distance, , and the average energy per symbol, , in this constellation. (c) Find the average number of nearest neighbors, , for this constellation as well as the asymptotic expression for the probability of symbol error for the ML receiver is an AWGN channel. Leave your answer in terms of , where is the average energy per bit. (d) Find the asymptotic relative efficiency of this modulation format relative to QPSK and express your answer in decibels. (e) Derive a union bound for the probability of symbol error for the ML receiver for the 32-CR constellation. Problem 2. A zero-mean bandpass noise process, , whose PSD is as shown is passed through the system
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PracticeExam1 - ECEN 661 -Modulation Theory Spring 2006...

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