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# Exam2PracticeSolutions - EE661-Modulation Theory Spring...

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EE661 -Modulation Theory Spring 2008 Practice Midterm Exam #2 The following problems were taken from previous exams. They were not given all in the same year so do not interpret the set of problems as representative of a complete exam, but rather take each problem as a representative problem. Problem 1. (40 points) (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 , . Partial Answer: For part (a) see the soultion to HW7, problem 1. To prove that the bound is tight, you simply want to make an argument that any other choice of paths to compare must lead to at least as great a distance. Details of the proof will vary. Problem 2. (25 points) An IID sequence of data symbols are precoded such that . A PAM sig-

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