Exam2Solutions

# Exam2Solutions - ECEN 661-Modulation Theory Spring 2006...

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ECEN 661 -Modulation Theory Spring 2006 Midterm Exam #2 Solutions Problem 1. (30 points) Let be a sequence of binary IID data bits where . These data bits are to be trans- mitted via PAM, but first they are precoded according to . The transmitted PAM signal (complex equivalent) is then of the form , where is the pulse shape and is the bit interval. The signal is then received in the pres- ence of Gausian noise . (a) Sketch a block diagram of the optimum (ML) receiver. Be sure carefully describe how each block functions. Answer: The discrete time channel model is . In vector form we have . The MLSe will minimize . The trellis diagram below show the branches labelled with the appropriate branch metrics. (b) Assuming the pulse shape is normalized so that , find the minimum distance of this signalling format. a n {} a n 1 ± b n 4 5 -- a n 3 5 a n 1 + = s l t () b n pt nT b n = p t T b r l t s l t n l t + = X r l t b t d nT b n 1 + T b MLSE a ˆ n r n b n p 2 t t d n n + b n n n + == rb n + = d 2 , r n b n 2 n = a n 1 +1 = a n 1 1 = r 1 75 + 2 r 1 2 r 1 15 2 r 1 + 2 r 2 2 r 2 + 2 r 2 2 r 2 + 2 p 2 t t d 1 =

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Answer: Consider the following two paths: , . The distance between these two paths is .
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Exam2Solutions - ECEN 661-Modulation Theory Spring 2006...

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