By Edward A. Lee, David G. Messerschmitt
This complement includes labored out options to the bankruptcy finish challenge units present in Digital verbal exchange, moment Edition, ISBN 0-7923-9391-0.
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Extra resources for Digital Communication: Solutions Manual
Sample text
Y(y 1£)Px (£) are shown below for each possible £ as a fimction of the observation y . (x) THRESHOLD THRESHOLD The decision regions are determined by three dtresholds. the middle of which is zero. The othec two can be found by finding the observation at which the receiver is indifferent between a decision +3 and a decision +1. 1) = Iy _11 2 _ 2021n(0A). 179) Solving this yields y =2 + ~a2In(4). 180) The thresholds are therefore at ± (2 + 'ha2In(4». 1 yields a decision £ = 1. 9-4. ;. 181) 9-S. (a) 51 =[1,O,OJ, 52 =[0,1 ,OJ, 53 =[0,0,1] .
O16 . 64 036 004 . 04 Performing the Viterbi algorithm, the surviving paths and their path meaies after each observation are shown in the following figure. 45 The decision is i" useful. = {O,I,I,O}, which is different from the decision in part (a). The knowledge of the lSI is 9-17. (a) The probability of error in the comparable system free of lSI is Q (1120"), where cfl is the noise in this system. 89440". This implies that 0' is about 1 dB smaller than 0", so the system with lSI has about 1 dB more noise margin than the system without lSI.
120) • Clearly we want to make the third term as large negative as we can. Since the £ can be have a phase that is any multiple of 1tI4, clearly the third term is minimized if£1 and £z are antipodal; that is, they have opposite phase. fl or 2. 123) d~ It is easy to verify that the third case is always the smallest for aliOS a < I, and hence d mill = 2,"1 - a . 124) Note that the minimum distance goes to zero as a-+l. 7-12. h.. =1 AI". f h;(1 -1cT)dl 2 a <'}:liA - t~ .. (KT - kT)2 =1 1". If the data symbols are drawn from a finite constellation, we can assume that K~ C 1.
