T he QPSK system of Example 11.13 can be generalized to an

Chapter 11, Problem 11.31

(choose chapter or problem)

T he QPSK system of Example 11.13 can be generalized to an M -ary phase shift keying (MPSK) system with M > 4 equally likely signals. The signal vectors are {so, .. . , Sj\1- 1}, where and ()i = 211i/ JV!. \i\fhen the ith message is sent, the received signal is X = Si+ N where N is a Gaussian (0, a-21) noise vector. (a) Sketch the acceptance set Ai for the hypothesis H i that Si was transmitted. (b) Find the largest value of d such that ( c) Use d to find an upper bound for the probability of error.

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