Problem 4 Consider the following M-ary digital communication system with M = 4. Assume that all symbols are equally probable and that each symbol is
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Digital communication problem.

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Problem 4 Consider the following M-ary digital communication system with M = 4. Assume that all symbols are equally
probable and that each symbol is transmitted within time duration 2" = ls over an AWGN charmel with double-
sided power spectral density NO/Z. Transmitter Receiver The expression of the transmit signal within T is shown below. 31(t) = 2 cos(2mf), 32(t) = 2 cos(41rt)
530?) = 2 cos(8:rrt), 34(t) = 2 cos(167rt). i) How many bit(s) isfare represented by one symbol? ii) At least how many basic function(s) isfare needed to represent all symbols? Give the expression(s) of
itfthem. iii) Let Pe (j, k) denote the pair-wise error probability between signals j and k. Find Pe (j, k) iv) Find the Union bound for the average symbol error rate.

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