A simple technique for evaluating the bit-error probability of coherent M-ary phase-shift keying (PSK) with any bit-mapping is proposed. Closed-form expressions are given in terms of error functions for half- and quadrant-plane probabilities in the decision space, avoiding the numerical evaluation of complicated integrals that occurs in the direct method. Bit error probability expressions for M-ary PSK with Gray, natural binary, and folded binary bit-mappings are derived.>
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Irshid et al. (1991) studied this question.
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