This paper provides a new, exact, and general expression involving 1-D and 2-D Q-functions for the bit error probability ofM-ary phase-shift keying (MPSK) under additive white Gaussian noise (AWGN) and fading channels when Gray code bit mapping is employed. Regular patterns in the error probability expression of thekth bit are observed while developing the bit error rate (BER) expression. From these patterns, we then derive a new BER expression for the MPSK constellation.
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Jeong et al. (2011) studied this question.
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