New BER Expression of MPSK

This paper provides a new, exact, and general expression involving 1-D and 2-D Q-functions for the bit error probability of
M
-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 the
k
th 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.