Generalized Closed-Form Expression for the Bit Error Probability of MPSK with Phase Noise

This study presents a general and closed-form expression for the bit error probability (BEP) of Gray-coded M -ary phase shift keying (MPSK) in the presence of phase noise in additive white Gaussian noise (AWGN) channel. Closed-form expressions are obtained by converting the AWGN channel noise to equivalent phase noise, under the approximation that the AWGN channel noise and the phase error are both Gaussian distributed. The only existing work in the literature with similar assumption only calculates the BEP for M ≤ 16. The proposed analysis in this study will facilitate the BEP calculation for higher order MPSK.