Generalized BER Expression of MPSK in the Presence of Phase Error

In this letter, we derive an exact and general closed-form expression for the bit error rate (BER) of Gray coded M-ary phase shift keying (MPSK) in the presence of a fixed phase error. We also propose a very simple and tight approximate expression from the derived exact expression. To validate the exactness of the proposed exact and general expression and the tightness of the proposed approximation, we compare the results obtained from the proposed expressions with those from computer simulations. We also present the average BER results of MPSK for random phase errors caused by phase-locked loop or imperfect channel estimation by using the derived expressions.