An alternative approach to the symbol error probability of coherent M-PSK systems having a phase error in an AWGN channel

This letter presents an alternative analytical expression for the symbol error probability (SEP) of the coherent M-ary phase shift keying (M-PSK) system when an arbitrary phase error exists in an additive white Gaussian noise (AWGN) channel. Unlike the previous work, it is shown that the SEP performance of the M-PSK system can be completely characterized by the one- and two-dimensional Gaussian Q-functions. The new expression is numerically more convenient to manipulate than the previous results by replacing the integral operations with the built-in functions commonly available in various mathematical software tool libraries.