Upper bounds on the symbol-error probability of MPSK with phase error using pawula F-function IV

This letter presents an alternative derivation of the Case IV of Pawula F-function and an approximation for the corresponding probability density function (pdf) in the presence of the Tikhonov distributed phase error. The pdf of Case IV is used to obtain new upper bounds for the conditional and average symbol-error probabilities of M-ary phase shift keying with phase error over additive white Gaussian noise channels. Numerical results demonstrate the validity of the upper bounds.