This letter presents an extended Pawula F-function for computing the error rate of generalized M-ary phase shift keying (MPSK) system in the presence of phase error, quadrature error, and I-Q gain mismatch over additive white Gaussian noise (AWGN) and fading channels. The extended Pawula F-function conditioned on an instantaneous fading carrier-to-noise ratio (CNR) is derived in the form of the Craig representation.

Two rotational transformations are used to derive a new expression for the symbol error probability (SEP) of an M-ary phase shift keying (MPSK) with an I-Q unbalance over additive white Gaussian noise (AWGN) and Rician fading channels. We used the new expression to investigate the effect of the I-Q unbalance on the MPSK SEP performance. Our investigation confirms that this approach is a convenient way to evaluate the average SEP of an MPSK for various cases of the Rician factor.

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.

In this letter, we derive an analytical expression for computing the symbol error probability (SEP) of the M-ary quadrature amplitude modulation (M-QAM) in the joint presence of phase/quadrature error and I/Q gain imbalance over an additive white Gaussian noise (AWGN) channel. The derived expression containing only the two-dimensional Gaussian Q-function can be used to compute the SEP of M-QAM in various fading channels by making use of the moment-generating function (MGF) approach.