An alternative expression for the symbol-error probability of MPSK in the presence of I/Q unbalance

This letter provides a new expression for the probability of the phase angle between two vectors perturbed by Gaussian noise with in-phase/quadrature-phase (I/Q) unbalance, in order to simplify the analysis of the error probabilities of M-ary phase-shift keying (MPSK). The error probabilities, symbol-error rates, or bit-error rates for MPSK with I/Q balance or unbalance, can be presented straightforwardly from the derived expression. Because the newly derived result is provided in terms of the conventional first-order Gaussian Q-function and the joint Gaussian Q-function with a correlation coefficient dependent on M, it readily allows rapid evaluation for various cases of practical interest.