Probability of an arbitrary wedge-shaped region of the MPSK system in the presence of quadrature error

The paper presents a new and simple expression for computing the probability on an arbitrary wedge-shaped region between two different phase angles when the signal vector is perturbed by two-dimensional Gaussian noise in the presence of a quadrature error. The two-dimensional Gaussian Q-function is used to characterize the expression. The expression can be very useful for computing the analytical error probability of the M-ary phase shift keying system operating in various channel environments.