Craig representation of the product of two Gaussian Q functions and its application

This paper introduces a Craig-type representation for the product of two one-dimensional Gaussian Q functions with arbitrary arguments, i.e., Q(x)Q(y). In the limits of y = x and y = 0, the form derived for Q(x)Q(y), immediately reduces to the Craig forms of Q²(x) and Q(x) respectively. To justify the value of the results, digital communication performance evaluation applications involving the product of two one-dimensional Gaussian Q functions are presented. The resulting single integrals are particularly useful in evaluating the bit-error probability of M-ary PSK (MPSK) systems. Moreover, introduced form is computationally desirable for evaluating Q(x)Q(y).