Average of product of two Gaussian Q functions as summation series and its significance in evaluating SEP integrals over fading channels

The product of two Gaussian Q-functions is actively used in computing the error probabilities of various digital modulation schemes. Evaluating symbol error probability (SEP) integral involving the product of Gaussian Q-functions over fading distributions is complicated. The closed-form solutions are not available always, therefore to derive these solutions approximations are used. In this paper, an approximation to the product of two Gaussian-Q functions as a sum of exponentials is presented. Further it is used to evaluate the error probabilities of modulation techniques over fading distributions in wide range of scenarios. The knowledge of moment generating function (MGF) of a fading model is sufficient enough to derive the closed-form solution to SEP integrals. Numerical results demonstrate superior accuracy of proposed approximation over other existing competing approximations. Furthermore the proposed solutions are fairly simple as the MGF of fading channels involve fundamental mathematical functions.