Numerical Approximations for the Gaussian Q-Function by Sums of Exponentials

Abstract

The accurate prediction of wireless systems’ performance is a key factor in the timely adoption of new technologies and systems’ design. In many cases, when evaluating the performance measures of a communication system with additive white Gaussian noise, integrals involving the Gaussian Q-function appear and closed-form solutions cannot be expressed in terms of elementary functions. This has motivated researchers to propose approximations and bounds for the Gaussian Q-function to facilitate expression manipulations. This paper gives a brief overview about the existing approximations of the Q-function. In addition, it summarizes<br/>and compares the different quadrature numerical integration techniques that can be applied in approximating the Gaussian Q-function in a tractable form as a weighted sum of exponentials.