A Survey on Approximations of One-Dimensional Gaussian Q-Function

Abstract

Predicting the digital communication system performance plays a very important role in the process of system design. This performance is usually quantified by symbol error probability or bit error probability. Computing these probabilities in presence of Additive White Gaussian Noise requires to work with integrals involving the Gaussian Qfunction, which cannot be expressed in closed-form in terms of elementary functions. As a result, approximating the Gaussian Q-function in closed-form expressions with high accuracy becomes a necessity. In this paper, we give an overview about the Gaussian Q-function approximations and via some illustrating examples, we discuss their accuracy, tractability as well as their computational complexity