Unified Analysis of the Average Gaussian Error Probability for a Class of Fading Channels

This paper focuses on the analysis of average Gaussian error probabilities in certain fading channels, i.e. we are interested in E[Q( √ pγ] where Q(·) is the Gaussian Q-function, p is a positive real number and γ is a nonnegative random variable. We present a unified analysis of the average Gaussian error probability, derive a compact expression in terms of the Lauricella F (n) D function that is applicable to a broad class of fading channels, and discuss the relation of this expression and expressions of this type recently appeared in literature. As an intermediate step in our derivations, we also obtain a compact expression for the outage probability of the same class of fading channels. Finally, we show how this unified analysis allows us to obtain novel performance analytical results. Index Terms Performance analysis, average bit error probability, outage probability, fading channels, Lauricella functions.