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

TL;DR

This paper provides a unified analytical framework for calculating average Gaussian error probabilities in various fading channels, deriving compact expressions using special functions, and offering new insights into channel performance analysis.

Contribution

It introduces a unified approach to analyze Gaussian error probabilities across multiple fading channels using Lauricella functions, and derives new expressions for outage probability.

Findings

Derived a compact expression for average Gaussian error probability.

Established a relation between error probability and outage probability expressions.

Provided novel performance analysis results for a broad class of fading channels.

Abstract

This paper focuses on the analysis of average Gaussian error probabilities in certain fading channels, i.e. we are interested in E[Q((p {\gamma})^(1/2))] where Q(.) is the Gaussian Q-function, p is a positive real number and {\gamma} 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 FD^(n) 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.