An efficient approximation to the correlated Nakagami-m sums and its application in equal gain diversity receivers

TL;DR

This paper introduces an efficient closed-form approximation for the distribution of sums of correlated Nakagami-m random variables, facilitating performance analysis of wireless diversity systems under complex fading conditions.

Contribution

It provides a novel approximation method for the sum distribution of correlated Nakagami-m RVs, valid for arbitrary correlation and identical fading parameters, with applications to diversity receiver performance.

Findings

Approximation becomes exact for maximal correlation.

Statistical validation confirms tightness of the approximation.

Application to EGC systems demonstrates practical utility.

Abstract

There are several cases in wireless communications theory where the statistics of the sum of independent or correlated Nakagami-m random variables (RVs) is necessary to be known. However, a closed-form solution to the distribution of this sum does not exist when the number of constituent RVs exceeds two, even for the special case of Rayleigh fading. In this paper, we present an efficient closed-form approximation for the distribution of the sum of arbitrary correlated Nakagami-m envelopes with identical and integer fading parameters. The distribution becomes exact for maximal correlation, while the tightness of the proposed approximation is validated statistically by using the Chi-square and the Kolmogorov-Smirnov goodness-of-fit tests. As an application, the approximation is used to study the performance of equal-gain combining (EGC) systems operating over arbitrary correlated Nakagami-m fading channels, by utilizing the available analytical results for the error-rate performance of an equivalent maximal-ratio combining (MRC) system.