Sum of arbitrarily correlated Gamma random variables with unequal parameters and its application in wireless communications

Abstract

Characterizing the distribution for the sum of correlated Gamma random variables (RVs), especially for the sum of those with unequal fading and power parameters, is still an open issue. In this paper, based on the Cholesky factorization on the covariance matrix and moments matching method, we propose an approximate expression for the probability density function (PDF) of the sum of correlated Gamma RVs with unequal fading and power parameters and arbitrary correlation matrix. The proposed PDF expression is simple, accurate, and closed-form and thus can be conveniently used for general performance analysis in wireless communications. Simulation results are used to confirm the validity of the proposed PDF expression. The performance analysis of maximal-ratio combining (MRC) diversity system and cellular mobile radio system in wireless communications using the proposed PDF expression is also presented. © 2016 IEEE.