On the MGF-Based Approximation of the Sum of Independent Gamma-Gamma Random Variables

Abstract

We study the use of moment generating function (MGF) method to approximate the distribution of the sum of independent, but not necessarily identical, Gamma-Gamma variables, which is crucial in performance evaluation of multiple- input multiple-output (MIMO) free-space optical (FSO) systems. We show that the MGF-based approximation method can flexibly provide sufficient accuracy in the upper and lower tails of the cumulative distribution function (CDF) for both identically and non- identically distributed cases. Comparisons to highlight the advantages of the proposed method over existing ones are also presented. We then apply the proposed method to analytically derive closed-form expressions for the outage probability and average bit-error rate of MIMO-FSO systems. Monte-Carlo simulations are also performed to validate analytical results.