A Simple, Accurate Approximation to the Sum of Gamma–Gamma Variates and Applications in MIMO Free-Space Optical Systems

In this letter, we propose a simple accurate closed-form approximation to the probability density function (pdf) of the sum of independent, identically distributed gamma-gamma (G-G) random variables. It is shown that the pdf of the G-G sum can be efficiently approximated by the pdf of an α-μ distribution. Based on this approach, simple precise approximations for important performance metrics of multiple-input multiple-output (MIMO) free-space optical systems operating over G-G fading are presented. The accuracy of the proposed method is substantiated by various numerically evaluated and computer simulation results.