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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.