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The Gamma-Gamma (GG) distribution has recently attracted the interest withinthe research community due to its involvement in various communication systems.In the context of RF wireless communications, GG distribution accurately modelsthe power statistics in composite shadowing/fading channels as well as incascade multipath fading channels, while in optical wireless (OW) systems, itdescribes the fluctuations of the irradiance of optical signals distorted byatmospheric turbulence. Although GG channel model offers analyticaltractability in the analysis of single input single output (SISO) wirelesssystems, difficulties arise when studying multiple input multiple output (MIMO)systems, where the distribution of the sum of independent GG variates isrequired. In this paper, we present a novel simple closed-form approximationfor the distribution of the sum of independent, but not necessarily identicallydistributed GG variates. It is shown that the probability density function(PDF) of the GG sum can be efficiently approximated either by the PDF of asingle GG distribution, or by a finite weighted sum of PDFs of GGdistributions. To reveal the importance of the proposed approximation, theperformance of RF wireless systems in the presence of composite fading, as wellas MIMO OW systems impaired by atmospheric turbulence, are investigated.Numerical results and simulations illustrate the accuracy of the proposedapproach.

On the Distribution of the Sum of Gamma-Gamma Variates and Applications in RF and Optical Wireless Communications