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

TL;DR

This paper introduces a simple closed-form approximation for the distribution of the sum of independent Gamma-Gamma variates, enabling better analysis of RF and optical wireless communication systems affected by fading and turbulence.

Contribution

It proposes a novel approximation method for the sum of Gamma-Gamma variates, facilitating analysis of complex MIMO systems in RF and optical wireless communications.

Findings

The approximation accurately models the sum distribution in simulations.

It improves the analysis of MIMO systems under fading and turbulence.

Numerical results confirm the effectiveness of the proposed method.

Abstract

The Gamma-Gamma (GG) distribution has recently attracted the interest within the research community due to its involvement in various communication systems. In the context of RF wireless communications, GG distribution accurately models the power statistics in composite shadowing/fading channels as well as in cascade multipath fading channels, while in optical wireless (OW) systems, it describes the fluctuations of the irradiance of optical signals distorted by atmospheric turbulence. Although GG channel model offers analytical tractability in the analysis of single input single output (SISO) wireless systems, difficulties arise when studying multiple input multiple output (MIMO) systems, where the distribution of the sum of independent GG variates is required. In this paper, we present a novel simple closed-form approximation for the distribution of the sum of independent, but not necessarily identically distributed GG variates. It is shown that the probability density function (PDF) of the GG sum can be efficiently approximated either by the PDF of a single GG distribution, or by a finite weighted sum of PDFs of GG distributions. To reveal the importance of the proposed approximation, the performance of RF wireless systems in the presence of composite fading, as well as MIMO OW systems impaired by atmospheric turbulence, are investigated. Numerical results and simulations illustrate the accuracy of the proposed approach.