On the Multivariate Gamma-Gamma ($\Gamma \Gamma$) Distribution with Arbitrary Correlation and Applications in Wireless Communications

摘要

The statistical properties of the multivariate Gamma-Gamma ($\Gamma \Gamma$)distribution with arbitrary correlation have remained unknown. In this paper,we provide analytical expressions for the joint probability density function(PDF), cumulative distribution function (CDF) and moment generation function ofthe multivariate $\Gamma \Gamma$ distribution with arbitrary correlation.Furthermore, we present novel approximating expressions for the PDF and CDF ofthe sum of $\Gamma \Gamma$ random variables with arbitrary correlation. Basedon this statistical analysis, we investigate the performance of radio frequencyand optical wireless communication systems. It is noteworthy that the presentedexpressions include several previous results in the literature as specialcases.