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

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 of the multivariate $\Gamma \Gamma$ distribution with arbitrary correlation. Furthermore, we present novel approximating expressions for the PDF and CDF of the sum of $\Gamma \Gamma$ random variables with arbitrary correlation. Based on this statistical analysis, we investigate the performance of radio frequency and optical wireless communication systems. It is noteworthy that the presented expressions include several previous results in the literature as special cases.Comment: 7 pages, 6 figures, accepted by IEEE Transactions on Vehicular Technolog

On the Computation of the Higher Order Statistics of the Channel Capacity over Generalized Fading Channels

The higher-order statistics (HOS) of the channel capacity $\mu_n=\mathbb{E}[\log^n(1+\gamma_{end})]$, where $n\in\mathbb{N}$ denotes the order of the statistics, has received relatively little attention in the literature, due in part to the intractability of its analysis. In this letter, we propose a novel and unified analysis, which is based on the moment generating function (MGF) technique, to exactly compute the HOS of the channel capacity. More precisely, our mathematical formalism can be readily applied to maximal-ratio-combining (MRC) receivers operating in generalized fading environments (i.e., the sum of the correlated noncentral chi-squared distributions / the correlated generalized Rician distributions). The mathematical formalism is illustrated by some numerical examples focussing on the correlated generalized fading environments.Comment: Submitted to IEEE Wireless Communications Letter, February 18, 201