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

Abstract

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.

7 pages, 6 figures, accepted by IEEE Transactions on Vehicular Technology

References in corpus (2)

• Unified Performance Analysis of Mixed Radio Frequency/Free-Space Optical Dual-Hop Transmission Systems
• On the Ergodic Capacity of MIMO Free-Space Optical Systems over Turbulence Channels

Cited by in corpus (4)

• Gamma distribution-based sampling for imbalanced data
• Unified Framework for the Effective Rate Analysis of Wireless Communication Systems over MISO Fading Channels
• On the Distribution of the Ratio of Products of Fisher-Snedecor $\mathcal{F}$ Random Variables and Its Applications
• Distribution of the Sum of Fisher-Snedecor $\mathcal{F}$ Random Variables and Its Applications