Infinite Series Representations of the Trivariate and Quadrivariate Nakagami-m distributions

In this paper, we derive new infinite series representations for the quadrivariate Nakagami-m distribution and cumulative distribution functions (cdf). we make use of the Miller´s approach and the Dougall´s identity to derive the joint density function. The classical joint density function of exponentially correlated Nakagami-m variables can be identified as a special case of our joint density function. Our results are based on the most general arbitrary correlation matrix possible. Moreover, the trivariate density function and cdf for an arbitrary correlation matrix is also derived from our main result. Bounds on the error resulting from truncation of the infinite series are also presented. Finally, numerical results are presented to verify the accuracy of our formulation.