New Statistical Results of Partial Sums of Ordered Gamma-Distributed RVs for Performance Evaluation of Wireless Communication Systems

Abstract

With the increase in the complexity of communication systems, order statistics have become increasingly significant in performance evaluation, especially for advanced diversity techniques over fading channels. However, existing analytical approaches are not useful owing to their high complexity. In this paper, we present novel and insightful statistical results of the partial sums of ordered Gamma-distributed random variables. By adopting a unified analytical framework to obtain the desired joint probability density function from the joint moment-generating function, we redefine and derive the common key functions specialized for the Gamma distribution. The derived formula is presented in the form of either general closed-form expressions or at least a single integral form instead of the originally complicated multiple-integral form. In terms of a feasible application of our results, we present a complete and general closed-form analysis of the statistics of the combined received signal-to-noise ratio of the distributed cyclic delay diversity with the cyclic prefix single-carrier scheme. We also show that our analytical results can provide potential mathematical solutions for other wireless communication systems. Selected numerical examples are presented and discussed to illustrate the effectiveness of the applied approach and related results. All the derived analytical results were compared and verified by using Monte Carlo simulations to verify the accuracy of our analysis.