An MGF-based Unified Framework to Determine the Joint Statistics of Partial Sums of Ordered Random Variables

TL;DR

This paper introduces a unified MGF-based framework for deriving the joint statistics of partial sums of ordered random variables, applicable to various scenarios in wireless communications.

Contribution

It provides a systematic method to obtain joint statistics of any partial sums of ordered RVs using MGFs and PDFs, including special cases with exponential RVs.

Findings

Closed-form expressions for exponential RVs.

Applicable to performance analysis in wireless systems.

Handles partial sums involving all or a subset of ordered RVs.

Abstract

Order statistics find applications in various areas of communications and signal processing. In this paper, we introduce an unified analytical framework to determine the joint statistics of partial sums of ordered random variables (RVs). With the proposed approach, we can systematically derive the joint statistics of any partial sums of ordered statistics, in terms of the moment generating function (MGF) and the probability density function (PDF). Our MGF-based approach applies not only when all the K ordered RVs are involved but also when only the Ks (Ks < K) best RVs are considered. In addition, we present the closed-form expressions for the exponential RV special case. These results apply to the performance analysis of various wireless communication systems over fading channels.