An MGF-based unified framework to determine the joint statistics of partial sums of ordered random variables

Authors:
Sung Sik Nam;Mohamed-Slim Alouini;Hong-Chuan Yang
Affiliations:
Department of Electronic Engineering, Hanyang University, Seoul, Korea and Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX;Electrical Engineering Program, Division of Physical Sciences and Engineering, King Abdullah University of Science and Technology Thuwal, Mekkah Province, Saudi Arabia and Electrical and Computer ...;Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC, Canada
Venue:
IEEE Transactions on Information Theory
Year:
2010

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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.