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

Nam, Sungsik; Alouini, Mohamed-Slim; Yang, Hongchuan

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

Type

Article

Authors

Nam, Sungsik
Alouini, Mohamed-Slim

Yang, Hongchuan

KAUST Department

Communication Theory Lab
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Physical Science and Engineering (PSE) Division

Date

2010-11

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. © 2006 IEEE.

Citation

Nam, S. S., Alouini, M.-S., & Yang, H.-C. (2010). An MGF-Based Unified Framework to Determine the Joint Statistics of Partial Sums of Ordered Random Variables. IEEE Transactions on Information Theory, 56(11), 5655–5672. doi:10.1109/tit.2010.2070271