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

Sungsik Nam; Hongchuan Yang; Mohamed-Slim Alouini; Dongin Kim

doi:10.1109/TSP.2014.2326624

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

Sungsik Nam, Hongchuan Yang, Mohamed-Slim Alouini, Dongin Kim

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

The joint statistics of partial sums of ordered random variables (RVs) are often needed for the accurate performance characterization of a wide variety of wireless communication systems. A unified analytical framework to determine the joint statistics of partial sums of ordered independent and identically distributed (i.i.d.) random variables was recently presented. However, the identical distribution assumption may not be valid in several real-world applications. With this motivation in mind, we consider in this paper the more general case in which the random variables are independent but not necessarily identically distributed (i.n.d.). More specifically, we extend the previous analysis and introduce a new more general unified analytical framework to determine the joint statistics of partial sums of ordered i.n.d. RVs. Our mathematical formalism is illustrated with an application on the exact performance analysis of the capture probability of generalized selection combining (GSC)-based RAKE receivers operating over frequency-selective fading channels with a non-uniform power delay profile. © 1991-2012 IEEE.

Original language	English (US)
Pages (from-to)	4270-4283
Number of pages	14
Journal	IEEE Transactions on Signal Processing
Volume	62
Issue number	16
DOIs	https://doi.org/10.1109/TSP.2014.2326624
State	Published - Aug 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (NRF-2014R1A5A1011478). This is an extended version of a paper which was presented at the IEEE International Symposium on Information Theory (ISIT 2013), Istanbul, Turkey, July 2013.

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering

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10.1109/TSP.2014.2326624

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title = "An MGF-based unified framework to determine the joint statistics of partial sums of ordered i.n.d. random variables",

abstract = "The joint statistics of partial sums of ordered random variables (RVs) are often needed for the accurate performance characterization of a wide variety of wireless communication systems. A unified analytical framework to determine the joint statistics of partial sums of ordered independent and identically distributed (i.i.d.) random variables was recently presented. However, the identical distribution assumption may not be valid in several real-world applications. With this motivation in mind, we consider in this paper the more general case in which the random variables are independent but not necessarily identically distributed (i.n.d.). More specifically, we extend the previous analysis and introduce a new more general unified analytical framework to determine the joint statistics of partial sums of ordered i.n.d. RVs. Our mathematical formalism is illustrated with an application on the exact performance analysis of the capture probability of generalized selection combining (GSC)-based RAKE receivers operating over frequency-selective fading channels with a non-uniform power delay profile. {\textcopyright} 1991-2012 IEEE.",

author = "Sungsik Nam and Hongchuan Yang and Mohamed-Slim Alouini and Dongin Kim",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This work was supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (NRF-2014R1A5A1011478). This is an extended version of a paper which was presented at the IEEE International Symposium on Information Theory (ISIT 2013), Istanbul, Turkey, July 2013.",

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N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This work was supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (NRF-2014R1A5A1011478). This is an extended version of a paper which was presented at the IEEE International Symposium on Information Theory (ISIT 2013), Istanbul, Turkey, July 2013.

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N2 - The joint statistics of partial sums of ordered random variables (RVs) are often needed for the accurate performance characterization of a wide variety of wireless communication systems. A unified analytical framework to determine the joint statistics of partial sums of ordered independent and identically distributed (i.i.d.) random variables was recently presented. However, the identical distribution assumption may not be valid in several real-world applications. With this motivation in mind, we consider in this paper the more general case in which the random variables are independent but not necessarily identically distributed (i.n.d.). More specifically, we extend the previous analysis and introduce a new more general unified analytical framework to determine the joint statistics of partial sums of ordered i.n.d. RVs. Our mathematical formalism is illustrated with an application on the exact performance analysis of the capture probability of generalized selection combining (GSC)-based RAKE receivers operating over frequency-selective fading channels with a non-uniform power delay profile. © 1991-2012 IEEE.

AB - The joint statistics of partial sums of ordered random variables (RVs) are often needed for the accurate performance characterization of a wide variety of wireless communication systems. A unified analytical framework to determine the joint statistics of partial sums of ordered independent and identically distributed (i.i.d.) random variables was recently presented. However, the identical distribution assumption may not be valid in several real-world applications. With this motivation in mind, we consider in this paper the more general case in which the random variables are independent but not necessarily identically distributed (i.n.d.). More specifically, we extend the previous analysis and introduce a new more general unified analytical framework to determine the joint statistics of partial sums of ordered i.n.d. RVs. Our mathematical formalism is illustrated with an application on the exact performance analysis of the capture probability of generalized selection combining (GSC)-based RAKE receivers operating over frequency-selective fading channels with a non-uniform power delay profile. © 1991-2012 IEEE.

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

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