NDLI: Infinite series representations of the trivariate and quadrivariate Rayleigh distribution and their applications

Content Provider	IEEE Xplore Digital Library
Author	Yunxia Chen Tellambura, C.
Copyright Year	1972
Abstract	Few theoretical results are known about the joint distribution of three or more arbitrarily correlated Rayleigh random variables (RVs). Consequently, theoretical performance results are unknown for three- and four-branch equal gain combining (EGC), selection combining (SC), and generalized SC (GSC) in correlated Rayleigh fading. This paper redresses this gap by deriving new infinite series representations for the joint probability density function (pdf) and the joint cumulative distribution function (cdf) of three and four correlated Rayleigh RVs. Bounds on the error resulting from truncating the infinite series are derived. A classical approach, due to Miller, is used to derive our results. Unfortunately, Miller's approach cannot be extended to more than four variates and, in fact, the quadrivariate case considered in this paper appears to be the most general result possible. For brevity, we treat only a limited number of applications in this paper. The new pdf and cdf expressions are used to derive the outage probability of three-branch SC, the moments of the EGC output signal-to-noise ratio (SNR), and the moment generating function of the GSC(2,3) output SNR in arbitrarily correlated Rayleigh fading. A novel application of Bonferroni's inequalities allows new outage bounds for multibranch SC in arbitrarily correlated Rayleigh channels.
Starting Page	2092
Ending Page	2101
Page Count	10
File Size	430280
File Format	PDF
ISSN	00906778
Volume Number	53
Issue Number	12
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-12-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Rayleigh channels Diversity reception Random variables Probability density function Distribution functions Fading Performance gain Signal to noise ratio Signal generators Cultural differences trivariate Rayleigh distribution Characteristic function (chf) diversity moment generating function (mgf) quadrivariate Rayleigh distribution
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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