Bounds on the Distribution of a Sum of Correlated Lognormal Random Variables and Their Application

The cumulative distribution function (cdf) of a sum of correlated or even independent lognormal random variables (RVs), which is of wide interest in wireless communications, remains unsolved despite long standing efforts. Several cdf approximations are thus widely used. This letter derives bounds fo...

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Bibliographic Details
Published in:IEEE transactions on communications 2008-08, Vol.56 (8), p.1241-1248
Main Author: Tellambura, C.
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Cellular networks
Channels
Correlation
Distribution functions
Diversity reception
Exact sciences and technology
Fading
Gain
Independent component analysis
Integral equations
Integrals
Interchannel interference
Mathematical analysis
Random variables
Shadow mapping
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Transmission and modulation (techniques and equipments)
Wireless communication
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Summary:The cumulative distribution function (cdf) of a sum of correlated or even independent lognormal random variables (RVs), which is of wide interest in wireless communications, remains unsolved despite long standing efforts. Several cdf approximations are thus widely used. This letter derives bounds for the cdf of a sum of 2 or 3 arbitrarily correlated lognormal RVs and of a sum of any number of equally-correlated lognormal RVs. The bounds are single-fold integrals of readily computable functions and extend previously known bounds for independent lognormal summands. An improved set of bounds are also derived which are expressed as 2-fold integrals. For correlated lognormal fading channels, new expressions are derived for the moments of the output SNR and amount of fading for maximal ratio combining (MRC), selection combining (SC) and equal gain combining (EGC) and outage probability expressions for SC.
ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2008.030947