On the utility of Laguerre series for the envelope pdf in multipath fading channels

Document Type

Article

Publication Date

12-1-2009

Abstract

It is well known that multipath fading significantly affects the performance of communication systems. In order to incorporate the impact of this random phenomenon on system analysis and design, in many cases, we need to calculate the probability density function (pdf) of the received signal envelope in multipath fading channels. In this paper, we consider a general multipath fading channel with arbitrary number of paths, where the amplitudes of multipath components are arbitrary correlated positive random variables, independent of phases, whereas the phases are independent and identically distributed random variables with uniform distributions. Since the integral form of the envelope pdf for such a general channel model is too complicated to be used for analytic calculations, we propose two infinite expansions for the pdf: a Laguerre series and a power series. Based on the tight uniform upper bounds on the truncation error of these two infinite series, we show that the Laguerre series is superior to the power series due to the fact that for a fixed number of terms, it yields a smaller truncation error. This Laguerre series with a finite number of terms, which expresses the envelope pdf just in terms of simple polynomial-exponential kernels, is particularly useful for mathematical performance prediction of communication systems in those indoor and outdoor multipath propagation environments, where the number of strong multipath components is small. © 2009 IEEE.

Identifier

77955644577 (Scopus)

Publication Title

IEEE Transactions on Information Theory

External Full Text Location

https://doi.org/10.1109/TIT.2009.2032824

ISSN

00189448

First Page

5652

Last Page

5662

Issue

12

Volume

55

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