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On a Ratio of Functions of Exponential Random Variables and Some Applications

Annavajjala, Ramesh and Chockalingam, A and Mohammed, Saif K (2010) On a Ratio of Functions of Exponential Random Variables and Some Applications. In: IEEE Transactions on Communications, 58 (11). pp. 3091-3097.

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Abstract

Consider L independent and identically distributed exponential random variables (r.vs) X-1, X-2 ,..., X-L and positive scalars b(1), b(2) ,..., b(L). In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (Sigma(L)(j=1) X-j)(2) / (Sigma(L)(j=1) b(j)X(j)). We show that the r.v Z appears in various communication systems such as i) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ii)M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and iii) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.

Item Type: Journal Article
Additional Information: Copyright 2010 IEEE. Personal use of this material is permitted.However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: Exponential random variables; distribution of ratio of two random variables; bivariate Laplace transform; mismatched statistics; partial-band interference
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 13 Dec 2010 09:49
Last Modified: 13 Dec 2010 09:49
URI: http://eprints.iisc.ernet.in/id/eprint/34460

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