On a ratio of functions of exponential random variables and some applications

Annavajjala, Ramesh ; Chockalingam, A. ; Mohammed, Saif. K. (2010) On a ratio of functions of exponential random variables and some applications IEEE Transactions on Communications, 58 (11). pp. 3091-3097. ISSN 0090-6778

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Official URL: http://ieeexplore.ieee.org/document/5590326/

Related URL: http://dx.doi.org/10.1109/TCOMM.2010.091710.100038


Consider L independent and identically distributed exponential random variables (r.vs) X1, X2,...,XL and positive scalars b1, b2,...,bL. 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 = (∑(j=1)L Xj)2/(∑(j=1)L bj Xj). 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:Article
Source:Copyright of this article belongs to Institute of Electrical and Electronics Engineers.
Keywords:Partial-Band Interference; Exponential Random Variables; Distribution of Ratio of Two Random Variables; Bivariate Laplace Transform; Mismatched Statistics
ID Code:100617
Deposited On:27 Mar 2017 06:48
Last Modified:27 Mar 2017 06:48

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