Gamma variate ratio distribution with application to CDMA performance analysis

TitleGamma variate ratio distribution with application to CDMA performance analysis
Publication TypeConference Paper
Year of Publication2005
AuthorsKwan, R., and C. Leung
Conference NameAdvances in Wired and Wireless Communication, 2005 IEEE/Sarnoff Symposium on
Pagination188 -191
Date Publishedapr.
Keywordsadaptive codes, adaptive modulation, adaptive modulation and coding, AMC, beta prime distribution, CDMA performance analysis, channel coding, code division multiple access, cumulative distribution function, fading channels, gamma distribution, gamma variate ratio distribution, hypergeometric function, modulation coding, moment generating function, Nakagami fading, outage probabilities, PDF, probability density function, throughput bounds, wireless communication systems

An expression for the probability density function (pdf), fR (r), is derived for the ratio, R, of gamma variates of the form R = X1/(a1X1 + a2X2), where a1 and a2 are constants and X1 and X2 are independent gamma distributed random variables. This distribution arises naturally in the performance analyses of wireless communication systems experiencing Nakagami fading. It is shown that fR(r) reduces to the standard beta distribution and the beta prime distribution in special cases. Expressions for the moments, the moment generating function (MGF) and the cumulative distribution function (cdf) of R are obtained in terms of the hypergeometric function. Finally, the use of fR(r) is illustrated by considering the problem of deriving outage probabilities and throughput bounds for a CDMA system employing adaptive modulation and coding (AMC)


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