Gamma variate ratio distribution with application to CDMA performance analysis
R. Kwan, Cyril Leung · 2006
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 a1and a2are constants and X1and X2are 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)