The distribution of ratio of random variable and product of two random variables and its application in performance analysis of multi-hop relaying communications over fading channels

In this paper, we present novel closed-form expressions for the probability density function (PDF) and cumulative distribution function (CDF) of ratio of random variable and product of two random variables for the cases where random variables are Rayleigh, Weibull, Nakagami-m and α-μ distributed. An application of obtained results in performance analysis of multi-hop wireless communication systems in different transmission environments is detailed described. The proposed theoretical analysis is also complemented by various graphically presented numerical results. Streszczenie. W artykule zaprezentowano wyrazenia na funkcje gestości prawdopodobienstwa PDF i kumulacyjną funkcje dystrybucji stosunku zmiennej przypadkowej i iloczynu dwoch zmiennych gdy zmienne przypadkowe są dystrybucją Rayleigh, Weibull, Nakagami-m i α-μ. Analiza ma zastosowanie do bezprzewodowych sieci komunikacyjnych w roznych warunkach transmisji. (Rozklad stosunku zmiennych przypadkowych i iloczynu tych zmiennych oraz wykorzystanie tych parametrow do analizy systemow komunikacji bezprzewodowej)

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