Probability Distributions of Products of Rayleigh and Nakagami-m Variables Using Mellin Transform

Abstract

In this contribution, we employ the Mellin transform to derive the expressions for probability density function (PDF) of the product of Nakagami-m and Gamma distributed random variables. As the special cases of the Nakagami-m and Gamma family, the PDF of the product of Rayleigh distributed random variables and that of the product of exponentially distributed Random variables are also derived. We exploit the fact that the Mellin transform of a product of independent and identically distributed random variables is the product of the Mellin transforms of the individual random variables. Using this approach, the PDF of the product of random variables is expressed in the form of an easily computable infinite series. Furthermore, application of the PDFs in digital communications using M-ary orthogonal modulation is illustrated.