Product of κ-μ and α-μ Distributions and Their Composite Fading Distributions

Abstract

In this study, product of two independent and non-identically distributed (i.n.i.d.) random variables (RVs) for κ-μ fading distribution and α-μ fading distribution is considered. The novel exact series formulas for the product of two i.n.i.d. fading distributions κ-μ and α-μ are derived instead of Fox H-function to solve the problem that Fox H-function with multiple RVs cannot be implemented in professional mathematical software packages as MATHEMATICA and MAPLE. Exact close-form expressions of probability density function (PDF) and cumulative distribution function (CDF) are deduced to represent provided product expressions and generalized composite multipath shadowing models. At last, these analytical results are validated with Monte Carlo simulations, it shows that for provided κ-μ/α-μ model nonlinear parameter has more important influence than multipath component in PDF and CDF when the ratio between the total power of the dominant components and the total power of the scattered waves is same.