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In this study, the product of two independent and non-identically distributed(i.n.i.d.) random variables (RVs) for \k{appa}-{\mu} fading distribution and{\alpha}-{\mu} fading distribution is considered. The method of the productmodel of RVs has been widely applied in numerous of communications fields, suchas cascaded fading channels, multiple input multiple output (MIMO) systems,radar communications and cognitive radio networks (CRs). The exact seriesexpressions of the product of two i.n.i.d. RVs X for \k{appa}-{\mu} variatesand Y for {\alpha}-{\mu} variates are derived instead of Fox H-function tosolve the problem that Fox H-function in the RVs product could not beimplemented in popular mathematical software packages as Mathematica and Maple.Novel Exact close-form expressions of probability density function (PDF) andcumulative distribution function (CDF) of proposed models are deduced topresent the series expressions of product and generalized composite multipathshadowing models. Furthermore, novel exact expressions of the ergodic channelcapacity (ECC) are obtained under optimal rate adaptation with constanttransmit power (ORA). At last, these analytical results are confirmed withmonte-carlo simulations to evaluate spectrum efficiency over generalizedcomposite shadowing fading scenarios in CRs.

Ergodic Capacity of Composite Fading Channels in Cognitive Radios with the Product of $\kappa$-$\mu$ and $\alpha$-$\mu$ Variates