A Generalized Non-Linear Composite Fading Model

This work is devoted to the formulation and derivation of the $\alpha{-}\kappa{-}\mu{/}$gamma distribution which corresponds to a physical fading model. The proposed distribution is composite and is constituted by the $\alpha{-}\kappa{-}\mu$ non-linear generalized multipath model and the gamma shadowing model. It also constitute the basis for deriving the $\alpha{-}\kappa{-}\mu$ \textit{Extreme}${/}$gamma model which accounts for non-linear severe multipath and shadowing effects and also includes the more widely known $\alpha{-}\mu$ and $\kappa{-}\mu$ models which includes as special cases the Rice, Weibull, Nakagami-$m$ and Rayleigh distributions. The derived models provide accurate characterisation of the simultaneous occurrence of multipath fading and shadowing effects. This is achieved thanks to the remarkable flexibility of their named parameters which have been shown to render them capable of providing good fittings to experimental data associated with realistic communication scenarios. This is also evident by the fact that they include as special cases the widely known composite fading models such as the recently reported $\kappa{-}\mu{/}$gamma model and the novel $\alpha{-}\mu{/}$gamma model. Novel analytic expressions are derived for the corresponding probability density function of these distributions which are expressed in a convenient algebraic form and can be efficiently utilized in the derivation of numerous vital measures in investigations related to the analytic performance evaluation of digital communications over composite multipath${/}$shadowing fading channels.