The $\alpha $ -$\eta $ -$\kappa $ -$\mu $ Fading Model

Abstract

A fading model—the $\alpha $ - $\eta $ - $\kappa $ - $\mu $ model—is proposed that accounts for virtually all relevant short-term propagation phenomena described in the literature. These phenomena include nonlinearity of the medium, power of the scattered waves, power of the dominant components, and number of multipath clusters. They are mapped onto physical parameters, and apart from the first one, which is assumed to influence only the resulting signal envelope, the others affect independently its in-phase and quadrature components. Imbalance parameters are then introduced so as to better assess the impact of these phenomena on the entire process. The signal is described by means of its envelope and phase probability density functions (pdfs). To this end, complex-based and envelope-based models are proposed and explored. An exact joint envelope-phase pdf is found in the closed form. The marginal statistics in these cases remain in the integral forms. Interestingly, the envelope density function obtained through the envelope-based model is found to compute more efficiently than that obtained through the complex model. In addition, capitalizing on the results in the literature, exact series-expansion formulations are found for the envelope pdf as well as for the envelope cumulative distribution function. To the best of the author’s knowledge, this is probably the most general and unifying, physically based, complex fading model proposed in the literature. Because of its comprehensiveness, a number of issues remain open and constitute a fertile field for investigation.