Higher Order Statistics for the $\alpha - \eta - \kappa - \mu$ Fading Model

Abstract

The aim of this paper is twofold: 1) to show that the newly proposed ${\alpha } - {\eta } - {\kappa } - {\mu }$ complex fading model provides the best fit for the envelope of a signal propagated in a millimeter wave in a given scenario and 2) to further improve the knowledge of this fading model through the derivation of some of its higher order statistics. The fitting process is carried out based on some field measurements campaigns conducted by independent research groups at the 28 GHz band as well as at the 60 GHz band available elsewhere in the literature. The higher order statistics concern the time derivative of the whole ${\alpha } - {\eta } - {\kappa } - {\mu }$ process with a view at obtaining important metrics, such as level crossing rate, average fade duration, and phase crossing rate. An extensive number of exact formulations for the corresponding statistics are derived. Through a small sample of plots, the flexibility provided by the physically based model becomes evident, showing its potential to be used in a variety of propagation scenarios.