On Level Crossings and Fade Durations in von Mises-Fisher Scattering Channels

TL;DR

This paper derives closed-form expressions for second-order statistics of von Mises-Fisher scattering channels, analyzing how scattering parameters influence level crossings and fade durations in mobile fading environments.

Contribution

It provides new analytical formulas for Doppler-related spectral moments in vMF channels, linking scattering characteristics to fading dynamics.

Findings

Isotropic scattering leads to highest LCR and lowest AFD.

Fading reduces with decreasing angular spread of scatterers.

Motion parallel to mean scattering direction results in lower LCR.

Abstract

This paper investigates the second-order statistics of multipath fading channels with von Mises-Fisher (vMF) distributed scatters. Simple closed-form expressions for the mean Doppler shift and Doppler spread are derived as the key spectral moments that capture the impact of mobility and scattering characteristics on level crossings and fade durations. These expressions are then used to analyze the influence of vMF parameters on the Level-Crossing Rate (LCR) and Average Fade Duration (AFD). The results show that isotropic scattering yields the highest LCR and the lowest AFD, while fading dynamics reduce with the decreasing angular spread of scatterers. Moreover, mobile antenna motion parallel to the mean scattering direction results in a lower LCR than the perpendicular motion, with the difference between the two cases increasing with the higher concentration of scatterers.