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

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) The results show that isotropic scattering yields the highest LCR, while fading dynamics reduce with the decreasing angular spread of scatterers. Moreover, obile 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.

Doppler Power Spectrum in Channels with von Mises-Fisher Distribution of Scatterers

This paper presents an analytical analysis of the Doppler spectrum in von Mises-Fisher (vMF) scattering channels. A closed-form expression for the Doppler spectrum is derived and used to investigate the impact of vMF scattering parameters, i.e., the mean direction and the degree of concentration of scatterers. The spectrum is observed to exhibit exponential behavior for the mobile antenna motion parallel to the mean direction of scatterers, while conforming to a Gaussian-like shape for the perpendicular motion. The validity of the obtained results is verified by comparison against the results of Monte Carlo simulations, where an exact match is observed.

Correlation Properties in Channels with von Mises-Fisher Distribution of Scatterers

This letter presents simple analytical expressions for the spatial and temporal correlation functions in channels with von Mises-Fisher (vMF) scattering. In contrast to previous results, the expressions presented here are exact and based only on elementary functions, clearly revealing the impact of the underlying parameters. The derived results are validated by a comparison against numerical integration result, where an exact match is observed. To demonstrate their utility, the presented results are used to analyze spatial correlation across different antenna array geometries and to investigate temporal correlation of a fluctuating radar signal from a moving target.