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

TL;DR

This paper derives a closed-form expression for the Doppler spectrum in channels with von Mises-Fisher distributed scatterers, revealing how scatterer concentration and direction affect the spectrum's shape, validated by simulations.

Contribution

It provides the first analytical Doppler spectrum expression for vMF scattering channels, linking scattering parameters to spectral behavior.

Findings

Spectrum is exponential for motion parallel to scatterer mean direction.

Spectrum is Gaussian-like for perpendicular motion.

Analytical results match Monte Carlo simulations exactly.

Abstract

This paper presents an analytical analysis of the Doppler spectrum in von Mises-Fisher (vMF) scattering channels. A simple closed-form expression for the Doppler spectrum is derived and used to investigate the impact of the vMF scattering parameters, i.e., the mean direction and the degree of concentration of scatterers. The spectrum is observed to exhibit exponential behavior for 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.