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

TL;DR

This paper derives exact, elementary-function-based analytical expressions for spatial and temporal correlation functions in channels with von Mises-Fisher scattering, enhancing understanding of their impact on antenna array and radar signal analysis.

Contribution

It provides the first exact, simple analytical expressions for correlation functions in vMF scattering channels, improving upon previous approximate models.

Findings

Exact correlation expressions match numerical integration results.

Analytical results reveal parameter impacts on spatial correlation.

Application to radar signals demonstrates practical utility.

Abstract

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.