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

2025-06-06

AI Summary

This study investigates multipath fading channels in directional scattering environments modeled by the von Mises–Fisher (vMF) distribution. It systematically analyzes how second-order statistical properties affect the level crossing rate (LCR) and average fade duration (AFD). Using spectral moment analysis of stochastic processes and closed-form Doppler-domain derivations, the work establishes, for the first time, explicit analytical mappings between vMF scattering parameters—namely, concentration parameter and principal scattering direction—and LCR/AFD. Closed-form expressions are derived for the mean Doppler shift and Doppler spread, quantifying the coupled impact of terminal mobility directionality and scattering geometry on fading dynamics. Theoretical results reveal that isotropic scattering maximizes LCR, whereas directional scattering significantly suppresses fading variations. Moreover, when the terminal’s motion aligns parallel to the principal scattering direction, LCR is markedly lower than in the orthogonal case, with this disparity intensifying as scattering concentration increases.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Application Domains: Mobility, Driving & Flight
• Intelligent Robots: Motion and Path Planning

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

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) 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.

Problem

• Analyzes level crossings and fade durations in vMF scattering channels
• Derives Doppler shift and spread for mobility impact on fading
• Examines vMF parameters' effect on Level-Crossing Rate dynamics

Innovation

• Closed-form expressions for Doppler moments
• Analysis of vMF parameters on LCR
• Impact of antenna motion on LCR