Diversity Spectra of Spatial Multipath Fading Processes

TL;DR

This paper introduces the concept of diversity spectra derived from the eigenvalues of the spatial autocorrelation kernel to analyze spatial multipath fading, aiding antenna array design and coding strategies.

Contribution

It provides a method to compute the diversity spectrum for arbitrary geometries and fading statistics, with rigorous accuracy estimates and practical applications.

Findings

Diversity spectra can be calculated for any geometry and fading statistics.

Numerical eigenvalues offer insights for antenna array optimization.

Diversity spectra help determine interleaving depth for coding gain.

Abstract

We analyse the spatial diversity of a multipath fading process for a finite region or curve in the plane. By means of the Karhunen-Lo\`eve (KL) expansion, this diversity can be characterised by the eigenvalue spectrum of the spatial autocorrelation kernel. This justifies to use the term diversity spectrum for it. We show how the diversity spectrum can be calculated for any such geometrical object and any fading statistics represented by the power azimuth spectrum (PAS). We give rigorous estimates for the accuracy of the numerically calculated eigenvalues. The numerically calculated diversity spectra provide useful hints for the optimisation of the geometry of an antenna array. Furthermore, for a channel coded system, they allow to evaluate the time interleaving depth that is necessary to exploit the diversity gain of the code.