Implementing Non-Universal Features with a Random Matrix Theory Approach: Application to Space-to-Configuration Multiplexing

TL;DR

This paper develops a hybrid random matrix theory approach to model and analyze the efficiency of space-to-configuration multiplexing in microwave chaotic cavities, accounting for system-specific features.

Contribution

It introduces a two-step hybrid method combining experimental data and random matrix theory to accurately model non-universal features in complex wave systems.

Findings

The method accurately reproduces the distribution of the effective rank.

System-specific features significantly influence channel correlations.

The approach is applicable to other complex wave phenomena.

Abstract

We consider the efficiency of multiplexing spatially encoded information across random configurations of a metasurface-programmable chaotic cavity in the microwave domain. The distribution of the effective rank of the channel matrix is studied to quantify the channel diversity and to assess a specific system's performance. System-specific features such as unstirred field components give rise to nontrivial inter-channel correlations and need to be properly accounted for in modelling based on random matrix theory. To address this challenge, we propose a two-step hybrid approach. Based on an ensemble of experimentally measured scattering matrices for different random metasurface configurations, we first learn a system-specific pair of coupling matrix and unstirred contribution to the Hamiltonian, and then add an appropriately weighted stirred contribution. We verify that our method is capable of reproducing the experimentally found distribution of the effective rank with good accuracy. The approach can also be applied to other wave phenomena in complex media.