  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.
