Load Impedances vs Polarizabilities: On the Compactness of Physics-Compliant Models of RIS-Parametrized Wireless Channels

Physics-compliant models of RIS-parametrized wireless channels currently describe the reconfigurability of the RIS elements either in terms of tunable load impedances or tunable polarizabilities. No efforts to compare or harmonize these two approaches exist to date, and similar results are independently derived with both approaches. Here, we compare the two approaches, notably in terms of their mathematical complexity. We argue that the polarizability approach is more “transparent” because polarizability is a local concept and the RIS configuration determines the radio environment's local scattering properties at the location of the RIS elements. In contrast, impedance is a non-local concept, and the impedance matrix only serves as a transit quantity in deriving the end-to-end channel matrix. We conclude that the polarizability formulation facilitates physical intuition and may offer lower computational complexity. The latter matters for physics-compliant channel estimation, as well as the latency and convergence of physics-compliant RIS optimization algorithms.