Physics-compliant channel models of RIS-parametrized radio environments require the inversion of an "interaction matrix" to capture the mutual coupling between wireless entities (transmitters, receivers, RIS, environmental scattering objects) due to proximity and reverberation. The computational cost of this matrix inversion is typically dictated by the environmental scattering objects in non-trivial radio environments, and scales unfavorably with the latter's complexity. In addition, many problems of interest in wireless communications (RIS optimization, fast fading, object or user-equipment localization, etc.) require the computation of multiple channel realizations. To overcome the potentially prohibitive computational cost of using physics-compliant channel models, we i) introduce an isospectral reduction of the interaction matrix from the canonical basis to an equivalent reduced basis of primary wireless entities (antennas and RIS), and ii) leverage the fact that interaction matrices for different channel realizations only differ regarding RIS configurations and/or some wireless entities' locations.

翻译：针对RIS参数化无线电环境的物理合规信道模型，需对"相互作用矩阵"求逆以捕获因邻近性和混响效应导致的无线实体（发射器、接收器、RIS、环境散射体）间的互耦。该矩阵求逆的计算开销通常由非平凡无线电环境中的环境散射体决定，并随其复杂度呈不利扩展。此外，无线通信中的诸多问题（RIS优化、快衰落、目标或用户设备定位等）需要计算多个信道实现。为克服物理合规信道模型可能产生的过高计算开销，本文：i) 引入从规范基到主要无线实体（天线与RIS）等价约化基的相互作用矩阵等谱约化；ii) 利用不同信道实现的相互作用矩阵仅因RIS配置和/或部分无线实体位置差异而变化的特性。