On the Tacit Linearity Assumption in Common Cascaded Models of RIS-Parametrized Wireless Channels

TL;DR

This paper derives the physical principles governing RIS-parametrized wireless channels, revealing inherent non-linearities and questioning the validity of common simplified models used in performance analysis and channel estimation.

Contribution

It provides a first-principles analytical framework for understanding the non-linear dependence of wireless channels on RIS configurations, highlighting when simplified models are valid.

Findings

Identifies physical parameters affecting series truncation in channel models.

Numerical and experimental validation of the derived models.

Raises concerns about the reliability of existing cascaded models.

Abstract

We analytically derive from first physical principles the functional dependence of wireless channels on the RIS configuration for generic (i.e., potentially complex-scattering) RIS-parametrized radio environments. The wireless channel is a linear input-output relation that depends non-linearly on the RIS configuration because of two independent mechanisms: i) proximity-induced mutual coupling between close-by RIS elements; ii) reverberation-induced long-range coupling between all RIS elements. Mathematically, this "structural" non-linearity originates from the inversion of an "interaction" matrix that can be cast as the sum of an infinite Born series [for i)] or Born-like series [for ii)] whose $K$th term physically represents paths involving $K$ bounces between the RIS elements [for i)] or wireless entities [for ii)]. We identify the key physical parameters that determine whether these series can be truncated after the first and second term, respectively, as tacitly done in common cascaded models of RIS-parametrized wireless channels. Numerical results obtained with the physics-compliant PhysFad model and experimental results obtained with a RIS prototype in an anechoic (echo-free) chamber and rich-scattering reverberation chambers corroborate our analysis. Our findings raise doubts about the reliability of existing performance analysis and channel-estimation protocols for cases in which cascaded models poorly describe the physical reality.