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

In a wireless system involving a reconfigurable intelligent surface (RIS), the wireless channel is a linear input-output relation that depends non-linearly on the RIS configuration: in particular, physics-compliant models involve the inversion of an 'interaction' matrix. In this paper, we identify two independent origins of this structural non-linearity: 1) proximity-induced mutual coupling between close-by RIS elements; and 2) reverberation-induced long-range coupling between all RIS elements arising from multi-path propagation in complex radio environments. Mathematically, we cast the 'interaction' matrix inversion as the sum of an infinite Born series [for 1)] or Born-like series [for 2)] whose Kth term physically represents paths involving K bounces between the RIS elements [for 1)] or wireless entities [for 2)]. 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. We also quantify the non-linearity of a channel's RIS parametrization in diverse numerical and experimental radio environments ranging from an anechoic (echo-free) chamber to rich-scattering reverberation chambers to corroborate our analysis. Our findings raise doubts about the reliability of existing performance analyses and channel-estimation protocols for cases in which cascaded models poorly describe the physical reality.