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

The wireless channel is a linear input-output relation that depends non-linearly on the RIS configuration: physics-compliant models involve the inversion of an “interaction” matrix. We identify two independent origins of this structural non-linearity: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> ) proximity-induced mutual coupling between close-by RIS elements; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> ) 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> )] or Born-like series [for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> )] whose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> th term physically represents paths involving <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> bounces between the RIS elements [for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> )] or wireless entities [for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> )]. 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.