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

arXiv: https://arxiv.org/abs/2302.04993 · HTML: https://mlsanity.com/paper/2302.04993/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2023.

## Built on by (most cited first, 6 of 6)

- [Backpropagation-free Training of Deep Physical Neural Networks](https://mlsanity.com/paper/2304.11042/) (2023)
- [Over-The-Air Extreme Learning Machines with XL Reception via Nonlinear Cascaded Metasurfaces](https://mlsanity.com/paper/2601.17749/) (2026)
- [On the Detection of Non-Cooperative RISs: Scan B-Testing via Deep Support Vector Data Description](https://mlsanity.com/paper/2411.03237/) (2024)
- [Programmable metasurfaces for future photonic artificial intelligence](https://mlsanity.com/paper/2505.11659/) (2025)
- [RIS-Enabled Smart Wireless Environments: Fundamentals and Distributed Optimization](https://mlsanity.com/paper/2512.18788/) (2025)
- [Over-The-Air Extreme Learning Machines with Nonlinear Stacked Intelligent Metasurfaces](https://mlsanity.com/paper/2608.27137/) (2026)

## Abstract (arXiv)

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 Kth 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.