Electromagnetically Consistent Bounds on Information Transfer in Real-World RIS-Parametrized Wireless Channels

TL;DR

This paper establishes electromagnetically consistent fundamental bounds on the maximum achievable information transfer in RIS-parametrized wireless channels, considering realistic hardware constraints and mutual coupling effects.

Contribution

It introduces a semidefinite relaxation approach to derive tight bounds on channel gain and information rate for RIS systems with realistic electromagnetic modeling.

Findings

SDR-based bounds are tighter than benchmark bounds.

Achieves at least 64% of the theoretical bound with standard optimization.

Applicable to experimental RIS systems, informing hardware and algorithm design.

Abstract

A reconfigurable intelligent surface (RIS) endows a wireless channel with programmability that can be leveraged to optimize wireless information transfer. While many works study algorithms for optimizing such a programmable channel, relatively little is known about fundamental bounds on the achievable information transfer. In particular, non-trivial bounds that are both electromagnetically consistent (e.g., aware of mutual coupling) and in line with realistic hardware constraints (e.g., few-bit-programmable, potentially lossy loads) are missing. Here, based on a rigorous multiport network model of a single-input single-output (SISO) channel parametrized by 1-bit-programmable RIS elements, we apply a semidefinite relaxation (SDR) to derive a fundamental bound on the achievable SISO channel gain enhancement. A bound on the maximum achievable rate of information transfer at a given noise level follows directly from Shannon's theorem. We apply our bound to several numerical and experimental examples of different RIS-parametrized radio environments. Compared to electromagnetically consistent benchmark bounding strategies (a norm-inequality bound and, where applicable, a relaxation to an idealized beyond-diagonal load network for which a global solution exists), we consistently observe that our SDR-based bound is notably tighter. We reach at least 64 % (but often 100 %) of our SDR-based bound with standard discrete optimization techniques. The applicability of our bound to concrete experimental systems makes it valuable to inform wireless practitioners, e.g., to evaluate RIS hardware design choices and algorithms to optimize the RIS configuration. Our work contributes to the development of an electromagnetic information theory for RIS-parametrized channels as well as other programmable wave systems such as dynamic metasurface antennas or real-life beyond-diagonal RISs.