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

Albert Salmi, Ville Viikari, Philipp del Hougne

TL;DR

This work develops electromagnetically consistent bounds on information transfer for RIS-parametrized wireless channels by modeling the end-to-end channel with a multiport network and solving a semidefinite-relaxation (SDR) of a quadratically constrained problem. It introduces three bounds—norm-inequality (NI), idealized BD-RIS (IBD), and SDR-based (SDR)—and shows SDR is consistently the tightest, with discrete RIS optimizations achieving 64-100% of the bound in both numerical and experimental tests. The analysis accounts for real hardware constraints such as 1-bit programmability and mutual coupling, providing a practical tool to evaluate RIS hardware and configuration strategies. This work marks a step toward an electromagnetic information theory for programmable wave systems and extends to beyond-diagonal RISs and related dynamic metasurface concepts.

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.

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

TL;DR

This work develops electromagnetically consistent bounds on information transfer for RIS-parametrized wireless channels by modeling the end-to-end channel with a multiport network and solving a semidefinite-relaxation (SDR) of a quadratically constrained problem. It introduces three bounds—norm-inequality (NI), idealized BD-RIS (IBD), and SDR-based (SDR)—and shows SDR is consistently the tightest, with discrete RIS optimizations achieving 64-100% of the bound in both numerical and experimental tests. The analysis accounts for real hardware constraints such as 1-bit programmability and mutual coupling, providing a practical tool to evaluate RIS hardware and configuration strategies. This work marks a step toward an electromagnetic information theory for programmable wave systems and extends to beyond-diagonal RISs and related dynamic metasurface concepts.

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.
Paper Structure (12 sections, 44 equations, 3 figures, 2 tables)

This paper contains 12 sections, 44 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. Parameter Ambiguities and Gauge Freedoms
  4. Bounds on Achievable SISO Channel Gain
  5. Norm-Inequality (NI) Bound
  6. Idealized-BD-RIS (IBD) Bound
  7. SDR-Based (SDR) Bound
  8. Discrete RIS Optimization Algorithms for SISO Channel Gain Maximization
  9. Full-Wave Numerical Results
  10. Experimental Results
  11. Discussion
  12. Conclusion

Figures (3)

  • Figure 1: Numerical setup from tapie2023systematic used in Sec. \ref{['sec_Numerical']}. The setup comprises 7 antennas (of which those indexed 1 and 3 are used to define the considered SISO channel while the remaining 5 are terminated in matched loads) and 64 RIS elements.
  • Figure 2: Bounds (NIO, IBD, SDR -- see Sec. \ref{['sec_Bounds']}) on the achievable channel gain (top row) and the Shannon capacity (with $P_\mathrm{T}=10\ \mathrm{mW}$ and $\sigma^2 = 10^{-5}\ \mathrm{mW}$; bottom row) in the RIS-parametrized SISO setup in Fig. \ref{['Fig1']} (all but two antennas are terminated in matched loads) as a function of $N_\mathrm{S}$ (horizontal axis) and for three different choices of $\{\alpha,\beta\}$ (different panels: PM, PIN, 01). The displayed bounds are the ones derived in Sec. \ref{['sec_Bounds']}; the IBD bound is only shown for the PM case because it requires the two available loads to have unit magnitude. In addition to the bounds, the outcomes of the four considered optimization strategies (GA, CD, ES, P-SDR -- see Sec. \ref{['sec_Opti']}) are displayed; ES is only shown for $N_\mathrm{S}\leq 20$.
  • Figure 3: Bounds (NIO, SDR -- see Sec. \ref{['sec_Bounds']}) on the achievable channel gain (middle row) and the Shannon capacity (with $P_\mathrm{T}=10\ \mathrm{mW}$ and $\sigma^2 = 10^{-5}\ \mathrm{mW}$; bottom row) in the RIS-parametrized SISO setups displayed in the top row (all but two antennas are terminated in matched loads), as a function of $N_\mathrm{S}$ (horizontal axis). In addition to the bounds, the outcomes of the four considered optimization strategies (GA, CD, ES, P-SDR -- see Sec. \ref{['sec_Opti']}) are displayed; ES is only shown for $N_\mathrm{S}\leq 20$.