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Experimental Reduced-Rank Mutual Coupling Representation and Estimation for Large RIS

Philipp del Hougne

TL;DR

This work tackles the practical challenge of estimating mutual coupling (MC) in large RIS arrays by introducing a flexible reduced-rank MC representation based on a Takagi decomposition of the MC matrix $S_{SS} = U Σ U^{T}$. By truncating to rank $k$, the method yields a model interpolation between full MC-aware dynamics and the MC-unaware CASC model, enabling a tunable balance between accuracy and complexity. The authors develop an experimental parameter estimation protocol to identify operational proxies for MC components and validate the approach on a 100-element RIS across three radio environments, showing environment-dependent benefits of MC awareness. End-to-end performance analyses reveal that higher ranks substantially improve sum-rate in MC-rich environments, while lower ranks suffice in weaker MC settings, making the rank knob practically valuable for RIS optimization in real deployments. Overall, the framework provides a practical pathway to MC-aware RIS design with quantified trade-offs, applicable to large-scale RIS deployments and varied propagation environments.

Abstract

Physics-consistent optimization of reconfigurable intelligent surfaces (RISs) is thwarted in practice by the difficulty of experimentally estimating the mutual coupling (MC) between RIS elements. For large RISs, experimental MC estimation is fundamentally challenging because of the quadratic scaling of the number of unknowns with the number of RIS elements. In this Letter, we present a generic and flexible reduced-rank MC representation that allows wireless practitioners to choose a trade-off between model complexity and accuracy. We experimentally validate the direct reduced-rank MC estimation for a 100-element RIS in three radio environments (rich scattering, attenuated scattering, free space). We observe a strong environmental dependence of the influence of rank reduction on accuracy. Model-based performance evaluations highlight that the importance of MC awareness in optimization depends strongly on the radio environment and the performance indicator.

Experimental Reduced-Rank Mutual Coupling Representation and Estimation for Large RIS

TL;DR

This work tackles the practical challenge of estimating mutual coupling (MC) in large RIS arrays by introducing a flexible reduced-rank MC representation based on a Takagi decomposition of the MC matrix . By truncating to rank , the method yields a model interpolation between full MC-aware dynamics and the MC-unaware CASC model, enabling a tunable balance between accuracy and complexity. The authors develop an experimental parameter estimation protocol to identify operational proxies for MC components and validate the approach on a 100-element RIS across three radio environments, showing environment-dependent benefits of MC awareness. End-to-end performance analyses reveal that higher ranks substantially improve sum-rate in MC-rich environments, while lower ranks suffice in weaker MC settings, making the rank knob practically valuable for RIS optimization in real deployments. Overall, the framework provides a practical pathway to MC-aware RIS design with quantified trade-offs, applicable to large-scale RIS deployments and varied propagation environments.

Abstract

Physics-consistent optimization of reconfigurable intelligent surfaces (RISs) is thwarted in practice by the difficulty of experimentally estimating the mutual coupling (MC) between RIS elements. For large RISs, experimental MC estimation is fundamentally challenging because of the quadratic scaling of the number of unknowns with the number of RIS elements. In this Letter, we present a generic and flexible reduced-rank MC representation that allows wireless practitioners to choose a trade-off between model complexity and accuracy. We experimentally validate the direct reduced-rank MC estimation for a 100-element RIS in three radio environments (rich scattering, attenuated scattering, free space). We observe a strong environmental dependence of the influence of rank reduction on accuracy. Model-based performance evaluations highlight that the importance of MC awareness in optimization depends strongly on the radio environment and the performance indicator.

Paper Structure

This paper contains 9 sections, 9 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Reduced-Rank MC Representation in MNT
  4. MNT Parameter Estimation Algorithm
  5. Experimental Validation and Performance Analysis
  6. Experimental Setups
  7. Experimental Reduced-Rank MNT Parameter Estimation
  8. Performance Evaluation
  9. Conclusion

Figures (1)

  • Figure 1: Achieved model accuracies $\zeta$ (evaluated with $M_\mathrm{test}=100$ unseen RIS configurations) as a function of the radio environments (distinct panels), $k$ (horizontal axis) and $M_\mathrm{train}$ (colors). The values of $R_\mathrm{eff}$ (indicated by a vertical dashed line) refer to the effective rank of $\tilde{\mathbf{S}}_\mathcal{SS}$ estimated with $k=N_\mathrm{S}=100$ and $M_\mathrm{train}=2300$. $k=0$ and $k=N_\mathrm{S}=100$ correspond, respectively, to CASC and the full MNT model.