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Electromagnetic Bounds on Realizing Targeted MIMO Transfer Functions in Real-World Systems with Wave-Domain Programmability

Philipp del Hougne

TL;DR

This work derives electromagnetically consistent bounds on how accurately a real-world wave-domain programmable system can realize a target linear operator, using a multiport-network model with 1-bit tunable elements. By formulating operator-synthesis as a quadratically constrained fractional-quadratic problem and applying semidefinite relaxation, the authors obtain rigorous upper bounds on both the Frobenius-norm gain and the fidelity between the realized and desired MIMO transfer functions. They validate these bounds on three experimental setups (two RIS-based and one DMA-based), revealing how inter-element coupling strength and the number of tunable elements influence bound tightness and achievable performance. The results demonstrate that strong coupling enhances wave-domain flexibility and that SDR bounds can closely track optimal discrete configurations, offering a principled way to screen architectures and guide design of programmable metasurface systems with practical hardware constraints.

Abstract

A key question for most applications involving reconfigurable linear wave systems is how accurately a desired linear operator can be realized by configuring the system's tunable elements. The relevance of this question spans from hybrid-MIMO analog combiners via computational meta-imagers to programmable wave-domain signal processing. Yet, no electromagnetically consistent bounds have been derived for the fidelity with which a desired operator can be realized in a real-world reconfigurable wave system. Here, we derive such bounds based on an electromagnetically consistent multiport-network model (capturing mutual coupling between tunable elements) and accounting for real-world hardware constraints (lossy, 1-bit-programmable elements). Specifically, we formulate the operator-synthesis task as a quadratically constrained fractional-quadratic problem and compute rigorous fidelity upper bounds based on semidefinite relaxation. We apply our technique to three distinct experimental setups. The first two setups are, respectively, a free-space and a rich-scattering $4\times 4$ MIMO channel at 2.45 GHz parameterized by a reconfigurable intelligent surface (RIS) comprising 100 1-bit-programmable elements. The third setup is a $4\times 4$ MIMO channel at 19 GHz from four feeds of a dynamic metasurface antenna (DMA) to four users. We systematically study how the achievable fidelity scales with the number of tunable elements, and we probe the tightness of our bounds by trying to find optimized configurations approaching the bounds with standard discrete-optimization techniques. We observe a strong influence of the coupling strength between tunable elements on our fidelity bound. For the two RIS-based setups, our bound attests to insufficient wave-domain flexibility for the considered operator synthesis.

Electromagnetic Bounds on Realizing Targeted MIMO Transfer Functions in Real-World Systems with Wave-Domain Programmability

TL;DR

This work derives electromagnetically consistent bounds on how accurately a real-world wave-domain programmable system can realize a target linear operator, using a multiport-network model with 1-bit tunable elements. By formulating operator-synthesis as a quadratically constrained fractional-quadratic problem and applying semidefinite relaxation, the authors obtain rigorous upper bounds on both the Frobenius-norm gain and the fidelity between the realized and desired MIMO transfer functions. They validate these bounds on three experimental setups (two RIS-based and one DMA-based), revealing how inter-element coupling strength and the number of tunable elements influence bound tightness and achievable performance. The results demonstrate that strong coupling enhances wave-domain flexibility and that SDR bounds can closely track optimal discrete configurations, offering a principled way to screen architectures and guide design of programmable metasurface systems with practical hardware constraints.

Abstract

A key question for most applications involving reconfigurable linear wave systems is how accurately a desired linear operator can be realized by configuring the system's tunable elements. The relevance of this question spans from hybrid-MIMO analog combiners via computational meta-imagers to programmable wave-domain signal processing. Yet, no electromagnetically consistent bounds have been derived for the fidelity with which a desired operator can be realized in a real-world reconfigurable wave system. Here, we derive such bounds based on an electromagnetically consistent multiport-network model (capturing mutual coupling between tunable elements) and accounting for real-world hardware constraints (lossy, 1-bit-programmable elements). Specifically, we formulate the operator-synthesis task as a quadratically constrained fractional-quadratic problem and compute rigorous fidelity upper bounds based on semidefinite relaxation. We apply our technique to three distinct experimental setups. The first two setups are, respectively, a free-space and a rich-scattering MIMO channel at 2.45 GHz parameterized by a reconfigurable intelligent surface (RIS) comprising 100 1-bit-programmable elements. The third setup is a MIMO channel at 19 GHz from four feeds of a dynamic metasurface antenna (DMA) to four users. We systematically study how the achievable fidelity scales with the number of tunable elements, and we probe the tightness of our bounds by trying to find optimized configurations approaching the bounds with standard discrete-optimization techniques. We observe a strong influence of the coupling strength between tunable elements on our fidelity bound. For the two RIS-based setups, our bound attests to insufficient wave-domain flexibility for the considered operator synthesis.
Paper Structure (11 sections, 41 equations, 3 figures, 1 table)

This paper contains 11 sections, 41 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. SDR-Based Bound on the Achievable Frobenius Norm of the MIMO Transfer Function
  4. SDR-Bounds on the Realizable MIMO Transfer Function Fidelity
  5. Discrete RIS Optimization Algorithms to Probe the Bound Tightness
  6. Experimental Results
  7. Experimental Setups
  8. Experimental Results: Frobenius-Norm Maximization
  9. Experimental Results: Fidelity Maximization
  10. Discussion
  11. Conclusion

Figures (3)

  • Figure 1: Experimental setups. (a) RIS-parametrized free-space MIMO channel. (b) RIS-parametrized rich-scattering MIMO channel. (c) Multi-feed-DMA multi-user MIMO channel. The four selected feeds are marked with blue dots, and the four selected user positions are highlighted with blue circles in the left inset.
  • Figure 2: NIO (blue) and SDR (green) bounds on the achievable Frobenius norm of the end-to-end channel matrix as a function of $N_\mathrm{S}$, for the three experimental setups in Fig. \ref{['Fig1']}. The bounds are contrasted with the outcomes of four discrete optimizations (thin lines - see Sec. \ref{['sec_Opti']}). The insets show a zoom on small values of $N_\mathrm{S}$.
  • Figure 3: SDR bounds on the achievable operator-synthesis fidelity (see (\ref{['eq:fidelity_def']}) for definition) for four different $\mathbf{H}_\mathrm{des}$ (indicated on the left) for the three considered experimental setups shown in Fig. \ref{['Fig1']}, and optimization outcomes trying to approach the bound. The four targeted $\mathbf{H}_\mathrm{des}$ operators are a scaled identity, a cyclic permutation, a scaled 4-point discrete-Fourier-transform matrix, and a random matrix.