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Wideband Modeling and Beamforming for Beyond Diagonal Reconfigurable Intelligent Surfaces

Hongyu Li, Matteo Nerini, Shanpu Shen, Bruno Clerckx

TL;DR

This work introduces a frequency-aware BD-RIS framework by modeling the reconfigurable admittance network with a lumped-circuit, frequency-dependent admittance matrix. The authors propose a linearized wideband model for the tunable susceptances, enabling tractable optimization of BD-RIS settings across OFDM subcarriers. They derive a BD-RIS design procedure using an unconstrained reformulation solved by a quasi-Newton method, followed by a standard water-filling step for power allocation. Simulations on a $2.4$ GHz, $300$ MHz bandwidth SISO-OFDM system demonstrate that wideband modeling and group-connected BD-RIS architectures significantly improve average rates compared to narrowband assumptions, underscoring the practical importance of frequency-dependent BD-RIS design.

Abstract

This work studies the wideband modeling and beamforming design of beyond diagonal reconfigurable intelligent surface (BD-RIS), which generalizes and goes beyond conventional RIS with diagonal phase shift matrices to achieve enhanced channel gain. Specifically, we investigate the response of BD-RIS in wideband systems by going back to its hardware circuit realizations. We propose a novel wideband model which has simple expressions while capturing the response variations of BD-RIS for signals with different frequencies. With this wideband model, we propose a BD-RIS design algorithm for an orthogonal frequency division multiplexing system to maximize the average rate over all subcarriers. Finally, we provide simulation results to evaluate the performance of the proposed design and show the importance of wideband modeling for BD-RIS.

Wideband Modeling and Beamforming for Beyond Diagonal Reconfigurable Intelligent Surfaces

TL;DR

This work introduces a frequency-aware BD-RIS framework by modeling the reconfigurable admittance network with a lumped-circuit, frequency-dependent admittance matrix. The authors propose a linearized wideband model for the tunable susceptances, enabling tractable optimization of BD-RIS settings across OFDM subcarriers. They derive a BD-RIS design procedure using an unconstrained reformulation solved by a quasi-Newton method, followed by a standard water-filling step for power allocation. Simulations on a GHz, MHz bandwidth SISO-OFDM system demonstrate that wideband modeling and group-connected BD-RIS architectures significantly improve average rates compared to narrowband assumptions, underscoring the practical importance of frequency-dependent BD-RIS design.

Abstract

This work studies the wideband modeling and beamforming design of beyond diagonal reconfigurable intelligent surface (BD-RIS), which generalizes and goes beyond conventional RIS with diagonal phase shift matrices to achieve enhanced channel gain. Specifically, we investigate the response of BD-RIS in wideband systems by going back to its hardware circuit realizations. We propose a novel wideband model which has simple expressions while capturing the response variations of BD-RIS for signals with different frequencies. With this wideband model, we propose a BD-RIS design algorithm for an orthogonal frequency division multiplexing system to maximize the average rate over all subcarriers. Finally, we provide simulation results to evaluate the performance of the proposed design and show the importance of wideband modeling for BD-RIS.
Paper Structure (14 sections, 16 equations, 4 figures)

This paper contains 14 sections, 16 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Wideband Modeling of BD-RIS
  3. Admittance Matrix of BD-RIS
  4. Wideband Modeling of Tunable Admittance
  5. Beamforming Design for BD-RIS Aided SISO-OFDM
  6. Problem Formulation
  7. Optimization
  8. BD-RIS Design
  9. Power Allocation
  10. Performance Evaluation
  11. Simulation Setup
  12. Benchmark Scheme
  13. System Performance
  14. Conclusion

Figures (4)

  • Figure 1: Example of an 4-element BD-RIS with group-connected reconfigurable admittance network and the equivalent circuit for each admittance.
  • Figure 2: The susceptance as a function of (a) frequency and (b) the value of susceptance at the center frequency $f_\mathrm{c} = 2.4$ GHz with $L_1 = 2.5$ nH, $L_2 = 0.7$ nH, and $C\in[0.2,3]$ pF for a practical varactor diode. The parameters $\alpha_j$, $\beta_j$, $\forall j\in\{1,2\}$ in the linear model (\ref{['eq:fitted_model']}) are set as $\alpha_1 = 1.2161\times10^{-9}$, $\alpha_2 = -1.9076$, $\beta_1 = 4.0925\times10^{-11}$, $\beta_2 = -0.098$.
  • Figure 3: Average rate versus transmit power $P$ with BD-RIS having different architectures ($M = 36$, $\bar{M}\in\{1,3,6\}$). The legend "WM" is short for wideband modeling; "SC" is short for single-connected ($\bar{M}=1$); "GC" is short for group-connected ($\bar{M}\in\{3,6\}$).
  • Figure 4: Average rate versus the number of RIS elements $M$ with BD-RIS having different architectures ($P = 30$ dBm, $\bar{M}\in\{1,3,6\}$).