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Movable Beyond-Diagonal Reconfigurable Intelligent Surfaces: Moving, Interconnecting, or Both?

Shuyue Xu, Matteo Nerini, Bruno Clerckx

TL;DR

This work introduces Movable Beyond-Diagonal RIS (MA-BD-RIS) to jointly optimize beamforming, BD-RIS configuration, and movable element positions in a MU-MISO downlink. It develops a low-complexity algorithm based on fractional programming, a partially proximal ADMM for BD-RIS design, and a surrogate-based placement update to efficiently solve the coupled problem, achieving near-optimal sum-rate performance. Key findings show that high movability yields significant gains in small-scale or rich-scattering scenarios, while stronger inter-element connectivity benefits large-scale RIS and higher transmit array dimensions, revealing a fundamental trade-off between connectivity and movability with practical design guidelines. The proposed framework and cadence of updates offer a scalable, admittance-based RIS design path that can adapt to varied deployment constraints and channel conditions.

Abstract

This letter proposes a movable beyond-diagonal reconfigurable intelligent surfaces (MA-BD-RIS) design, combining inter-element connectivity and movability for channel enhancement. We study a MA-BD-RIS assisted multi-user multiple input single output system where beamforming, BD-RIS configuration, and elements positions are jointly optimized to maximize the sum-rate. An efficient algorithm is developed, incorporating closed-form beamforming, a low-complexity partially proximal alternating direction method of multipliers for BD-RIS design, and successive convex approximation for element placement. Simulations show that the high-movability structure yields superior performance in small-scale RIS and rich scattering scenarios, while the high-connectivity structure dominates in large-scale RIS and massive transmit array configurations.

Movable Beyond-Diagonal Reconfigurable Intelligent Surfaces: Moving, Interconnecting, or Both?

TL;DR

This work introduces Movable Beyond-Diagonal RIS (MA-BD-RIS) to jointly optimize beamforming, BD-RIS configuration, and movable element positions in a MU-MISO downlink. It develops a low-complexity algorithm based on fractional programming, a partially proximal ADMM for BD-RIS design, and a surrogate-based placement update to efficiently solve the coupled problem, achieving near-optimal sum-rate performance. Key findings show that high movability yields significant gains in small-scale or rich-scattering scenarios, while stronger inter-element connectivity benefits large-scale RIS and higher transmit array dimensions, revealing a fundamental trade-off between connectivity and movability with practical design guidelines. The proposed framework and cadence of updates offer a scalable, admittance-based RIS design path that can adapt to varied deployment constraints and channel conditions.

Abstract

This letter proposes a movable beyond-diagonal reconfigurable intelligent surfaces (MA-BD-RIS) design, combining inter-element connectivity and movability for channel enhancement. We study a MA-BD-RIS assisted multi-user multiple input single output system where beamforming, BD-RIS configuration, and elements positions are jointly optimized to maximize the sum-rate. An efficient algorithm is developed, incorporating closed-form beamforming, a low-complexity partially proximal alternating direction method of multipliers for BD-RIS design, and successive convex approximation for element placement. Simulations show that the high-movability structure yields superior performance in small-scale RIS and rich scattering scenarios, while the high-connectivity structure dominates in large-scale RIS and massive transmit array configurations.
Paper Structure (12 sections, 24 equations, 4 figures)

This paper contains 12 sections, 24 equations, 4 figures.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Field-Response Based Channel Model
  4. Problem formulation
  5. Algorithm Design
  6. Optimization of $\rho_k$ and ${\psi}_k$
  7. Optimization of $\bm{W}$
  8. Optimization of $\bm{\Theta}$ and $\bm{B}$
  9. Optimization of $\bm{c}$
  10. Simulation Results
  11. Conclusion
  12. Calculation of $\mu(\bm{c_g})$

Figures (4)

  • Figure 1: Model of the MA-BD-RIS aided MU-MISO system.
  • Figure 2: Achievable rate vs. number of RIS elemnets $M$, with $N_t = 4$.
  • Figure 3: Achievable rate vs. number of RIS elemnets $M$, with $L=6$.
  • Figure 4: Achievable rate vs. scale factor $l_s$, with $M\!=\!64$, $L\!\!=\!6$, $N_t \!= \!4$.