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Scalable and Near-Optimal Discrete Phase Shift Optimization for Reconfigurable Intelligent Surfaces with Over 20,000 Elements

Yuto Hama, Daisuke Kitayama, Kensuke Inaba, Toshimori Honjo, Hiroki Takesue, Naoki Ishikawa, Hiroyuki Takahashi

Abstract

This paper proposes a novel optimization framework for discrete phase shifts of a reconfigurable intelligent surface (RIS) using a coherent Ising machine (CIM). Unlike conventional methods based on iterative convex approximation or combinatorial search with exponentially increasing complexity, the CIM physically explores the solution space of Ising Hamiltonians through collective mode competition in a network of optical oscillators, enabling efficient large-scale discrete optimization. We formulate the RIS discrete phase optimization problem as a quadratic Ising model, which supports both binary and quaternary phase shifts by appropriately mapping quantized phase states to spin variables. Using a real hardware CIM, we experimentally solve quadratic optimization problems for RISs with up to 22,201 elements. The results demonstrate that the proposed method achieves physically consistent beam patterns under both line-of-sight and non-line-of-sight environments and attains the theoretical gain when transitioning from binary to quaternary phase shift. To further enhance scalability, we introduce a spin-size reduction approach that removes spins deterministically fixed by dominant channel components. This technique efficiently reduces the problem size for CIM in line-of-sight conditions without performance loss. These results confirm that CIM-based optimization offers a practical and highly scalable solution for large RIS deployments with discrete phase shift constraints.

Scalable and Near-Optimal Discrete Phase Shift Optimization for Reconfigurable Intelligent Surfaces with Over 20,000 Elements

Abstract

This paper proposes a novel optimization framework for discrete phase shifts of a reconfigurable intelligent surface (RIS) using a coherent Ising machine (CIM). Unlike conventional methods based on iterative convex approximation or combinatorial search with exponentially increasing complexity, the CIM physically explores the solution space of Ising Hamiltonians through collective mode competition in a network of optical oscillators, enabling efficient large-scale discrete optimization. We formulate the RIS discrete phase optimization problem as a quadratic Ising model, which supports both binary and quaternary phase shifts by appropriately mapping quantized phase states to spin variables. Using a real hardware CIM, we experimentally solve quadratic optimization problems for RISs with up to 22,201 elements. The results demonstrate that the proposed method achieves physically consistent beam patterns under both line-of-sight and non-line-of-sight environments and attains the theoretical gain when transitioning from binary to quaternary phase shift. To further enhance scalability, we introduce a spin-size reduction approach that removes spins deterministically fixed by dominant channel components. This technique efficiently reduces the problem size for CIM in line-of-sight conditions without performance loss. These results confirm that CIM-based optimization offers a practical and highly scalable solution for large RIS deployments with discrete phase shift constraints.

Paper Structure

This paper contains 26 sections, 40 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. Symbol Representation
  4. Channel Model
  5. Direct Channel
  6. RIS-Assisted Reflected Channel
  7. Discrete Phase Shift
  8. Binary Phase Shift ($L = 2$)
  9. Quaternary Phase Shift ($L = 4$)
  10. Discrete Phase Shift Optimization Based on Coherent Ising Machine
  11. Principle of Coherent Ising Machine
  12. Problem Formulation
  13. Binary Phase Shift
  14. Quaternary Phase Shift
  15. Spin-Size Reduction For Large-Scale Ising Optimization
  16. ...and 11 more sections

Figures (11)

  • Figure 1: The system model of RIS-assisted single user downlink communication.
  • Figure 2: Discrete phase shifts with phase shift levels of $L = 2$ (left) and $L=4$ (right).
  • Figure 3: The geometric evaluation model of RIS-assisted single user downlink communication.
  • Figure 4: Photograph of the hardware CIM used in this work.
  • Figure 5: The channel gain comparison using different binary phase shift schemes of RIS over NLoS channel ($N_\text{RIS} = 5476$). For reference, the values at $d = 50$ m are $-63.70$ dB, $-63.70$ dB, and $-63.95$ dB for CIM, successive, and Fresnel, respectively.
  • ...and 6 more figures