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Optimal Configuration of Reconfigurable Intelligent Surfaces With Non-uniform Phase Quantization

Jialong Lu, Rujing Xiong, Tiebin Mi, Ke Yin, Robert Caiming Qiu

TL;DR

The paper tackles RIS beamforming under non-uniform discrete phase quantization by formulating a discrete optimization to minimize transmit power under an SNR constraint. It introduces a globally optimal Partition-and-Traversal (PAT) algorithm for single-user scenarios and an Efficient PAT (E-PAT) extension for multi-user cases, achieving near-optimal performance with substantially reduced complexity. Through extensive simulations, the authors quantify the impact of unit- and array-level non-uniformities and demonstrate that PAT attains global optimality while E-PAT provides scalable performance with linear-like complexity under appropriate parameter choices. The work offers practical guidance for RIS hardware with non-uniform phase quantization and lays groundwork for extending to widerband and MIMO RIS systems.

Abstract

The existing methods for reconfigurable intelligent surface (RIS) beamforming in wireless communications are typically limited to uniform phase quantization. However, in practical applications, engineering challenges and design requirements often lead to non-uniform phase and bit resolution of RIS units, which limits the performance potential of these methods. To address this issue, this paper pioneers the study of discrete non-uniform phase configuration in RIS-assisted multiple-input single-output (MISO) communication and formulates an optimization model to characterize the problem. For single-user scenarios, the paper proposes a partition-andtraversal (PAT) algorithm that efficiently achieves the global optimal solution through systematic search and traversal. For larger-scale multi-user scenarios, aiming to balance performance and computational complexity, an enhanced PAT-based algorithm (E-PAT) is developed. By optimizing the search strategy, the E-PAT algorithm significantly reduces computational overhead and achieves linear complexity. Numerical simulations confirm the effectiveness and superiority of the proposed PAT and EPAT algorithms. Additionally, we provide a detailed analysis of the impact of non-uniform phase quantization on system performance.

Optimal Configuration of Reconfigurable Intelligent Surfaces With Non-uniform Phase Quantization

TL;DR

The paper tackles RIS beamforming under non-uniform discrete phase quantization by formulating a discrete optimization to minimize transmit power under an SNR constraint. It introduces a globally optimal Partition-and-Traversal (PAT) algorithm for single-user scenarios and an Efficient PAT (E-PAT) extension for multi-user cases, achieving near-optimal performance with substantially reduced complexity. Through extensive simulations, the authors quantify the impact of unit- and array-level non-uniformities and demonstrate that PAT attains global optimality while E-PAT provides scalable performance with linear-like complexity under appropriate parameter choices. The work offers practical guidance for RIS hardware with non-uniform phase quantization and lays groundwork for extending to widerband and MIMO RIS systems.

Abstract

The existing methods for reconfigurable intelligent surface (RIS) beamforming in wireless communications are typically limited to uniform phase quantization. However, in practical applications, engineering challenges and design requirements often lead to non-uniform phase and bit resolution of RIS units, which limits the performance potential of these methods. To address this issue, this paper pioneers the study of discrete non-uniform phase configuration in RIS-assisted multiple-input single-output (MISO) communication and formulates an optimization model to characterize the problem. For single-user scenarios, the paper proposes a partition-andtraversal (PAT) algorithm that efficiently achieves the global optimal solution through systematic search and traversal. For larger-scale multi-user scenarios, aiming to balance performance and computational complexity, an enhanced PAT-based algorithm (E-PAT) is developed. By optimizing the search strategy, the E-PAT algorithm significantly reduces computational overhead and achieves linear complexity. Numerical simulations confirm the effectiveness and superiority of the proposed PAT and EPAT algorithms. Additionally, we provide a detailed analysis of the impact of non-uniform phase quantization on system performance.
Paper Structure (27 sections, 1 theorem, 27 equations, 12 figures, 1 table, 1 algorithm)

This paper contains 27 sections, 1 theorem, 27 equations, 12 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contributions
  3. Organization
  4. Notations
  5. System Model And Problem Formulation
  6. System Model
  7. Beamforming Problem Formulation
  8. Global optimum for single-user scenarios
  9. Simplification Through Problem Reformulation
  10. A Partition-and-Traversal Algorithm For Positive Semidefinite Quadratic Maximization
  11. An Equivalent Formulation for Positive Semidefinite Quadratic Maximization
  12. Subregion Partitioning
  13. Determination and Traversal of subregions
  14. Evolutionary Algorithm for Multi-user Scenarios
  15. Problem reformulation
  16. ...and 12 more sections

Key Result

Theorem 1

An $N$-dimensional simplex has at least $\left(\right)$$n$-dimensional faces.

Figures (12)

  • Figure 1: multi-RIS-assisted multi-user communication.
  • Figure 2: schematic diagram of the radiation model
  • Figure 3: The spatial partitioning of $\overline{\mathbf{v}}$ results in each subregion corresponding to a distinct $\mathbf{v}$.
  • Figure 4: An intersection point can determine all the subregions connected to it.
  • Figure 5: The search process of the E-PAT algorithm (with the red dot indicating the optimal solution).
  • ...and 7 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof