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Joint Active and Passive Beamforming Optimization for Beyond Diagonal RIS-aided Multi-User Communications

Xiaohua Zhou, Tianyu Fang, Yijie Mao

TL;DR

This work tackles joint active and beyond-diagonal RIS passive beamforming for a multi-user downlink, formulating a weighted sum-rate optimization under a symmetric unitary BD-RIS constraint. It introduces FP-PSLA, a unified alternating-optimization framework that combines fractional programming with a projected successive linear approximation, yielding closed-form updates for both passive and active beamforming and projections onto the BD-RIS and transmit-domains. The approach delivers near-optimal WSR with markedly reduced computational complexity compared with baseline methods, enabling scalable BD-RIS deployment in large networks. Numerical results demonstrate fast convergence and substantial CPU-time savings while maintaining strong performance, highlighting the practical viability of BD-RIS in future wireless systems.

Abstract

Benefiting from its capability to generalize existing reconfigurable intelligent surface (RIS) architectures and provide additional design flexibility via interactions between RIS elements, beyond-diagonal RIS (BD-RIS) has attracted considerable research interests recently. However, due to the symmetric and unitary passive beamforming constraint imposed on BD-RIS, existing joint active and passive beamforming optimization algorithms for BD-RIS either exhibit high computational complexity to achieve near optimal solutions or rely on heuristic algorithms with substantial performance loss. In this paper, we address this issue by proposing an efficient optimization framework for BD-RIS assisted multi-user multi-antenna communication networks. Specifically, we solve the weighted sum rate maximization problem by introducing a novel beamforming optimization algorithm that alternately optimizes active and passive beamforming matrices using iterative closed-form solutions. Numerical results demonstrate that our algorithm significantly reduces computational complexity while ensuring a sub-optimal solution.

Joint Active and Passive Beamforming Optimization for Beyond Diagonal RIS-aided Multi-User Communications

TL;DR

This work tackles joint active and beyond-diagonal RIS passive beamforming for a multi-user downlink, formulating a weighted sum-rate optimization under a symmetric unitary BD-RIS constraint. It introduces FP-PSLA, a unified alternating-optimization framework that combines fractional programming with a projected successive linear approximation, yielding closed-form updates for both passive and active beamforming and projections onto the BD-RIS and transmit-domains. The approach delivers near-optimal WSR with markedly reduced computational complexity compared with baseline methods, enabling scalable BD-RIS deployment in large networks. Numerical results demonstrate fast convergence and substantial CPU-time savings while maintaining strong performance, highlighting the practical viability of BD-RIS in future wireless systems.

Abstract

Benefiting from its capability to generalize existing reconfigurable intelligent surface (RIS) architectures and provide additional design flexibility via interactions between RIS elements, beyond-diagonal RIS (BD-RIS) has attracted considerable research interests recently. However, due to the symmetric and unitary passive beamforming constraint imposed on BD-RIS, existing joint active and passive beamforming optimization algorithms for BD-RIS either exhibit high computational complexity to achieve near optimal solutions or rely on heuristic algorithms with substantial performance loss. In this paper, we address this issue by proposing an efficient optimization framework for BD-RIS assisted multi-user multi-antenna communication networks. Specifically, we solve the weighted sum rate maximization problem by introducing a novel beamforming optimization algorithm that alternately optimizes active and passive beamforming matrices using iterative closed-form solutions. Numerical results demonstrate that our algorithm significantly reduces computational complexity while ensuring a sub-optimal solution.
Paper Structure (10 sections, 3 theorems, 28 equations, 1 figure, 1 table, 1 algorithm)

This paper contains 10 sections, 3 theorems, 28 equations, 1 figure, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Proposed Optimization Framework
  4. Fractional Programming Reformulation
  5. Passive Beamforming Optimization
  6. Active Beamforming Optimization
  7. Alternating Optimization for Problem \ref{['P1']}
  8. Convergence Analysis
  9. Numerical Results
  10. Conclusion

Key Result

Lemma 1

By introducing auxiliary variables $\bm \alpha =\{\alpha_{1}, \cdots, \alpha_K \}, \bm \beta=\{\beta_1, \cdots, \beta_K\}$, problem P1 is equivalently reformulated as: where

Figures (1)

  • Figure 1: Analysis of the proposed algorithm.

Theorems & Definitions (4)

  • Lemma 1
  • Lemma 2
  • Definition 1
  • Theorem 1