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Graph Neural Network based Active and Passive Beamforming for Distributed STAR-RIS-Assisted Multi-User MISO Systems

Ha An Le, Trinh Van Chien, Wan Choi

TL;DR

The paper tackles the challenging problem of joint active and passive beamforming in distributed STAR-RIS assisted MU-MISO networks under energy-splitting, aiming to maximize sum rate under a transmit power constraint. It introduces a two-track approach: an AO-SCA method that achieves a KKT point but with high complexity, and a novel heterogeneous graph neural network (BHGNN) that models STAR-RIS elements and users as a heterogeneous graph and learns the joint beamforming policy via HGMP. The BHGNN demonstrates near-optimal performance relative to AO-SCA-EXH benchmarks while significantly reducing online computation and generalizing across varying numbers of RISs, RIS elements, and users. This work provides a scalable, data-driven solution with strong permutation-equivariance properties, making it suitable for dynamic, large-scale STAR-RIS deployments in future wireless networks.

Abstract

This paper investigates a joint active and passive beamforming design for distributed simultaneous transmitting and reflecting (STAR) reconfigurable intelligent surface (RIS) assisted multi-user (MU)- mutiple input single output (MISO) systems, where the energy splitting (ES) mode is considered for the STAR-RIS. We aim to design the active beamforming vectors at the base station (BS) and the passive beamforming at the STAR-RIS to maximize the user sum rate under transmitting power constraints. The formulated problem is non-convex and nontrivial to obtain the global optimum due to the coupling between active beamforming vectors and STAR-RIS phase shifts. To efficiently solve the problem, we propose a novel graph neural network (GNN)-based framework. Specifically, we first model the interactions among users and network entities are using a heterogeneous graph representation. A heterogeneous graph neural network (HGNN) implementation is then introduced to directly optimizes beamforming vectors and STAR-RIS coefficients with the system objective. Numerical results show that the proposed approach yields efficient performance compared to the previous benchmarks. Furthermore, the proposed GNN is scalable with various system configurations.

Graph Neural Network based Active and Passive Beamforming for Distributed STAR-RIS-Assisted Multi-User MISO Systems

TL;DR

The paper tackles the challenging problem of joint active and passive beamforming in distributed STAR-RIS assisted MU-MISO networks under energy-splitting, aiming to maximize sum rate under a transmit power constraint. It introduces a two-track approach: an AO-SCA method that achieves a KKT point but with high complexity, and a novel heterogeneous graph neural network (BHGNN) that models STAR-RIS elements and users as a heterogeneous graph and learns the joint beamforming policy via HGMP. The BHGNN demonstrates near-optimal performance relative to AO-SCA-EXH benchmarks while significantly reducing online computation and generalizing across varying numbers of RISs, RIS elements, and users. This work provides a scalable, data-driven solution with strong permutation-equivariance properties, making it suitable for dynamic, large-scale STAR-RIS deployments in future wireless networks.

Abstract

This paper investigates a joint active and passive beamforming design for distributed simultaneous transmitting and reflecting (STAR) reconfigurable intelligent surface (RIS) assisted multi-user (MU)- mutiple input single output (MISO) systems, where the energy splitting (ES) mode is considered for the STAR-RIS. We aim to design the active beamforming vectors at the base station (BS) and the passive beamforming at the STAR-RIS to maximize the user sum rate under transmitting power constraints. The formulated problem is non-convex and nontrivial to obtain the global optimum due to the coupling between active beamforming vectors and STAR-RIS phase shifts. To efficiently solve the problem, we propose a novel graph neural network (GNN)-based framework. Specifically, we first model the interactions among users and network entities are using a heterogeneous graph representation. A heterogeneous graph neural network (HGNN) implementation is then introduced to directly optimizes beamforming vectors and STAR-RIS coefficients with the system objective. Numerical results show that the proposed approach yields efficient performance compared to the previous benchmarks. Furthermore, the proposed GNN is scalable with various system configurations.
Paper Structure (22 sections, 2 theorems, 36 equations, 7 figures, 3 tables, 2 algorithms)

This paper contains 22 sections, 2 theorems, 36 equations, 7 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System model and problem formulation
  3. System model
  4. Problem Formulation
  5. AO-based Solution of Beamforming Optimization Problem
  6. Graph Neural Network-based Solution
  7. Properties of the joint beamforming design policy
  8. Graphical Representation of STAR-RIS systems
  9. Properties of the proposed HGMP
  10. Permutation equivariance
  11. Scalability to different system configurations
  12. Implementation of Heterogeneous Graph Neural Network
  13. Training the BHGNN
  14. Optimization With User QoS Constraint
  15. Complexity Analysis
  16. ...and 7 more sections

Key Result

Lemma 1

The objective in eq:PenaltyObj achieved by Algorithm alg:cap is monotonically increasing and the variables $({\mathbf{s}}^{\chi})^{(n)}$, ${\alpha}_k^{(n)}$, ${\eta}_k^{(n)}$ converge to the points that fulfill the KKT of the problem eq:PenaltyObj.

Figures (7)

  • Figure 1: The considered distributed STAR-RIS system model.
  • Figure 2: The graph representation of the distributed STAR-RISs systems.
  • Figure 3: $(a)$ The message passing procedure in the proposed HGNN between two layers. The aggregation from edge is omitted for clarity. $(b)$ The aggregation at the RIS vertex with edge feature.
  • Figure 4: The training convergence of the proposed BHGNN model with $N_t = 16, K = 8, L = 4, M = 4$.
  • Figure 5: The sum rate performance versus total number of STAR-RIS elements of the examined methods, with $K = 8, N_t = 16$.
  • ...and 2 more figures

Theorems & Definitions (3)

  • Lemma 1
  • Remark 1
  • Proposition 1