Spectral- and Energy-efficient Multi-BS Multi-RIS Pinching-antenna Systems: A GNN-based Approach

Technical Summary: Spectral- and Energy-efficient Multi-BS Multi-RIS Pinching-antenna Systems

Problem Statement
This paper addresses the coordinated downlink transmission in a multi-base station (multi-BS), multi-reconfigurable intelligent surface (multi-RIS)-assisted pinching-antenna (PA) system. In this architecture, each user equipment (UE) is served by a single BS, where each BS is equipped with movable PAs deployed on parallel waveguides. The system aims to maximize either the sum rate (SR) or energy efficiency (EE) by jointly optimizing four tightly coupled variables:

1. PA Placement: The physical positions of movable antennas on waveguides.
2. RIS Phase Shifts: The reflection coefficients of the intelligent surfaces.
3. Transmit Beamforming: The baseband precoding vectors.
4. BS-UE Association: The mapping of UEs to specific BSs.

The optimization is constrained by inter-PA spacing requirements, total power budgets, and unit-modulus constraints for RIS phases. The problem is characterized as a highly coupled mixed-variable optimization task involving continuous, binary, and unit-modulus variables. Traditional iterative algorithms are deemed computationally prohibitive and suffer from poor scalability in large-scale, dynamic network topologies.

Methodology
To solve this complex optimization problem, the authors propose a three-stage Graph Neural Network (GNN) trained in an unsupervised, end-to-end manner. The framework is designed to handle the relational structure of the network (BSs, RISs, and UEs) and ensure feasibility of the output variables without relying on penalty terms in the loss function.

The proposed architecture consists of three sequential stages:

1. Stage 1 (ChanGNN): Utilizes a heterogeneous graph representation containing BS, UE, and RIS nodes. It employs Complex Heterogeneous Graph Attention Layers (CHAL) to jointly learn PA positions and RIS phase shifts based on node locations.
   • Feasibility Mechanism: PA positions are reconstructed from auxiliary spacing variables using sigmoid scaling and normalization to satisfy minimum spacing and boundary constraints. RIS phases are normalized to unit modulus.
2. Stage 2 (BeamGNN): Utilizes a homogeneous graph where nodes represent BS-UE links. It employs Complex Graph Attention Layers (CGAL) to learn transmit beamforming vectors.
   • Feasibility Mechanism: The network outputs hybrid coefficients and power allocations, which are processed through a Hybrid Zero-Forcing and Maximum Ratio Transmission (HZM) learning scheme to generate valid beamforming vectors.
3. Stage 3 (AssocGNN): Operates on the same homogeneous graph but focuses on beamforming gain features to determine the BS-UE association matrix.
   • Feasibility Mechanism: A Gumbel-Softmax relaxation is used during training to allow differentiable optimization of the binary association variables, followed by a hard assignment (argmax) during inference. Per-BS power normalization ensures power budget constraints are met.

The model integrates both heterogeneous and homogeneous graph representations to capture diverse interactions (e.g., BS-RIS, intra-BS interference, inter-BS competition).

Key Contributions

• Unified Optimization Framework: The paper formulates SR and EE maximization problems for a multi-BS multi-RIS PA system, jointly optimizing PA placement, RIS configuration, beamforming, and association under practical constraints.
• Three-Stage GNN Architecture: The authors propose a novel architecture (ChanGNN, BeamGNN, AssocGNN) that explicitly models heterogeneous and homogeneous interactions. It introduces feasibility-preserving readout mechanisms for all decision variables, ensuring constraints are satisfied by design rather than soft penalties.
• Scalability and Generalization: The proposed method is designed to be scalable to unseen numbers of UEs, BSs, and RISs through parameter sharing and graph-based inductive bias, avoiding the need for retraining when network size changes.

Numerical Results
Extensive simulations demonstrate that the proposed three-stage GNN consistently outperforms representative system baselines (e.g., systems without RIS, fixed-PA systems, random association) and model baselines (e.g., MLPs, single-stage HANs, standard GATs).

• Performance: The joint optimization of PA mobility and RIS reconfiguration yields significant gains in both SR and EE compared to systems utilizing only one of these technologies.
• Generalization: The model generalizes well to unseen problem sizes (different numbers of UEs, BSs, and RISs) and maintains performance even with moderate topology mismatches between training and testing.
• Efficiency: The inference time remains at the millisecond level, making the approach suitable for online deployment.
• Ablation Studies: Results confirm the necessity of message passing, residual connections, and complex-valued mappings in each stage. The study also shows that performance gains from PA mobility increase with the number of PAs, eventually saturating due to diminishing spatial degrees of freedom.

Significance
The paper claims to present the first effective transmission design for PA systems within the challenging context of coordinated multi-BS multi-RIS assistance. By bridging the gap between transmitter-side spatial reconfiguration (PA) and environment-side wave control (RIS), the proposed framework offers a practically viable solution for future 6G wireless communications. The work highlights that combining flexible antenna architectures with intelligent surfaces, managed by a scalable deep learning framework, can significantly enhance spectral and energy efficiency in dynamic, multi-cell environments.