Graph Neural Network-Based Energy-Efficient Optimization for RIS-Assisted Wireless Networks

Reconfigurable Intelligent Surfaces (RISs) are recognized as a promising solution for enhancing the energy efficiency (EE) of next-generation wireless networks, attributable to their low power consumption and signal enhancement capabilities. To address the EE maximization in RIS-aided multi-user wireless networks, we propose an innovative graph neural network (GNN)-based framework for the joint optimization of base station (BS) beamforming and RISs phase shifts. The framework models the network as a heterogeneous graph, enabling the GNN to capture complex interactions between RIS and user equipment (UE) nodes. We introduce two distinct feature initialization methods—Vertex-initialized GNN (VIGNN) and Edge-initialized GNN (EIGNN)—and develop specialized loss functions to guide the learning process, with theoretical analyses confirming their convergence. Extensive numerical simulations for both single-cell and cell-free scenarios validate the effectiveness of our approach, achieving up to a 5% improvement in EE over conventional methods and showcasing its scalability and adaptability in dynamic network environments.