Robust Optimization for Multi-STAR-IRS-Aided Multi-Cell Communication System Based on GNN-Enhanced Partially Distributed Multi-Agent

Simultaneously transmitting and reflecting intelligent reflecting surface (STAR-IRS) is recognized as a promising auxiliary technology to enhance the coverage of networks. In this work, we study a multi-STAR-IRS-assisted downlink multi-cell communication system in which STAR-IRSs are strategically deployed within cells to assist transmission from base stations (BSs) to user equipments (UEs). We aim to maximize energy efficiency by designing robust beamforming for active beamforming matrices at all BSs, passive reflection beamforming, and transmission beamforming matrices at all STAR-IRSs in the presence of imperfect channel state information (CSI). Due to the non-convexity of the original optimization problem, a deep reinforcement learning (DRL)-based algorithm is developed. Initially, the optimization problem is modeled as a multi-agent Markov decision problem. Next, to reduce interaction among cells, we propose a graph neural network (GNN)-enhanced partially distributed multi-agent deep reinforcement learning algorithm, based on a centralized training and decentralized execution framework. Therein, the agents alternatively learn robust policies for beamforming optimization against channel errors, where the robust training strategy is applied for training networks to narrow the mismatch between the perfect and imperfect CSI. Additionally, GNNs are incorporated to facilitate effective collaboration within cell agents. Simulation results confirm the efficacy of the proposed algorithm, showcasing its superior system energy efficiency performance compared to benchmarks. Moreover, the results reveal the robustness of the proposed algorithm against imperfect CSI and its ability to reduce the performance gap with the perfect CSI-based system.