Multi-Agent Deep Reinforcement Learning for Energy Efficient Multi-Hop STAR-RIS-Assisted Transmissions

Simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) provides a promising way to expand coverage in wireless communications. However, limitation of single STAR-RIS inspire us to integrate the concept of multi-hop transmissions, as focused on RIS in existing research. Therefore, we propose the novel architecture of multi-hop STAR-RISs to achieve a wider range of full-plane service coverage. In this paper, we intend to solve active beamforming of the base station and passive beamforming of STAR-RISs, aiming for maximizing the energy efficiency constrained by hardware limitation of STAR-RISs. Furthermore, we investigate the impact of the on-off state of STAR-RIS elements on energy efficiency. To tackle the complex problem, a Multi-Agent Global and locAl deep Reinforcement learning (MAGAR) algorithm is designed. The global agent elevates the collaboration among local agents, which focus on individual learning. In numerical results, we observe the significant improvement of MAGAR compared to the other benchmarks, including Q-learning, multi-agent deep Q network (DQN) with golbal reward, and multi-agent DQN with local rewards. Moreover, the proposed architecture of multi-hop STAR-RISs achieves the highest energy efficiency compared to mode switching based STAR-RISs, conventional RISs and deployment without RISs or STAR-RISs.