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.

翻译：同时透射反射可重构智能表面（STAR-RIS）为扩展无线通信覆盖范围提供了一种前景广阔的技术途径。然而，单STAR-RIS的覆盖局限促使我们借鉴现有研究中关于可重构智能表面（RIS）的多跳传输思路，引入多跳传输机制。为此，我们提出了一种新型的多跳STAR-RIS架构，以实现更广范围的全平面服务覆盖。本文旨在联合优化基站的主动波束成形与STAR-RIS的被动波束成形，目标是在STAR-RIS硬件限制约束下最大化系统能效。此外，我们还探究了STAR-RIS单元开关状态对能效的影响。为应对这一复杂优化问题，我们设计了一种全局与局部协同的多智能体深度强化学习（MAGAR）算法。全局智能体负责提升各局部智能体间的协作效能，而局部智能体则专注于个体层面的学习。数值结果表明，与Q学习、基于全局奖励的多智能体深度Q网络（DQN）以及基于局部奖励的多智能体DQN等基准算法相比，MAGAR算法性能显著提升。此外，与基于模式切换的STAR-RIS、传统RIS以及未部署RIS/STAR-RIS的方案相比，所提出的多跳STAR-RIS架构实现了最高的系统能效。