This paper considers a multi-group multicasting scenario facilitated by a reconfigurable intelligent surface (RIS). We propose a fast and scalable algorithm for the joint design of the base station (BS) multicast beamforming and the RIS passive beamforming to minimize the transmit power subject to the quality-of-service (QoS) constraints. By exploring the structure of the joint optimization problem, we show that this QoS problem can be broken into a BS multicast QoS subproblem and an RIS max-min-fair (MMF) multicast subproblem, which are solved alternatingly. In our proposed algorithm, we utilize the optimal multicast beamforming structure to obtain the BS beamformers efficiently. Furthermore, we reformulate the challenging RIS multicast subproblem and employ a first-order projected subgradient algorithm (PSA) to solve it, which yields closed-form updates. Simulation results show the efficacy of our proposed algorithm in performance and computational cost compared to other alternative methods.

翻译：本文探讨了由可重构智能表面（RIS）支持的多组多播场景。我们提出了一种快速且可扩展的算法，用于联合设计基站（BS）多播波束成形与RIS无源波束成形，以在满足服务质量（QoS）约束的前提下最小化发射功率。通过分析联合优化问题的结构，我们证明该QoS问题可分解为BS多播QoS子问题与RIS最大最小公平（MMF）多播子问题，并交替求解。在所提算法中，我们利用最优多播波束成形结构高效获取BS波束成形向量。此外，我们对具有挑战性的RIS多播子问题进行重构，并采用一阶投影次梯度算法（PSA）求解，该算法可得到闭式更新解。仿真结果表明，与其它替代方法相比，所提算法在性能与计算成本方面均具有有效性。