Efficient Design of Multi-group Multicast Beamforming via Reconfigurable Intelligent Surface

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 sub gradient 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.