Joint Beamforming for Multi-Functional Reconfigurable Intelligent Surface-Aided MISO Networks

In this correspondence, we study the joint beamforming problem in an multi-functional reconfigurable intelligent surface (MF-RIS) assisted wireless network. Considering the power budgets at the base station and MF-RIS, we formulate a joint beamforming problem for weighted sum-rate maximization. For solving this problem efficiently, we reformulate it as a weighted minimum-mean-square-error (WMMSE) problem by introducing a decoder scalar. Then, we develop a low-complexity WMMSE (LC-WMMSE) algorithm, where the decoder, WMMSE factor, and transmit beamforming are obtained in closed forms. Numerical results reveal that: 1) Our MF-RIS attains a higher throughput compared to existing RISs (i.e., passive and active counterparts). 2) The proposed LC-WMMSE algorithm outperforms the conventional WMMSE algorithm in performance and convergence speed.