Accelerated joint beamforming for MF-RIS-Aided MU-MISO communication system

Multi-functional reconfigurable intelligent surfaces (MF-RISs) offer promising advantages for the development of next-generation wireless networks by simultaneously supporting both signal reflection, refraction, and amplification. This paper focuses on the beamforming design for an MF-RIS-aided multiuser multiple-input single-output (MU-MISO) downlink system, aiming to maximize the system sum rate while satisfying total base station (BS) transmit power and MF-RIS power constraints. The formulated optimization problem is strongly non-convex due to the highly coupled nature of its variables. To tackle this challenge, we adopt the fractional programming (FP) framework and propose an iterative optimization algorithm based on a quadratic reformulation of the beamforming problem. Furthermore, we incorporate the Nesterov momentum technique to accelerate convergence. The numerical results confirm the effectiveness of the proposed algorithm, demonstrating the improvement in performance and convergence speed of our proposal under the same energy budget compared to the conventional FP-based scheme.