Over the Air Based Distributed Beamforming Design for RIS Aided Cell-Free MIMO Systems

The integration of reconfigurable intelligent surface(RIS) and Cell-Free multiple-input multiple-output (CFMIMO) has the potential to become a new trend in 6G. This paper studies the weighted sum-rate(WSR) maximization problem in RIS-aided CF-MIMO networks. We first convert the non-convex WSR maximization into weighted sum-mean square error(MSE) minimization. To decentralize the problem, we utilize the alternating optimization to design the suboptimal beamforming with the goal of weighted sum-MSE minimization. To reduce the signaling overheads related to acquiring the necessary correlation information among APs for designing active beamforming at each AP locally, we introduce a special over-the-air signaling combination scheme. Facing the constraint of discrete phase shifts of RIS, we deploy the proximal gradient descent to optimize the passive beamforming. Simulation results indicate that our proposed scheme achieves lower complexity and higher scalability, approaching the WSR of centralized and distributed-backhaul methods, while outperforming the non-collaborative Local-MMSE method.