A Beamforming Holistic Optimization Architecture for RIS-Assisted Cell-Free Massive MIMO Systems in 6G Green Communications

The synergistic deployment of multiple reconfigurable intelligent surfaces (RISs) alongside base stations (BSs) unlocks substantial benefits, encompassing capacity boost, energy efficiency, etc., making the RIS-assisted Cell-Free network a cornerstone architecture for 6G network. Motivated by this, we introduce a shared interactive simplification (SIS) architecture and low complexity joint beamforming strategy specifically designed for RIS-assisted Cell-Free multiple-input multiple-output (MIMO) systems. In SIS architecture, a pre-computed repository of phase shift sequences is shared between BSs and RISs, enabling the BSs to communicate solely the index of the optimal sequence, which markedly diminishes the feedback link burden and alleviates computational limitation. To bolster this architecture, the limit approximation particle swarm optimization-discrete mapping (LAPSO-DM) enhanced by fully convolutional networks (FCN) beamforming is developed, which leverages continuous unconstrained optimization to approximate the theoretically converged suboptimal solution, followed by a discrete mapping process, thereby enhancing computational efficiency. Furthermore, precise deterministic approximations derived from random matrix theory (RMT) are employed to streamline joint beamforming in large-scale Cell-Free MIMO systems. Simulation results are provided to evaluate the accuracy of various limiting and asymptotic results obtained in this work.