Joint Beamforming and Power Allocation Design for Stacked Intelligent Metasurfaces-Aided Cell-Free Massive MIMO Systems

Stacked intelligent metasurfaces (SIM) is considered a revolutionary technology that enables powerful signal processing directly in the electromagnetic (EM) wave domain and has significant energy-saving advantages. In this work, we explore the performance of a SIM-aided cell-free massive multiple-input multiple-output (CF-mMIMO) system that incorporates joint beamforming and power allocation. Specifically, we jointly design the transmit power allocation at access points (APs) and the wave-based beamforming at SIMs for maximizing the system sum rate. An alternating optimization (AO)-based iterative algorithm is proposed for solving the complex non-convex problem, which is decomposed into two subproblems. For the transmit power allocation subproblem, maximum ratio transmission (MRT) is employed to maximize signal receiving power. For the optimization subproblem of SIM phase shifts, a proficient gradient ascent algorithm is deployed to ensure convergence to a local optimum. Simulation results show an enhancement in the performance of the proposed AO algorithm compared to baseline methods. Additionally, numerical results contrast with those of RIS-aided CF-mMIMO systems, highlighting the advantages of SIMs in CF networks and demonstrating the efficacy of SIM-enabled wave-based beamforming design, where increasing the number of meta-atoms and layers of SIMs is beneficial for improving the sum rate.