Cell-Free Massive MIMO SWIPT with Beyond Diagonal Reconfigurable Intelligent Surfaces

We investigate the integration of beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) into cell-free massive multiple-input multiple-output (CF-mMIMO) systems to enhance simultaneous wireless information and power transfer (SWIPT). To simultaneously support two groups of users—energy receivers (ERs) and information receivers (IRs)— without sacrificing time-frequency resources, a subset of access points (APs) is dedicated to serving ERs with the aid of a BD-RIS, while the remaining APs focus on supporting IRs. A protective partial zero-forcing precoding technique is implemented at the APs to manage the non-coherent interference between the ERs and IRs. Subsequently, closed-form expressions for the spectral efficiency of the IRs and the average sum of harvested energy (HE) at the ERs are leveraged to formulate a comprehensive optimization problem. This problem jointly optimizes the AP selection, AP power control, and scattering matrix design at the BD-RIS, all based on long-term statistical channel state information. This challenging problem is then effectively transformed into more tractable forms. To solve these sub-problems, efficient algorithms are proposed, including a heuristic search for the scattering matrix design, as well as successive convex approximation and deep reinforcement learning methods for the joint AP mode selection and power control design. Numerical results show that a BD-RIS with a group- or fully-connected architecture achieves significant EH gains over the conventional diagonal RIS, especially delivering up to a 7-fold increase in the average sum of HE when a heuristic-based scattering matrix design is employed.