Optimizing Power Consumption, Energy Efficiency, and Sum-Rate Using Beyond Diagonal RIS—A Unified Approach

Reconfigurable intelligent surface (RIS) has been envisioned as a highly promising technology for future wireless communication networks. Very recently, a novel beyond diagonal (BD)-RIS architecture has been proposed. This new architecture remarkably extends the traditional diagonal RIS model and yields much more powerful beamforming capability. Meanwhile, however, the emerging symmetry and orthogonality conditions imposed onto BD-RIS’ reflection matrix make its optimization highly difficult, especially when BD-RIS must satisfy numerous additional constraints. This difficulty arises in many BD-RIS applications and has remained unsolved so far. To resolve the above challenge, leveraging the penalty dual decomposition methodology, this paper proposes a novel unified approach that can optimize BD-RIS configuration when it is involved in any number of nonconvex constraints. Especially, we utilize our new approach to solve the power minimization and energy efficiency maximization problems when BD-RIS involves multiple quality-of-service constraints, which have not yet been solved in the literature. Besides, our new approach can also efficiently solve the sum-rate maximization in the BD-RIS assisted system by providing a new analytic-update-based solution, which is more efficient than existing methods. Extensive numerical results demonstrate the effectiveness of our new approach and the significant benefit of BD-RIS over the conventional diagonal RIS.