Beyond Diagonal RIS Aided Power Minimization Beamforming for MIMO Systems

Beyond diagonal reconfigurable intelligent surfaces (BD-RIS) with interconnected reflecting elements present an emerging technology for manipulating the propagation environment, and their new structure requires careful investigation. In this paper, we explore BD-RIS-aided power minimization beamforming, where the BD-RIS scattering matrix and transmit beamforming are jointly optimized under nonconvex constraints related to signal-to-interference-plus-noise ratio (SINR) thresholds and the structure of the scattering matrix. To efficiently solve the problem, we propose a single-loop algorithm, where we adopt a variable splitting strategy with an auxiliary variable to split the scattering matrix, and then alternately update the resulting variables. Through further derivations, we show that each nonconvex subproblem can be solved efficiently. Simulation results demonstrate the high efficiency of our proposed single-loop algorithm and the effectiveness of BD-RIS in improving performance.