Energy-Efficient Beamforming Design for Double-RIS Aided Multi-User MIMO Systems

In order to research the influence of joint beamforming on system performance within RIS aided systems, a double-RIS aided multiple-input multiple-output (MIMO) system is considered in this study, and the optimal energy efficiency (EE) within this system is investigated. To be specific, by optimizing the transmit beamforming at the BS, the phase shifts of the RISs and the receive beamforming at user terminals jointly, the EE of the double-RIS aided system is maximized. In order to address the complex problem, an alternating optimization (AO) algorithm is designed. This algorithm utilizes fractional programming (FP) and semidefinite relaxation (SDR) methods. In addition, a theoretical analysis is conducted on the double-RIS aided system’s EE performance. Simulations verify our analytical results and show that, compared with the benchmark scheme that ignores the receive beamforming, the proposed optimization scheme achieves at least 10% increase in energy efficiency performance.