Energy-Efficient Beamforming Design for Cooperative Double-IRS Aided Multi-User MIMO

In this paper, we investigate the effect of cooperative double Intelligent reflecting surfaces (IRS) in improving the energy efficiency (EE) of a multi-user multiple-input multiple-output (MIMO) system. Under the general channel setup with the co-existence of both double-IRS and single-IRS reflection links, we aim to maximize the total EE of the system by jointly designing the transmit beamforming at the base station (BS) and the reflecting beamforming at the IRSs. The proposed problem is subject to the transmit power constraint at the BS, the individual minimum signal-to-interference-plus-noise ratio (SINR) requirements of the users and the unit modulus constraints of the IRS phase shifts. Due to the non-convex constraints and the coupling between variables, we decompose the original problem into two subproblems and propose an effective alternating optimization (AO) algorithm based on the techniques of fractional programming (FP) and semi-definite relaxation (SDR) to solve it. Simulation results validate the significant advantages of the proposed algorithm over benchmark schemes, as well as the effectiveness of cooperative double-IRS deployment in improving the EE performance of the system.