A double self-sustainable reconfigurable intelligent surfaces (RISs) assisted multi-user multiple input multiple output (MIMO) system is investigated. Two RISs are equipped with energy harvesting circuit to achieve self-sustainable transmission. The aim is to minimize the transmission power at the base station (BS), while guaranteeing the quality of service (QoS) requirements of the users and meeting the power consumption requirements of the RISs. A block coordinate descent (BCD) algorithm based on the penalty-based method and successive convex approximation (SCA) is employed to alternatively optimize the active beamforming at the BS and the phase shifts, as well as amplitude coefficients of two RISs. Simulation results show that the required power consumption at the BS for the proposed double self-sustainable RISs system is significantly reduced compared to conventional RIS systems.
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