  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.
