By reconfiguring the propagation environment of electromagnetic waves artificially, reconfigurable intelligent surfaces (RISs) have been regarded as a promising and revolutionary hardware technology to improve the energy and spectrum efficiency of wireless networks. In this paper, we study a RIS aided multiuser multiple-input multiple-output (MIMO) wireless power transfer (WPT) system, where the transmitter is equipped with a constant-envelope analog beamformer. First, we maximize the total received power of the users by jointly optimizing the beamformer at transmitter and the phase-shifts at the RIS, and propose two alternating optimization based suboptimal solutions by leveraging the semidefinite relaxation (SDR) and the successive convex approximation (SCA) techniques respectively. Then, considering the user fairness, we formulate another problem to maximize the total received power subject to the users individual minimum received power constraints. A low complexity iterative algorithm based on both alternating direction method of multipliers (ADMM) and SCA techniques is proposed to solve this problem. In the case of multiple users, we further analyze the asymptotic performance as the number of RIS elements approaches infinity, and bound the performance loss caused by RIS phase quantization. Numerical results show the correctness of the analysis results and the effectiveness of the proposed algorithms.
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