Energy harvesting maximization for multiuser MIMO SWIPT systems with intelligent reflecting surfaces

This paper studies the harvested energy maximization in an intelligent reflecting surface (IRS) aided multiuser multiple-input multiple-output (MIMO) simultaneous wireless information and power transfer (SWIPT) system in which the users can exploit power-splitting (PS) techniques for information decoding and energy harvesting (EH) simultaneously. A design problem is mathematically formulated as a joint optimization problem of transmit precoding (TPC) matrices at the base station (BS), the phase shifts at the IRS, and EH PS factors at the users to maximize the total harvested energy at the users while guaranteeing the quality of service requirements in terms of minimum achievable user rates and minimum harvested energy at each user. Considering the nonlinear EH models of the practical EH circuits at the users and unit-modulus constraints of the IRS phase shifters, the design problem becomes a highly nonlinear and non-convex optimization problem of the coupled matrix variables. To tackle the mathematical challenges in seeking the optimal solutions, we adopt alternating optimization to decompose the original design problem into two subproblems. The first subproblem is to jointly determine the TPC matrices at the BS and PS factors at the users while the second subproblem is to obtain the phase shifts at the IRS. Since each subproblem is still a non-convex optimization problem, we employ the minorization-maximization method to devise lower bound concave functions for the nonlinear EH and user rate functions and find the appropriate convex inner sets of the feasible sets to transform the optimization problems into convex ones. Verified by simulation results that the convergence of the proposed iterative algorithm is guaranteed and the total harvested energy is significantly improved as the multiuser MIMO SWIPT system is aided by the IRS with optimal phase shifts.