Optimal Transmit Strategy for MIMO WPT Systems With Non-linear Energy Harvesting

In this paper, we study multiple-input multiple-output (MIMO) wireless power transfer (WPT) systems, where the energy harvester (EH) node is equipped with multiple nonlinear rectennas. We characterize the optimal transmit strategy by the optimal distribution of the transmit symbol vector that maximizes the average harvested power at the EH subject to a constraint on the power budget of the transmitter. We show that the optimal transmit strategy employs scalar unit-norm input symbols with arbitrary phase and two beamforming vectors, which are determined as solutions of a non-convex optimization problem. To solve this problem, we propose an iterative algorithm based on a two-dimensional grid search, semidefinite relaxation, and successive convex approximation. Our simulation results reveal that the proposed MIMO WPT design significantly outperforms two baseline schemes based on a linear EH model and a single beamforming vector, respectively. Finally, we show that the average harvested power grows linearly with the number of rectennas at the EH node and saturates for a large number of TX antennas.