Harvested Power Region of Two-user MISO WPT Systems With Non-linear EH Nodes

In this paper, we determine the harvested power region of a two-user multiple-input single-output (MISO) wireless power transfer (WPT) system for a non-linear model of the rectennas at the energy harvester (EH) nodes. To this end, we characterize the distributions of the transmit symbol vector that achieve individual points on the boundary of this region. Each distribution is obtained as solution of an optimization problem where we maximize a weighted sum of the average harvested powers at the EH nodes under a constraint on the power budget of the transmitter. We prove that the optimal transmit strategy employs two beamforming vectors and scalar unit norm transmit symbols with arbitrary phase. To determine the beamforming vectors, we propose an iterative algorithm based on a two-dimensional grid search, semi-definite relaxation, and successive convex approximation. Our numerical results reveal that the proposed design outperforms two baseline schemes based on a linear EH model and a single beamforming vector, respectively. Finally, we observe that the harvested power region is convex and the power harvested at one EH node can be traded for a higher harvested power at the other node.