  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.
