  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.
