  In this paper, we study the optimal waveform design for wireless power
transfer (WPT) from a multi-antenna energy transmitter (ET) to multiple
single-antenna energy receivers (ERs) simultaneously in multi-path
frequency-selective channels. First, we propose a refined nonlinear
current-voltage model of the diode in the ER rectifier, and accordingly derive
new expressions for the output direct current (DC) voltage and corresponding
harvested power at the ER. Leveraging this new rectenna model, we first
consider the single-ER case and study the multisine-based power waveform design
based on the wireless channel to maximize the harvested power at the ER. We
propose two efficient algorithms for finding high-quality suboptimal solutions
to this non-convex optimization problem. Next, we extend our formulated
waveform design problem to the general multi-ER case for maximizing the
weighted sum of the harvested powers by all ERs, and propose an efficient
difference-of-convex functions programming (DCP)-based algorithm for solving
this problem. Finally, we demonstrate the superior performance of our proposed
waveform designs based on the new rectenna model over existing schemes/models
via simulations.
