  This paper studies a cognitive or secondary multi-antenna wireless power
transfer (WPT) system over a multi-carrier channel, which shares the same
spectrum with a primary wireless information transfer (WIT) system that employs
adaptive water-filling power allocation. By controlling the transmit energy
beamforming over sub-carriers (SCs), the secondary energy transmitter (S-ET)
can directly charge the secondary energy receiver (S-ER), even purposely
interfere with the primary WIT system, such that the primary information
transmitter (P-IT) can reactively adjust its power allocation (based on
water-filling) to facilitate the S-ER's energy harvesting. We investigate how
the secondary WPT system can exploit the primary WIT system's reactive power
allocation, for improving the wireless energy harvesting performance. In
particular, our objective is to maximize the total energy received at the S-ER
from both the S-ET and the P-IT, by optimizing the S-ET's energy beamforming
over SCs, subject to its maximum transmit power constraint, and the maximum
interference power constraint imposed at the primary information receiver
(P-IR) to protect the primary WIT. Although the formulated problem is
non-convex and difficult to be optimally solved in general, we propose an
efficient algorithm to obtain a high-quality solution by employing the Lagrange
dual method together with a one-dimensional search. We also present two
benchmark energy beamforming designs based on the zero-forcing (ZF) and
maximum-ratio-transmission (MRT) principles, respectively, as well as the
conventional design without considering the primary WIT system's reaction.
Numerical results show that our proposed design leads to significantly improved
energy harvesting performance at the S-ER, as compared to these benchmark
schemes.
