  In this paper, we consider a three-node cooperative wireless powered
communication system consisting of a multi-antenna hybrid access point (H-AP)
and a single-antenna relay and a single-antenna user. The energy constrained
relay and user first harvest energy in the downlink and then the relay assists
the user using the harvested power for information transmission in the uplink.
The optimal energy beamforming vector and the time split between harvest and
cooperation are investigated. To reduce the computational complexity,
suboptimal designs are also studied, where closed-form expressions are derived
for the energy beamforming vector and the time split. For comparison purposes,
we also present a detailed performance analysis in terms of the achievable
outage probability and the average throughput of an intuitive energy
beamforming scheme, where the H-AP directs all the energy towards the user. The
findings of the paper suggest that implementing multiple antennas at the H-AP
can significantly improve the system performance, and the closed-form
suboptimal energy beamforming vector and time split yields near optimal
performance. Also, for the intuitive beamforming scheme, a diversity order of
(N+1)/2 can be achieved, where N is the number of antennas at the H-AP.
