  This letter studies a multi-antenna wireless powered communication (WPC)
system with co-channel energy and information transfer, where a wireless device
(WD), powered up by wireless energy transfer (WET) from an energy transmitter
(ET), communicates to an information receiver (IR) over the same frequency
band. We maximize the achievable data rate from the WD to the IR by jointly
optimizing the energy beamforming at the ET and the information beamforming at
the WD, subject to their individual transmit power constraints. We obtain the
optimal solution to this problem in closed-form, where the optimal energy
beamforming at the ET achieves a best energy/interference tradeoff between
maximizing the energy transfer efficiency to the WD and minimizing the
co-channel interference to the IR. Numerical results show that our proposed
optimal co-channel design is superior to other reference schemes.
