  In this paper, we investigate the capacity of a point-to-point, full-duplex
(FD), wirelessly powered communication system impaired by self-interference.
This system is comprised of an energy transmitter (ET) and an energy harvesting
user (EHU), both operating in a FD mode. The ET transmits energy towards the
EHU. The EHU harvests this energy and uses it to transmit information back to
the ET. As a result of the FD mode, both nodes are affected by
self-interference. The self-interference has a different effect at the two
nodes: it impairs the decoding of the received signal at the ET, however, it
provides an additional source of energy for the EHU. This paper derives the
capacity of this communication system assuming a processing cost at the EHU and
additive white Gaussian noise channel with block fading. Thereby, we show that
the capacity achieving scheme is relatively simple and therefore applicable to
devices with limited resources. Moreover, our numerical results show
significant improvements in terms of data rate when the capacity achieving
strategy is employed compared to half-duplex transmission. Moreover, we show
the positive and negative effects of the self-interference at the EHU and the
ET, respectively. Furthermore, we show the crippling effect of the processing
cost and demonstrate that failing to take it into consideration gives a false
impression in terms of achievable rate.
