  In this paper, we investigate the optimal design of a wireless-powered covert
communication (WP-CC) system, in which a probabilistic accumulate-then-transmit
(ATT) protocol is proposed to maximize the communication covertness subject to
a quality-of-service (QoS) requirement on communication. Specifically, in the
considered WP-CC system, a full-duplex (FD) receiver transmits artificial noise
(AN) to simultaneously charge an energy-constrained transmitter and to confuse
a warden's detection on the transmitter's communication activity. With the
probabilistic ATT protocol, the transmitter sends its information with a prior
probability, i.e., $p$, conditioned on the available energy being sufficient.
Our analysis shows that the probabilistic ATT protocol can achieve higher
covertness than the traditional ATT protocol with $p=1$. In order to facilitate
the optimal design of the WP-CC system, we also derive the warden's minimum
detection error probability and characterize the effective covert rate from the
transmitter to the receiver to quantify the communication covertness and
quality, respectively. The derived analytical results facilitate the joint
optimization of the probability $p$ and the information transmit power. We
further present the optimal design of a cable-powered covert communication
(CP-CC) system as a benchmark for comparison. Our simulation shows that the
proposed probabilistic ATT protocol (with a varying $p$) can achieve the
covertness upper bound determined by the CP-CC system, while the traditional
ATT protocol (with $p=1$) cannot, which again confirms the benefits brought by
the proposed probabilistic ATT in covert communications.
