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 wardens detection on the transmitters 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 wardens 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.
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