Device-to-device (D2D) communications underlaid cellular networks have emerged as a promising network architecture to provide extended coverage and high data rate for various Internet of Things (IoT) applications. However, because of the inherent openness and broadcasting nature of wireless communications, such networks face severe risks of data privacy disclosure. This paper investigates the covert communications in such networks for providing enhanced privacy protection. Specifically, this paper explores the critical covert rate performance in a full-duplex D2D communication underlaid cellular network consisting of a base station, a cellular user, a D2D pair with a transmitter and a full-duplex receiver, and a warden, where the D2D receiver can operate over either the full-duplex (FD) mode or the half-duplex (HD) mode. We first derive transmission outage probabilities of cellular and D2D links under the FD and HD modes, respectively. Based on these probabilities, we further provide theoretical modelling for the covert rate under each mode and explore the corresponding covert rate maximization by jointly optimizing the transmit powers of the D2D pair and the cellular user. To improve the covert rate performance, we propose a general mode in which the D2D receiver can flexibly switch between these two modes. Under the general mode, we also investigate the theoretical modelling and maximization problems of covert rate. Finally, we present extensive numerical results to illustrate the covert rate performances under the FD, HD, and general modes.

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