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The study of the fundamental limits of covert communications, where a transmitter Alice wants to send information to a desired recipient Bob without detection of that transmission by an attentive and capable warden Willie, has emerged recently as a topic of great research interest. Previous work has assumed that the distribution of the multipath fading on the channel, which we term the channel distribution information (CDI), is known to Alice, hence facilitating her characterization of Willie's capabilities to detect the signal. However, in practice, Willie tends to be passive and the environment heterogeneous, implying a lack of signaling interchange between the transmitter and Willie makes it difficult if not impossible for Alice to estimate the CDI exactly and provide covertness guarantees. In this paper, we address this issue by developing covert communication schemes for various assumptions on Alice's imperfect CDI: 1) when the transmitter knows the channel distribution is within some distance of a nominal distribution; 2) when only the mean and variance of the channel distribution are available; 3) when Alice knows the channel distribution is complex Gaussian but the variance is unknown. In each case, we formulate new optimization problems to find the power allocations that maximize covert rate subject to a covertness requirement under uncertain CDI. Moreover, Willie may be able to estimate CDI exactly or be faced with an error in estimation, and we investigate two these issues. Numerical results are presented to compare the proposed schemes from various aspects, for attaining desirable covert system performance. [ABSTRACT FROM AUTHOR]

Covert communication is often limited in rate because it is difficult to hide the signal in the background noise. Recent work has shown that jamming can significantly improve the rate at which covert communication can be conducted, but this jamming signal has a devastating effect on the receiver. To tackle this issue, we equip the jammer with multiple antennas so that it can employ beamforming to place the intended receiver in the null space of the jamming. Moreover, in order to increase rate in this network, we equip the transmitter with an antenna array to be able to perform 3-dimensional (3D) beamforming toward its intended recipient. To evaluate this design, we formulate an optimization problem and present an iterative algorithm to solve it. Moreover, since Willie is passive, it is possible that Alice is not able to estimate the location of Willie perfectly. Hence, we investigate a new practical scenario in which the information about Willie's location is imperfect at Alice. Numerical results consider both the rate of covert communication with the proposed architecture and the gap between the result from our optimization and that obtained from exhaustive search. Numerical results highlight that the optimality gap is on average approximately 10%, and 3D beamforming compared to 2D beamforming increases covert rate by approximately 70%. [ABSTRACT FROM AUTHOR]