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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%.

Covert Communication Using Null Space and 3D Beamforming: Uncertainty of Willie's Location Information