Distance-Angle Beamforming for Covert Communications via Frequency Diverse Array: Toward Two-Dimensional Covertness

In this paper, we study the beamforming schemes via the novel frequency diverse array (FDA) on enhancing covert communications performance. We first consider the ideal scenario where the channel state information (CSI) is perfectly known at the transmitter. Then we characterize the key role of minimizing the correlation of the communication and detection channels in boosting the covertness of the system, which also provides a theoretical design principle for FDA-specific carrier frequency scheduling. By exploiting the optimization framework block successive upper bound minimization (BSUM), we propose a frequency scheduling method which leads to a two-phase beamforming scheme to facilitate the covert transmission. Subsequently, we extend the scenario to the more practical one with partial CSI. By leveraging the convex hull, we manage to transform the formulated semi-infinite programming problem to an equivalent semi-definite one which can be solved optimally. In addition, we present a process to construct the optimal beamforming vector. To mitigate the channel correlations in this scenario, we generalize the steps of BSUM and propose an algorithm to schedule the frequencies efficiently. Afterwards, a three-phase robust beamforming scheme is summarized, which boosts the covert rate significantly. Numerical results are provided to demonstrate the superiority of the proposed schemes.