Covert mmWave Communications with Finite Blocklength Against Spatially Random Wardens

In this paper, we investigate covert millimeter wave (mmWave) communications with finite blocklength, where a multi-antenna transmitter sends covert messages to a legitimate receiver in the presence of spatially random wardens. Both the phase array (PA) and linear frequency diverse array (LFDA) beamforming schemes, which are designed to maximize the antenna gain from the transmitter to the legitimate receiver, are investigated to improve the covert communication performance. First, the novel expressions of covert communication constraint and average effective covert throughput (AECT) are derived for both beamforming schemes. Then, taking into account the constraint of maximal available blocklength, the optimal transmit power and blocklength are determined for maximizing the AECT. Typically, comparing to the benchmark with fixed blocklength, the enhancement of AECT by utilizing the optimized blocklength enlarges as the density of wardens increases. In addition, it is observed that increasing the maximal available blocklength cannot always improve the maximum AECT due to the trade-off between the transmit power and blocklength. Furthermore, it is shown that the maximum AECT varies for different directions of the legitimate receiver under both the beamforming schemes, and the transmitter can adaptively choose the PA or LFDA beamforming scheme to improve the covertness performance against spatially random wardens.