Covert communication with beamforming over MISO channels in the finite blocklength regime

This paper considers beamforming techniques for covert communication over multiple input single output (MISO) channels with finite blocklength. We first show that the optimal input distribution for covert communication over complex Gaussian channels is circular symmetric complex Gaussian. By reviewing our previous results on the throughput of Gaussian random coding over additive white Gaussian noise (AWGN) channels, the achievability and converse bounds on the attainable throughput over MISO channels are analyzed. Then, the optimal beamforming strategies and their relationship with the transmitting power are thoroughly investigated in a variety of situations in terms of several types of channel state information available at both ends of the system. We reveal the fact that the maximal allowable transmit power is not constrained by covertness requirement when there is full channel information of the adversary, while there is an upper bound of the transmit power which is based on beamforming and an outage-based covertness criterion if there is only partial channel information of the adversary. Finally, numerical results are presented to show that the throughput of covert communication can be increased notably by adopting a proper beamforming strategy in MISO channels in comparison with the single antenna case.