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.

本文考虑了在具有有限块长度的多输入单输出 (MISO) 通道上进行隐蔽通信的波束成形技术。我们首先表明，复杂高斯通道上隐蔽通信的最佳输入分布是圆对称复高斯分布。通过回顾我们之前关于加性高斯白噪声 (AWGN) 通道上高斯随机编码吞吐量的结果，分析了 MISO 通道上可达到的吞吐量的可实现性和逆界。然后，根据系统两端可用的几种类型的信道状态信息，在各种情况下彻底研究最佳波束成形策略及其与发射功率的关系。我们揭示了这样一个事实，即当有对手的完整信道信息时，最大允许发射功率不受隐蔽性要求的约束，而存在基于波束成形的发射功率上限和基于中断的隐蔽性准则，如果存在只是对手的部分信道信息。最后，数值结果表明，与单天线情况相比，在 MISO 信道中采用适当的波束成形策略可以显着提高隐蔽通信的吞吐量。