Achieving Positive Covert Capacity over the MIMO AWGN Channels.

Covert communication, i.e., communication with a low probability of detection, has attracted a huge body of work. Recent studies have concluded that the maximal covert coding rate of the discrete memoryless channels and the additive white Gaussian noise (AWGN) channels is diminishing with the blocklength, $n$: only $\mathcal{O}(\sqrt{n})$ nats can be transmitted covertly and reliably over such channels. As a result, the covert capacity is zero. In this paper, we study covert communication over multiple-input multiple-output (MIMO) AWGN channels. We show that the square root law can be overcome and a non-zero covert capacity can be achieved in a particular regime, where the number of transmitting antennas is scaled in a specific way, relative to the blocklength. Furthermore, the covert capacity of MIMO AWGN channels is shown to converge to the capacity of MIMO AWGN channels under certain conditions. In addition, we characterize the covert capacity and the covert degrees-of-freedom of MIMO AWGN channels under general conditions (arbitrary number of transmitting antennas). We derive the order-optimal scaling law of the number of covert nats when the maximal covert coding rate is diminishing. Lastly, we provide a comparative discussion for the case in which secrecy and energy undetectability constraints are combined.