Positive Covert Capacity of the MIMO AWGN Channels.

Covert communication, i.e., communication with a low probability of detection (LPD), has attracted a huge body of work. Recent studies concluded that the covert coding rates of the discrete memoryless channels and the additive white Gaussian noise (AWGN) channels are 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 show that the square root law can be overcome if the number of transmitting antennas is scaled. Thus, the covert capacity of the multiple-input multiple-output (MIMO) AWGN channels is shown to converge to the capacity of the MIMO AWGN channels under certain conditions. As a result, a positive covert capacity can be achieved. In addition, we characterize the covert capacity and the covert degrees-of-freedom of the MIMO AWGN channels. Besides, we derive the order-optimal scaling laws for the number of covert nats when the covert coding rate is diminishing. Moreover, we provide the scaling laws for the well-conditioned, the unit-rank MIMO AWGN channels as well as when the channel state information of the illegitimate receiver is only known to have a bounded spectral norm. Lastly, secrecy and LPD conditions are jointly investigated.