Covert rate characterization under multi-antenna detection: A study on warden's CSI availability and noise uncertainty

In this paper, we investigate covert communications under multi-antenna detection, and explore the impacts of the warden's channel state information (CSI) availability and the noise uncertainty on system covert capability. The detection performance at warden is analyzed in two cases under the perfect and statistical CSI at warden, respectively. In particular, for the former one, the warden utilizes the likelihood ratio (LR) detector, while for the latter one, the generalized likelihood ratio (GLR) detector is adopted. We first consider the scenario where the blocklength is finite, and demonstrate that the covert rate under both cases asymptotically goes to zero as the blocklength goes to infinity. Subsequently, we take the noise uncertainty at the warden into account which leads to positive covert rate, and characterize the covert rate for infinite blocklength. Specially, we derive the optimal transmit power for the legitimate transmitter that maximizes the covert rate. Besides, the rate gap under two cases, with different CSI availability at the warden, can be presented in closed form. Finally, numerical results validate the effectiveness of our theoretical analysis and also demonstrate the impacts of the factors studied on the system covertness.