Abstract:  In the environment with noise uncertainty, the one-way covert communication was investigated under the best-case scenarios for the detection of a warden. First, given that receivers have detection limits, the channel-based precoding was applied to ensure that the power of signals converged at the receiver exceeds its detection limit, whereas the power of signals diffused at the warden is below its detection limit, achieving covert transmission based on the difference of wireless channels. Second, the closed-form expression of the average ergodic covert rate was derived. The theoretical analyses and simulation experiments results indicate that the uncontrollable noise uncertainty in environments has negative effects on covert transmission in the best-case scenarios for the warden. However, positive covert rates can still be achieved by controlling power and the antenna number.