Covert Communications Against an Adversary With Low-SNR Sensing Capability in Nakagami Fading

We show how to achieve covert communications in the presence of a warden equipped with sensing capabilities, even at a low signal to noise ratio (SNR). The warden Willie tries to minimize its false alarm and missed detection probabilities for weak signals. To this end, Willie selects optimal detection threshold for sensing particular legitimate users who want to cover their communication. Our solution to guarantee covertness involves deriving the lower bound for the sum of missed detection and false alarm probabilities, i.e., the mistake at the warden. To hide the message exchange, we derive the conditions for the minimum probability of mistake at Willie to be greater than a threshold. Our simulation results elucidate the roles played by various parameters, such as the number of samples, the target mistake threshold, the amount of noise uncertainty, etc., in undetectable communications over Nakagami fading. Our analysis demonstrates the feasibility of positive-rate hidden communications against a watchful adversary whose receiver is designed to be sensitive to weak SNR.