Covert Communication with Multi-users Cooperation at Unequal Distances

This study explores an uplink multi-users covert communication system where certain users cooperate to hide messages from a covert user. A recent work investigated the multi-users covert communication system in which all the users are located at an equal distance from the legitimate receiver and a warden. In contrast, our work extends the existing work to an unequal distance scenario, where users are at unequal distances from the legitimate receiver. In particular, we establish that an on-off scheme, previously proven to be optimal in the equal distance scenario, remains optimal in the unequal distance scenario. The optimality of the on-off scheme enables us to derive expressions of the minimum detection error probability and outage probability in closed-forms. In addition, the closed-form expressions allow us to turn the parameter optimization into a simple one-dimensional search problem. Finally, the theoretical results developed in this work are validated by comparing extensive performance evaluations utilizing the theoretical results and Monte Carlo simulations.