Covert Communications Over Multiple Overt Channels

We explore leveraging the multiplicity of overt (public) messages, destined for different receivers through different channels, for hiding the transmission of a covert (private) message. The transmitter hides the covert message against a warden by superimposing it onto an overt message. We determine the optimum rule for choosing the overt message to maximize the total detection error probability (sum of the probability of false alarm and missed detection) at the warden. In addition, the channel variation is exploited to minimize the throughput loss on the overt message caused by the superimposition of the covert message. We show that the maximum total detection error probability converges fast to 1 as the number of overt messages (channels) increases; the total detection error probability is independent of the transmission power; and that a positive covert rate (bits per channel use) can be achieved while keeping the total detection error probability arbitrarily close to 1. These findings indicate that the multiplicity of overt messages (channels) and channel variations can be exploited to achieve a positive covert rate.