Power allocation for covert communication, with application to underwater acoustic channel

In this paper we consider the problem of spectral power allocation for enabling covert communication. We define the communication as covert if its very presence cannot be detected by a third party. As energy detectors are simple and commonplace, we consider the communication to be covert if it is conducted with minimal SNR values in each frequency bin, in the aim that a non cooperative receiver (the eavesdropper) will be unable to detect the transmission. As it is possible to lower SNR values while maintaining reliable communication by simply reducing the transmission rate, we suggest a criterion for SNR minimization while imposing minimal required capacity. The obtained result demonstrates the relationship between channel bandwidth, required minimal capacity, available power resources, and its required spectral allocation. We then examine this power allocation problem in the context of an underwater acoustic channel, and discuss the required spectral shaping that achieves covert communication.