Maximizing Miss Detection for Covert Communication under Practical Constraints

The goal of covert communication is to establish a communication link between two parties, Alice and Bob, while assuring that a third party, the warden Willie, will not be able to detect the very presence of communication. If the means available to Willie in order to detect transmissions are not limited, requiring Willie's false alarm (FA) plus miss detection (MD) probabilities to be arbitrarily close to 1, results in covert communication with asymptotically negligible rate between Alice and Bob. However, in practice, Alice will require some minimal transmission rate\mathrm R_\min to Bob, below which she would prefer not to transmit at all. Willie, on the other hand, might use a practical detector, and fix some false alarm probability. In this paper, we discuss the optimal power allocation by the transmitter Alice, which will result in maximal miss detection probability by Willie, while assuring some minimal channel capacity requirement between Alice and Bob. In particular, assuming that Willie utilizes a filter-bank of energy detectors, we derive the optimal power allocation to maximize Willie's miss detection probability (for low to moderate SNR) and show that it results in constant SNR values along the transmission bandwidth.