Covert Joint Communication and Sensing under Variational Distance Constraint

We consider the problem of joint communication and sensing with covertness constraint, in which the transmitter needs to design a signal to simultaneously communicate and probe a channel while escaping detection by a passive eavesdropper. Because of the covertness constraint, the weight of transmitted codewords needs to obey the square-root law. We show the existence of a coding scheme with Pulse Position Modulation that achieves the optimal performance between communication throughput and state sensing-error exponent while remaining covert with respect to a passive eavesdropper. For a binary-input discrete memoryless channel, we show that the performance is solely determined by the covertness constraint, and we characterize the optimal pair of achievable rate and error exponent.