Perfectly Covert Communication with a Reflective Panel

Covert communication is focused on hiding the mere existence of communication from unwanted listeners via the physical layer. In this work, we consider the problem of perfect covert communication in wireless networks. Specifically, harnessing an Intelligent Reflecting Surface (IRS), we turn our attention to schemes that allow the transmitter to completely hide the communication, with zero energy at the unwanted listener (Willie) and hence zero probability of detection. Applications of such schemes go beyond simple covertness, as we prevent detectability or decoding even when the codebook, timings, and channel characteristics are known to Willie. That is, perfect covertness also ensures Willie is unable to decode, even assuming communication took place and knowing the codebook. We define perfect covertness, give a necessary and sufficient condition for it in IRS-assisted communication, and define the optimization problem. For $N=2$ IRS elements, we analyze the probability of finding a solution and derive its closed form. We then investigate the problem of $N>2$ IRS elements by analyzing the probability of such a zero-detection solution. We prove that this probability converges to $1$ as the number of IRS tends to infinity. We provide an iterative algorithm to find a perfectly covert solution and prove its convergence. The results are also supported by simulations, showing that a small amount of IRS elements allows for a positive rate at the legitimate user yet with zero probability of detection at an unwanted listener.