An Unsupervised Normalizing Flow-Based Neyman-Pearson Detector for Covert Communications in the Presence of Disco Reconfigurable Intelligent Surfaces

Covert communications, also known as low probability of detection (LPD) communications, offer a higher level of privacy protection compared to cryptography and physical-layer security (PLS) by hiding the transmission within ambient environments. Here, we investigate covert communications in the presence of a disco reconfigurable intelligent surface (DRIS) deployed by the warden Willie, which simultaneously reduces his detection error probabilities and degrades the communication performance between Alice and Bob, without relying on either channel state information (CSI) or additional jamming power. However, the introduction of the DRIS renders it intractable for Willie to construct a Neyman-Pearson (NP) detector, since the probability density function (PDF) of the test statistic is analytically intractable under the Alice-Bob transmission hypothesis. Moreover, given the adversarial relationship between Willie and Alice/Bob, it is unrealistic to assume that Willie has access to a labeled training dataset. To address these challenges, we propose an unsupervised masked autoregressive flow (MAF)-based NP detection framework that exploits prior knowledge inherent in covert communications. We further define the false alarm rate (FAR) and the missed detection rate (MDR) as monitoring performance metrics for Willie, and the signal-to-jamming-plus-noise ratio (SJNR) as a communication performance metric for Alice-Bob transmissions. Furthermore, we derive theoretical expressions for SJNR and uncover unique properties of covert communications in the presence of a DRIS. Simulations validate the theory and show that the proposed unsupervised MAF-based NP detector achieves performance comparable to its supervised counterpart.