Unsupervised Semi-Parametric Plug-in Likelihood-Ratio Detection for Covert Communications in the Presence of Disco Reconfigurable Intelligent Surfaces
Covert communications, also referred to as low probability of detection (LPD) communications, provide a higher level of privacy protection than cryptography and physical-layer security (PLS) by hiding transmissions in the ambient environment. In this work, we investigate covert communications in the presence of a disco reconfigurable intelligent surface (DRIS) deployed by the warden Willie, which reduces Willie's detection error probability (DEP), i.e., the sum of the false alarm rate (FAR) and the miss detection rate (MDR), 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 makes it analytically intractable for Willie to construct the Neyman-Pearson (NP) detector, which is the optimal detector for monitoring potential covert transmissions between Alice and Bob. To this end, we develop an unsupervised semi-parametric plug-in likelihood-ratio detector for Willie. The proposed detector retains the parametric Gamma reference model under the silent hypothesis without requiring prior knowledge of noise, and learns from unlabeled data a one-dimensional monotone normalizing flow model for the analytically intractable distribution under the transmission hypothesis. In particular, it exploits the structural prior inherent in covert communications that Willie's observations reduce to noise only when Alice and Bob are silent. The monitoring performance at Willie is evaluated in terms of DEP, while the communication impact on Alice and Bob is quantified by the signal-to-jamming-plus-noise ratio (SJNR). Simulation results verify the analysis and show that the proposed unsupervised plug-in likelihood-ratio detector achieves monitoring performance close to that of its supervised counterpart.