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.

💡 Research Summary

This paper investigates covert (low‑probability‑of‑detection) communications in a novel adversarial setting where the warden Willie equips a disco‑style reconfigurable intelligent surface (DRIS) to both improve his detection capability and degrade the legitimate link between Alice and Bob. The DRIS consists of many reflecting elements whose phase and amplitude coefficients change randomly and rapidly over time, thereby breaking the usual time‑division‑duplex channel reciprocity (active channel aging) and rendering the probability density function (PDF) of Willie’s test statistic under the transmission hypothesis (H₁) analytically intractable. Moreover, because Willie and the covert users are adversaries, Willie cannot rely on a labeled dataset that distinguishes H₀ (silence) from H₁ (transmission).

To overcome these challenges, the authors propose an unsupervised Neyman‑Pearson detector based on a masked autoregressive flow (MAF), a type of normalizing flow (NF) that provides exact likelihood evaluation for complex distributions. The key insight is that under H₀ Willie observes pure additive white Gaussian noise, a fact that can be exploited to train the MAF using only noise samples. Once trained, the MAF estimates the likelihood of any observed test statistic; the log‑likelihood is then compared against a threshold chosen to satisfy a prescribed false‑alarm rate (FAR), yielding an optimal (in the NP sense) decision rule without any labeled data.

The paper defines two performance metrics for Willie—false alarm rate (FAR) and missed detection rate (MDR)—and a communication‑quality metric for Alice‑Bob—the signal‑to‑jamming‑plus‑noise ratio (SJNR). By modeling the cascaded Alice‑DRIS‑Willie channel as h_{wD}=g·diag(φ)·h_{wI}, where φ(t) are the random DRIS coefficients, the authors derive closed‑form expressions for the statistical moments of h_{wD}. An asymptotic analysis shows that as the number of DRIS elements N_D grows, h_{wD} converges to a complex Gaussian distribution, and the SJNR at Bob can be approximated as

 SJNR ≈ P₀|h_{ab}|² / (P₀ E