Graph Koopman Autoencoder for Predictive Covert Communication Against UAV Surveillance

TL;DR

This work tackles covert communication against UAV surveillance by predicting unknown nonlinear UAV trajectories with a Graph Koopman Autoencoder (GKAE) that fuses a graph neural network encoder with a Koopman-invariant latent space. The predicted UAV positions feed into a power-control scheme that minimizes the maximum received power at UAVs, keeping it below the detection threshold $\tilde{P}_{\text{det}}$. The GKAE architecture, trained with a two-term loss, achieves accurate long-horizon predictions (e.g., 4 UAVs over $p=80$ steps with $\varepsilon_{\text{pred}} \approx 0.0025$) and enables effective LPD in terrestrial ad-hoc networks; a simplified P2' makes the optimization tractable while preserving connectivity. Overall, the approach demonstrates that combining graph learning with Koopman theory can yield scalable, low-latency trajectory prediction and secure power-control strategies in UAV-rich surveillance environments.

Abstract

Low Probability of Detection (LPD) communication aims to obscure the very presence of radio frequency (RF) signals, going beyond just hiding the content of the communication. However, the use of Unmanned Aerial Vehicles (UAVs) introduces a challenge, as UAVs can detect RF signals from the ground by hovering over specific areas of interest. With the growing utilization of UAVs in modern surveillance, there is a crucial need for a thorough understanding of their unknown nonlinear dynamic trajectories to effectively implement LPD communication. Unfortunately, this critical information is often not readily available, posing a significant hurdle in LPD communication. To address this issue, we consider a case-study for enabling terrestrial LPD communication in the presence of multiple UAVs that are engaged in surveillance. We introduce a novel framework that combines graph neural networks (GNN) with Koopman theory to predict the trajectories of multiple fixed-wing UAVs over an extended prediction horizon. Using the predicted UAV locations, we enable LPD communication in a terrestrial ad-hoc network by controlling nodes' transmit powers to keep the received power at UAVs' predicted locations minimized. Our extensive simulations validate the efficacy of the proposed framework in accurately predicting the trajectories of multiple UAVs, thereby effectively establishing LPD communication.

Figures (6)

• Figure 1: An illustration of covert communication against UAV surveillance (top), wherein ground nodes (bottom) adjust transmit power for achieving low probability of detection based on UAV trajectory prediction by their associated central unit (left).
• Figure 2: Graph-based Koopman autoencoder (GKAE) architecture.
• Figure 3: Training convergence and prediction errors of GKAE with respect to different Koopman matrix of dimension $b$.
• Figure 4: Predicted 4 UAV trajectories for $p = 80$ time steps.
• Figure 5: Received power at UAVs, transmit power with respect to the number $N$ of ground nodes, and to the minimum number $\tilde{C}$ of required communication links.