  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.
