Robust and Adaptive Beamforming for Covert ISAC Under Dual Uncertainties

The coupling between radar and communication beams poses a central challenge to the beamforming design of covert integrated sensing and communication (ISAC) systems, as it distorts both the radar echo and the signal leakage observable at a passive eavesdropper. This challenge is further compounded by dual uncertainties at the eavesdropper, namely imperfect channel state information and unknown noise power, which collectively govern the admissible leakage level. Consequently, this paper addresses the joint beamforming optimization for covert ISAC under such practical uncertainties, aiming to maximize the radar mutual information (MI) while satisfying both covertness and quality of service (QoS) requirements. Towards this end, we first derive an analytical expression for radar MI that explicitly captures the effect of beam coupling. We then characterize the minimum detection error probability (MDEP) at the eavesdropper, which yields a rigorous worst-case security boundary for covert operation. The resulting joint beamforming design leads to a highly nonconvex optimization problem that is difficult to solve directly. For quasi-static scenarios, we develop a robust optimization (RO) method based on the S-procedure and semidefinite relaxation (SDR), which provides a theoretical benchmark with guaranteed covert reliability. For highly dynamic environments, static robust optimization is computationally costly and lacks adaptability. We therefore propose a robust proximal policy optimization (PPO-RB) algorithm, which embeds RO-derived worst-case covert and QoS violation metrics into the reward via adaptive Lagrangian penalties. Simulation results show that the proposed methods leverage the dual uncertainties to enlarge the feasible covert region while ensuring radar sensing performance, communication service quality, and covert security in both static and dynamic settings.