An integration of satellites and terrestrial networks is crucial for
enhancing performance of next generation communication systems. Jedoch, the
networks are hindered by the long-distance path loss and security risks in
dense urban environments. In this work, we propose a satellite-terrestrial
covert communication system assisted by the aerial active simultaneous
transmitting and reflecting reconfigurable intelligent surface (AASTAR-RIS) to
improve the channel capacity while ensuring the transmission covertness.
Specifically, we first derive the minimal detection error probability (DEP)
under the worst condition that the Warden has perfect channel state information
(CSI). Then, we formulate an AASTAR-RIS-assisted satellite-terrestrial covert
communication optimization problem (ASCCOP) to maximize the sum of the fair
channel capacity for all ground users while meeting the strict covert
constraint, by jointly optimizing the trajectory and active beamforming of the
AASTAR-RIS. Due to the challenges posed by the complex and high-dimensional
state-action spaces as well as the need for efficient exploration in dynamic
environments, we propose a generative deterministic policy gradient (GDPG)
algorithm, which is a generative deep reinforcement learning (Drl) method to
solve the ASCCOP. Concretely, the generative diffusion model (GDM) is utilized
as the policy representation of the algorithm to enhance the exploration
process by generating diverse and high-quality samples through a series of
denoising steps. Moreover, we incorporate an action gradient mechanism to
accomplish the policy improvement of the algorithm, which refines the better
state-action pairs through the gradient ascent. Simulation results demonstrate
that the proposed approach significantly outperforms important benchmarks.

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