  This paper investigates joint channel estimation and device activity
detection in the LEO satellite-enabled grant-free random access systems with
large differential delay and Doppler shift. In addition, the multiple-input
multiple-output (MIMO) with orthogonal time-frequency space modulation (OTFS)
is utilized to combat the dynamics of the terrestrial-satellite link. To
simplify the computation process, we estimate the channel tensor in parallel
along the delay dimension. Then, the deep learning and expectation-maximization
approach are integrated into the generalized approximate message passing with
cross-correlation--based Gaussian prior to capture the channel sparsity in the
delay-Doppler-angle domain and learn the hyperparameters. Finally, active
devices are detected by computing energy of the estimated channel. Simulation
results demonstrate that the proposed algorithms outperform conventional
methods.
