  This paper considers the joint channel estimation and device activity
detection in the grant-free random access systems, where a large number of
Internet-of-Things devices intend to communicate with a low-earth orbit
satellite in a sporadic way. In addition, the massive multiple-input
multiple-output (MIMO) with orthogonal time-frequency space (OTFS) modulation
is adopted to combat the dynamics of the terrestrial-satellite link. We first
analyze the input-output relationship of the single-input single-output OTFS
when the large delay and Doppler shift both exist, and then extend it to the
grant-free random access with massive MIMO-OTFS. Next, by exploring the
sparsity of channel in the delay-Doppler-angle domain, a two-dimensional
pattern coupled hierarchical prior with the sparse Bayesian learning and
covariance-free method (TDSBL-CF) is developed for the channel estimation.
Then, the active devices are detected by computing the energy of the estimated
channel. Finally, the generalized approximate message passing algorithm
combined with the sparse Bayesian learning and two-dimensional convolution
(ConvSBL-GAMP) is proposed to decrease the computations of the TDSBL-CF
algorithm. Simulation results demonstrate that the proposed algorithms
outperform conventional methods.
