  Low earth orbit (LEO) satellite has been considered as a potential supplement
for the terrestrial Internet of Things (IoT). In this paper, we consider
grant-free non-orthogonal random access (GF-NORA) in orthogonal frequency
division multiplexing (OFDM) system to increase access capacity and reduce
access latency for LEO satellite-IoT. We focus on the joint device activity
detection (DAD) and channel estimation (CE) problem at the satellite access
point. The delay and the Doppler effect of the LEO satellite channel are
assumed to be partially compensated. We propose an OFDM-symbol repetition
technique to better distinguish the residual Doppler frequency shifts, and
present a grid-based parametric probability model to characterize channel
sparsity in the delay-Doppler-user domain, as well as to characterize the
relationship between the channel states and the device activity. Based on that,
we develop a robust Bayesian message passing algorithm named modified variance
state propagation (MVSP) for joint DAD and CE. Moreover, to tackle the mismatch
between the real channel and its on-grid representation, an
expectation-maximization (EM) framework is proposed to learn the grid
parameters. Simulation results demonstrate that our proposed algorithms
significantly outperform the existing approaches in both activity detection
probability and channel estimation accuracy.
