  With recent advances on the dense low-earth orbit (LEO) constellation, LEO
satellite network has become one promising solution to providing global
coverage for Internet-of-Things (IoT) services. Confronted with the sporadic
transmission from randomly activated IoT devices, we consider the random access
(RA) mechanism, and propose a grant-free RA (GF-RA) scheme to reduce the access
delay to the mobile LEO satellites. A Bernoulli-Rician message passing with
expectation maximization (BR-MP-EM) algorithm is proposed for this
terrestrial-satellite GF-RA system to address the user activity detection (UAD)
and channel estimation (CE) problem. This BR-MP-EM algorithm is divided into
two stages. In the inner iterations, the Bernoulli messages and Rician messages
are updated for the joint UAD and CE problem. Based on the output of the inner
iterations, the expectation maximization (EM) method is employed in the outer
iterations to update the hyper-parameters related to the channel impairments.
Finally, simulation results show the UAD and CE accuracy of the proposed
BR-MP-EM algorithm, as well as the robustness against the channel impairments.
