This paper investigates joint device identification, channel estimation, and signal detection for LEO satellite-enabled grant-free random access, where a multiple-input multipleoutput (MIMO) system with orthogonal time-frequency space modulation (OTFS) is utilized to combat the dynamics of the terrestrial-satellite link (TSL). We divide the receiver structure into three modules: first, a linear module for identifying active devices, which leverages the generalized approximate message passing (GAMP) algorithm to eliminate inter-user interference in the delay-Doppler domain; second, a non-linear module adopting the message passing algorithm to jointly estimate channel and detect transmit signals; the third aided by Markov random field (MRF) aims to explore the three dimensional block sparsity of channel in the delay-Doppler-angle domain. The soft information is exchanged iteratively between these three modules by careful scheduling. Furthermore, the expectation-maximization algorithm is embedded to learn the hyperparameters in prior distributions. Simulation results demonstrate that the proposed scheme outperforms the conventional methods significantly in terms of activity error rate, channel estimation accuracy, and symbol error rate.
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