  This paper investigates joint device identification, channel estimation, and
symbol detection for cooperative multi-satellite-enhanced random access, where
orthogonal time-frequency space modulation with the large antenna array is
utilized to combat the dynamics of the terrestrial-satellite links (TSLs). We
introduce the generalized complex exponential basis expansion model to
parameterize TSLs, thereby reducing the pilot overhead. By exploiting the block
sparsity of the TSLs in the angular domain, a message passing algorithm is
designed for initial channel estimation. Subsequently, we examine two
cooperative modes to leverage the spatial diversity within satellite
constellations: the centralized mode, where computations are performed at a
high-power central server, and the distributed mode, where computations are
offloaded to edge satellites with minimal signaling overhead. Specifically, in
the centralized mode, device identification is achieved by aggregating backhaul
information from edge satellites, and channel estimation and symbol detection
are jointly enhanced through a structured approximate expectation propagation
(AEP) algorithm. In the distributed mode, edge satellites share channel
information and exchange soft information about data symbols, leading to a
distributed version of AEP. The introduced basis expansion model for TSLs
enables the efficient implementation of both centralized and distributed
algorithms via fast Fourier transform. Simulation results demonstrate that
proposed schemes significantly outperform conventional algorithms in terms of
the activity error rate, the normalized mean squared error, and the symbol
error rate. Notably, the distributed mode achieves performance comparable to
the centralized mode with only two exchanges of soft information about data
symbols within the constellation.
