  In this paper, we investigate the massive multiple-input multiple-output
orthogonal frequency division multiplexing channel estimation for
low-earth-orbit satellite communication systems. First, we use the angle-delay
domain channel to characterize the space-frequency domain channel. Then, we
show that the asymptotic minimum mean square error (MMSE) of the channel
estimation can be minimized if the array response vectors of the user terminals
(UTs) that use the same pilot are orthogonal. Inspired by this, we design an
efficient graph-based pilot allocation strategy to enhance the channel
estimation performance. In addition, we devise a novel two-stage channel
estimation (TSCE) approach, in which the received signals at the satellite are
manipulated with per-subcarrier space domain processing followed by per-user
frequency domain processing. Moreover, the space domain processing of each UT
is shown to be identical for all the subcarriers, and an asymptotically optimal
vector for the per-subcarrier space domain linear processing is derived. The
frequency domain processing can be efficiently implemented by means of the fast
Toeplitz system solver. Simulation results show that the proposed TSCE approach
can achieve a near performance to the MMSE estimation with much lower
complexity.
