  Low earth orbit (LEO) satellite communications are expected to be
incorporated in future wireless networks, in particular 5G and beyond networks,
to provide global wireless access with enhanced data rates. Massive MIMO
techniques, though widely used in terrestrial communication systems, have not
been applied to LEO satellite communication systems. In this paper, we propose
a massive MIMO transmission scheme with full frequency reuse (FFR) for LEO
satellite communication systems and exploit statistical channel state
information (sCSI) to address the difficulty of obtaining instantaneous CSI
(iCSI) at the transmitter. We first establish the massive MIMO channel model
for LEO satellite communications and simplify the transmission designs via
performing Doppler and delay compensations at user terminals (UTs). Then, we
develop the low-complexity sCSI based downlink (DL) precoder and uplink (UL)
receiver in closed-form, aiming to maximize the average
signal-to-leakage-plus-noise ratio (ASLNR) and the average
signal-to-interference-plus-noise ratio (ASINR), respectively. It is shown that
the DL ASLNRs and UL ASINRs of all UTs reach their upper bounds under some
channel condition. Motivated by this, we propose a space angle based user
grouping (SAUG) algorithm to schedule the served UTs into different groups,
where each group of UTs use the same time and frequency resource. The proposed
algorithm is asymptotically optimal in the sense that the lower and upper
bounds of the achievable rate coincide when the number of satellite antennas or
UT groups is sufficiently large. Numerical results demonstrate that the
proposed massive MIMO transmission scheme with FFR significantly enhances the
data rate of LEO satellite communication systems. Notably, the proposed sCSI
based precoder and receiver achieve the similar performance with the iCSI based
ones that are often infeasible in practice.
