  We consider in this paper a new intelligent reflecting surface (IRS)-aided
LEO satellite communication system, by utilizing the controllable phase shifts
of massive passive reflecting elements to achieve flexible beamforming, which
copes with the time-varying channel between the high-mobility satellite (SAT)
and ground node (GN) cost-effectively. In particular, we propose a new
architecture for IRS-aided LEO satellite communication where IRSs are deployed
at both sides of the SAT and GN, and study their cooperative passive
beamforming (CPB) design over line-of-sight (LoS)-dominant single-reflection
and double-reflection channels. Specifically, we jointly optimize the active
transmit/receive beamforming at the SAT/GN as well as the CPB at two-sided IRSs
to maximize the overall channel gain from the SAT to each GN. Interestingly, we
show that under LoS channel conditions, the high-dimensional SAT-GN channel can
be decomposed into the outer product of two low-dimensional vectors. By
exploiting the decomposed SAT-GN channel, we decouple the original beamforming
optimization problem into two simpler subproblems corresponding to the SAT and
GN sides, respectively, which are both solved in closed-form. Furthermore, we
propose an efficient transmission protocol to conduct channel estimation and
beam tracking, which only requires independent processing of the SAT and GN in
a distributed manner, thus substantially reducing the implementation
complexity. Simulation results validate the performance advantages of the
proposed IRS-aided LEO satellite communication system with two-sided
cooperative IRSs, as compared to various baseline schemes such as the
conventional reflect-array and one-sided IRS.
