  In this paper, we investigate channel estimation for a large intelligent
surface (LIS) aided multiple-input multiple-output (MIMO) communication system.
Due to the close proximity of communication devices and LIS terminal, the
desired channels can be modeled as line-of-sight channels which are
ill-conditioned. To estimate these channel matrices with high quality, we
propose a two-stage channel estimation method. In particular, we employ the
conventional time-division duplexing based MIMO channel estimation technique in
the first stage to estimate the direct MIMO channel between the end terminals.
In the second stage, we propose to use a recently developed bilinear adaptive
vector approximate message passing (BAdVAMP) algorithm to estimate
ill-conditioned LIS channels. The BAdVAMP method has been shown to be accurate
and robust for ill-conditioned dictionary learning problems in compressed
sensing. We also propose a phase shift design for the LIS using the estimated
channels. Specifically, we formulate an optimization problem that maximizes the
total channel gain at the user. A closed-form expression to obtain the phase
shift of each passive element in the LIS is also derived. Numerical results
show that the proposed BAdVAMP based LIS channel estimation performs better
than its counterpart scheme bilinear generalized AMP (BiGAMP), especially when
channel matrices are ill-conditioned.
