  In this paper, we study the high-resolution channel estimation problem for
intelligent reflecting surface (IRS)-assisted millimeter wave (mmWave)
multiple-input-multiple-output (MIMO) communications, which is a prerequisite
to guarantee further high-rate data transmission. Considering the typical
sparsity of mmWave channels, we formulate the cascaded channel estimation
problem from a sparse signal recovery perspective, and then propose a novel
two-step cascaded channel estimation protocol to estimate the cascaded
user-IRS-base station channel with high-resolution for IRS-assisted mmWave MIMO
communications. More specifically, the first step is to estimate the coarse
angular domain information (ADI) and further establish the robust uplink by
beam training. In the second step, by exploiting the coarse ADI, an adaptive
grid matching pursuit (AGMP) algorithm is proposed to estimate the
high-resolution cascaded channel state information (CSI) with low complexity.
Simulation results verify that the proposed two-step channel estimation
protocol significantly outperforms the state-of-the-art scheme, i.e., beam
training based channel estimation, and meanwhile can reap near-optimal system
performance achieved by perfect CSI.
