  In this paper, we consider channel estimation for intelligent reflecting
surface (IRS)-assisted millimeter wave (mmWave) systems, where an IRS is
deployed to assist the data transmission from the base station (BS) to a user.
It is shown that for the purpose of joint active and passive beamforming, the
knowledge of a large-size cascade channel matrix needs to be acquired. To
reduce the training overhead, the inherent sparsity in mmWave channels is
exploited. By utilizing properties of Katri-Rao and Kronecker products, we find
a sparse representation of the cascade channel and convert cascade channel
estimation into a sparse signal recovery problem. Simulation results show that
our proposed method can provide an accurate channel estimate and achieve a
substantial training overhead reduction.
