  In this letter, we optimize the channel estimator of the cascaded channel in
an intelligent reflecting surface (IRS)-assisted millimeter wave (mmWave)
multi-antenna system. In this system, the receiver is equipped with a hybrid
architecture adopting quantized beamforming. Different from traditional
multiple-input multiple-output (MIMO) systems, the design of channel estimation
is challenging since the IRS is usually a passive array with limited signal
processing capability. We derive the optimized channel estimator in a closed
form by reformulating the problem of cascaded channel estimation in this
system, leveraging the typical mean-squared error (MSE) criterion. Considering
the presence of possible channel sparsity in mmWave channels, we generalize the
proposed method by exploiting the channel sparsity for further performance
enhancement and computational complexity reduction. Simulation results verify
that the proposed estimator significantly outperforms the existing ones.
