  Reconfigurable intelligent surfaces (RISs) have been proposed as a key
enabler to improve the coverage of the signals and mitigate the frequent
blockages in millimeter wave (mmWave) multiple-input multiple-output (MIMO)
communications. However, the channel state information (CSI) acquisition is one
of the major challenges for the practical deployment of the RIS. The passive
RIS without any baseband processing capabilities brings difficulty on the
channel estimation (CE), since the individual channels or the cascaded one can
be estimated only at base station (BS) via uplink training or mobile station
(MS) via downlink training. In order to facilitate the CSI acquisition, we
focus on the hybrid RIS architecture, where a small number of elements are
active and able to receive and process the pilot signals at the RIS. The CE is
performed in two stages by following the atomic norm minimization to recover
the channel parameters, i.e., angles of departure (AoDs), angles of arrival
(AoAs), and propagation path gains. Simulation results show that the proposed
scheme can outperform the passive RIS CE under the same training overhead.
Furthermore, we also study the theoretical performance limits in terms of mean
square error (MSE) via Cram\'er-Rao lower bound (CRLB) analyses.
