  Reconfigurable intelligent surface (RIS) has emerged as a promising
technology for improving capacity and extending coverage of wireless networks.
In this work, we consider RIS-aided millimeter wave (mmWave) multiple-input and
multiple-output (MIMO) communications, where acquiring accurate channel state
information is challenging due to the high dimensionality of channels. To fully
exploit the structures of the channels, we formulate the channel estimation as
a hierarchically structured matrix recovery problem, and design a
low-complexity message passing algorithm to solve it. Simulation results
demonstrate the superiority of the proposed algorithm and its performance close
to the oracle bound.
