  Reconfigurable intelligent surface (RIS) is very promising for wireless
networks to achieve high energy efficiency, extended coverage, improved
capacity, massive connectivity, etc. To unleash the full potentials of
RIS-aided communications, acquiring accurate channel state information is
crucial, which however is very challenging. For RIS-aided multiple-input and
multiple-output (MIMO) communications, the existing channel estimation methods
have computational complexity growing rapidly with the number of RIS units $N$
(e.g., in the order of $N^2$ or $N^3$) and/or have special requirements on the
matrices involved (e.g., the matrices need to be sparse for algorithm
convergence to achieve satisfactory performance), which hinder their
applications. In this work, instead of using the conventional signal model in
the literature, we derive a new signal model obtained through proper
vectorization and reduction operations. Then, leveraging the unitary
approximate message passing (UAMP), we develop a more efficient channel
estimator that has complexity linear with $N$ and does not have special
requirements on the relevant matrices, thanks to the robustness of UAMP. These
facilitate the applications of the proposed algorithm to a general RIS-aided
MIMO system with a larger $N$. Moreover, extensive numerical results show that
the proposed estimator delivers much better performance and/or requires
significantly less number of training symbols, thereby leading to notable
reductions in both training overhead and latency.
