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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.

Efficient Channel Estimation for RIS-Aided MIMO Communications With Unitary Approximate Message Passing