This paper studies the problem of slow-moving channel estimation (CE) in the physical layer of a reconfigurable intelligent surface (RIS)-aided multiple-input multiple-output (MIMO) communications system. Acquiring accurate channel state information (CSI) in such a system is one of the critical challenges due to a large number of RIS elements, especially under mobility with its characteristic Doppler effect. In this paper, we propose a channel estimation framework based on the tensor decomposition method to decouple the conventional cascaded channel. We formulate the uplink training signals as a third-order tensor, which admits a CANDECOMP/PARAFAC (CP) model with three factor matrices containing the CSI and phase information of the RIS. We further utilize the third factor matrix featured in the Vandermonde structure and decompose the received tensor signals with a higher rank into three factor matrices. Additionally, we develop algorithms to estimate parameters of the low-velocity user terminal (UT) - RIS channel from the resultant factor matrices. The numerical results indicate that our proposed tensor-based algorithms allow the estimation of individual UT - RIS and RIS - base station (BS) channels with expected accuracy and strong robustness.
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