  The deployment of reconfigurable intelligent surfaces (RISs) in a
communication system provides control over the propagation environment, which
facilitates the augmentation of a multitude of communication objectives. As
these performance gains are highly dependent on the applied phase shifts at the
RIS, accurate channel state information at the transceivers is imperative.
However, not only do RISs traditionally lack signal processing capabilities,
but their end-to-end channels also consist of multiple components. Hence,
conventional channel estimation (CE) algorithms become incompatible with
RIS-aided communication systems as they fail to provide the necessary
information about the channel components, which are essential for a beneficial
RIS configuration. To enable the full potential of RISs, we propose to use
tensor-decomposition-based CE, which facilitates smart configuration of the RIS
by providing the required channel components. We use canonical polyadic (CP)
decomposition, that exploits a structured time domain pilot sequence. Compared
to other state-of-the-art decomposition methods, the proposed Semi-Algebraic CP
decomposition via Simultaneous Matrix Diagonalization (SECSI) algorithm is more
time efficient as it does not require an iterative process. The benefits of
SECSI for RIS-aided networks are validated with numerical results, which show
the improved individual and end-to-end CE accuracy of SECSI.
