  This letter proposes a high-resolution channel estimation for reconfigurable
intelligent surface (RIS)-assisted communication networks. We exploit the
inherent geometrical structure of the Terahertz propagation channel, including
the antenna array geometries at the base station, the RIS, and the user
equipment to design a tensor-based high-resolution channel estimator, referred
to as the higher-dimensional rank-one approximations (HDR) method. By
exploiting the geometrical structure of the combined base station-RIS-user
equipment channel, the proposed HDR estimator recasts parametric channel
estimation as a single sixth-order rank-one tensor approximation problem, which
can be efficiently solved using higher-order singular value decomposition to
deliver parallel estimates of each channel component vector. Numerical results
show that the proposed method provides significantly more accurate parameter
estimates compared to the competing state-of-the-art Khatri-Rao factorization
and least squares methods. The HDR method also leads to higher spectral
efficiency than its competitors, especially in the low signal-to-noise ratio
regime, while having similar computational complexity as the classical least
squares method.
