Nested Tensor-Based Channel Estimation for Stacked Intelligent Metasurface-Assisted Wireless Networks

Stacked intelligent metasurface (SIM) is an emerging technology that uses multiple reconfigurable intelligent surface (RIS) layers to enable wave-based beamforming. Both channel estimation and the calibration of inter-layer channel coefficients, that is, the channels between consecutive RIS layers, play a crucial role in the performance of SIM-assisted systems. However, the execution of these essential tasks can be challenging due to the large dimensionality inherent in the SIM architecture. In this letter, we address this challenge by proposing a novel tensor-based joint channel estimation and inter-layer channel coefficients calibration protocol exploiting the PARATUCK2 decomposition and the alternating least squares method, which can be applied to an SIM-assisted multi-user multiple-input single-output system to reduce the complexity of the multi-layer SIM structure. Numerical results prove the superiority of the proposed scheme in comparison with state-of-the-art schemes. Specifically, the proposed tensor-based protocol can achieve a normalized mean squared error of less than 0.01, which is orders of magnitude better than state-of-the-art schemes for SIM-assisted systems, while incurring similar levels of computational complexity or training overhead.