Near-Field Channel Estimation for XL-RIS Assisted Multi-User XL-MIMO Systems: Hybrid Beamforming Architectures

Channel estimation is one of the key challenges for the deployment of extremely large-scale reconfigurable intelligent surface (XL-RIS) assisted multiple-input multiple-output (MIMO) systems. In this paper, we study the channel estimation problem for XL-RIS assisted multi-user XL-MIMO systems with hybrid beamforming structures. For this system, we propose an {\em unified} channel estimation method that yields a notable estimation accuracy in the near-field BS-RIS and near-field RIS-User channels (in short, near-near field channels), far-near field channels, and far-far field channels. Our key idea is that the effective (or cascaded) channels to be estimated can be each factorized as the product of low-rank matrices (i.e., the product of the common (or user-independent) matrix and the user-specific coefficient matrix). The common matrix whose columns are the basis of the column space of the BS-RIS channel matrix is efficiently estimated via a {\em collaborative} low-rank approximation (CLRA). Leveraging the hybrid beamforming structures, we develop an efficient iterative algorithm that jointly optimizes the user-specific coefficient matrices. Via experiments and complexity analysis, we verify the effectiveness of the proposed channel estimation method (named CLRA-JO) in the aforementioned three classes of wireless channels.