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

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