In this work, we investigate the joint visibility region (VR) detection and channel estimation (CE) problem for extremely large-scale multiple-input-multiple-output (XL-MIMO) systems considering both the spherical wavefront effect and spatial non-stationary (SnS) property. Unlike existing SnS CE methods that rely on the statistical characteristics of channels in the spatial or delay domain, we propose an approach that simultaneously exploits the antenna-domain spatial correlation and the wavenumber-domain sparsity of SnS channels. To this end, we introduce a two-stage VR detection and CE scheme. In the first stage, the belief regarding the visibility of antennas is obtained through a VR detection-oriented message passing (VRDO-MP) scheme, which fully exploits the spatial correlation among adjacent antenna elements. In the second stage, leveraging the VR information and wavenumber-domain sparsity, we accurately estimate the SnS channel employing the belief-based orthogonal matching pursuit (BB-OMP) method. Simulations show that the proposed algorithms lead to a significant enhancement in VR detection and CE accuracy as compared to existing methods, especially in low signal-to-noise ratio (SNR) scenarios.

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