  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.
