  Extremely large-scale massive MIMO (XL-MIMO) has been reviewed as a promising
technology for future wireless communications. The deployment of XL-MIMO,
especially at high-frequency bands, leads to users being located in the
near-field region instead of the conventional far-field. This letter proposes
efficient model-based deep learning algorithms for estimating the near-field
wireless channel of XL-MIMO communications. In particular, we first formulate
the XL-MIMO near-field channel estimation task as a compressed sensing problem
using the spatial gridding-based sparsifying dictionary, and then solve the
resulting problem by applying the Learning Iterative Shrinkage and Thresholding
Algorithm (LISTA). Due to the near-field characteristic, the spatial
gridding-based sparsifying dictionary may result in low channel estimation
accuracy and a heavy computational burden. To address this issue, we further
propose a new sparsifying dictionary learning-LISTA (SDL-LISTA) algorithm that
formulates the sparsifying dictionary as a neural network layer and embeds it
into LISTA neural network. The numerical results show that our proposed
algorithms outperform non-learning benchmark schemes, and SDL-LISTA achieves
better performance than LISTA with ten times atoms reduction.
