  Future sixth-generation (6G) systems are expected to leverage extremely
large-scale multiple-input multiple-output (XL-MIMO) technology, which
significantly expands the range of the near-field region. While accurate
channel estimation is essential for beamforming and data detection, the unique
characteristics of near-field channels pose additional challenges to the
effective acquisition of channel state information. In this paper, we propose a
novel codebook design, which allows efficient near-field channel estimation
with significantly reduced codebook size. Specifically, we consider the
eigen-problem based on the near-field electromagnetic wave transmission model.
Moreover, we derive the general form of the eigenvectors associated with the
near-field channel matrix, revealing their noteworthy connection to the
discrete prolate spheroidal sequence (DPSS). Based on the proposed near-field
codebook design, we further introduce a two-step channel estimation scheme.
Simulation results demonstrate that the proposed codebook design not only
achieves superior sparsification performance of near-field channels with a
lower leakage effect, but also significantly improves the accuracy in
compressive sensing channel estimation.
