  Extremely large-scale multiple-input-multiple-output (XL-MIMO) with hybrid
precoding is a promising technique to meet the high data rate requirements for
future 6G communications. To realize efficient hybrid precoding, it is
essential to obtain accurate channel state information. Existing channel
estimation algorithms with low pilot overhead heavily rely on the channel
sparsity in the angle domain, which is achieved by the classical far-field
planar wavefront assumption. However, due to the non-negligible near-field
spherical wavefront property in XL-MIMO systems, this channel sparsity in the
angle domain is not available anymore, and thus existing far-field channel
estimation schemes will suffer from severe performance loss. To address this
problem, in this paper we study the near-field channel estimation by exploiting
the polar-domain sparse representation of the near-field XL-MIMO channel.
Specifically, unlike the classical angle-domain representation that only
considers the angle information of the channel, we propose a new polar-domain
representation, which simultaneously accounts for both the angle and distance
information. In this way, the near-field channel also exhibits sparsity in the
polar domain. By exploiting the channel sparsity in the polar domain, we
propose the on-grid and off-grid near-field channel estimation schemes for
XL-MIMO. Firstly, an on-grid polar-domain simultaneous orthogonal matching
pursuit (P-SOMP) algorithm is proposed to efficiently estimate the near-field
channel. Furthermore, to solve the resolution limitation of the on-grid P-SOMP
algorithm, an off-grid polar-domain simultaneous iterative gridless weighted
(P-SIGW) algorithm is proposed to improve the estimation accuracy, where the
parameters of the near-field channel are directly estimated. Finally, numerical
results are provided to verify the effectiveness of the proposed schemes.
