  The employment of extremely large antenna arrays and high-frequency signaling
makes future 6G wireless communications likely to operate in the near-field
region. In this case, the spherical wave assumption which takes into account
both the user angle and distance is more accurate than the conventional planar
one that is only related to the user angle. Therefore, the conventional planar
wave based far-field channel model as well as its associated estimation
algorithms needs to be reconsidered. Here we first propose a
distance-parameterized angular-domain sparse model to represent the near-field
channel. In this model, the user distance is included in the dictionary as an
unknown parameter, so that the number of dictionary columns depends only on the
angular space division. This is different from the existing polar-domain
near-field channel model where the dictionary is constructed on an
angle-distance two-dimensional (2D) space. Next, based on this model, joint
dictionary learning and sparse recovery based channel estimation methods are
proposed for both line of sight (LoS) and multi-path settings. To further
demonstrate the effectiveness of the suggested algorithms, recovery conditions
and computational complexity are studied. Our analysis shows that with the
decrease of distance estimation error in the dictionary, the angular-domain
sparse vector can be exactly recovered after a few iterations. The high storage
burden and dictionary coherence issues that arise in the polar-domain 2D
representation are well addressed. Finally, simulations in multi-user
communication scenarios support the superiority of the proposed near-field
channel sparse representation and estimation over the existing polar-domain
method in channel estimation error.
