  Near-field communications present new opportunities over near-field channels,
however, the spherical wavefront propagation makes near-field signal processing
challenging. In this context, this paper proposes efficient near-field channel
estimation methods for wideband MIMO mmWave systems with the aid of extremely
large-scale reconfigurable intelligent surfaces (XL-RIS). For the wideband
signals reflected by the analog RIS, we characterize their near-field beam
squint effect in both angle and distance domains. Based on the mathematical
analysis of the near-field beam patterns over all frequencies, a wideband
spherical-domain dictionary is constructed by minimizing the coherence of two
arbitrary beams. In light of this, we formulate a two-dimensional compressive
sensing problem to recover the channel parameter based on the spherical-domain
sparsity of mmWave channels. To this end, we present a correlation
coefficient-based atom matching method within our proposed multi-frequency
parallelizable subspace recovery framework for efficient solutions.
Additionally, we propose a two-dimensional oracle estimator as a benchmark and
derive its lower bound across all subcarriers. Our findings emphasize the
significance of system hyperparameters and the sensing matrix of each
subcarrier in determining the accuracy of the estimation. Finally, numerical
results show that our proposed method achieves considerable performance
compared with the lower bound and has a time complexity linear to the number of
RIS elements.
