Near-Field Channel Estimation for Extremely Large-Scale Reconfigurable Intelligent Surface (XL-RIS)-Aided Wideband mmWave Systems

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.