Efficient Off-Grid Near-Field Cascade Channel Estimation for XL-IRS Systems via Tucker Decomposition

Accurate cascaded channel state information is pivotal for unlocking the transformative capabilities of extremely large-scale intelligent reflecting surfaces (XL-IRS) in next-generation wireless networks. However, the expansive aperture of XL-IRSs induces spherical wavefront propagation due to near-field (NF) effects, complicating cascaded channel estimation. Conventional dictionary-based methods suffer from cumulative quantization errors and prohibitive computational complexity, particularly in practical uniform planar array (UPA)-structured array systems. To overcome these issues, we firstly propose a tensor modelization method for NF cascaded channels by exploiting the tensor product among the horizontal and vertical response vectors of the UPA-structured base station (BS) and the incident-reflective array response vector of the IRS. This tensor structure leverages the spatial characteristics of cascade channel, enabling independent estimation of the factor matrices to improve channel estimation efficiency. Meanwhile, to avoid quantization errors, we propose an off-grid cascaded channel estimation framework based on sparse Tucker decomposition. Specifically, we model the received signal as a Tucker tensor, where the sparse core tensor captures path gain-delay terms and three factor dictionary matrices are spanned by the BS array responses and the NF IRS array responses. Then, we formulate a sparse core tensor minimization problem with tri-modal logsum sparsity constraints to tackle the NP-hard challenge. Finally, the estimation method is further accelerated through higher-order singular value decomposition preprocessing, combined with the majorization-minimization strategy and a tailored tensor over-relaxation fast iterative shrinkage-thresholding technique. To evaluate the proposed algorithm, we derive the Cramér-Rao lower bound and conduct the convergence analysis. Simulations demonstrate that the proposed scheme achieves an 13.6 dB improvement in terms of the normalized mean square error compared to benchmark methods with significantly reduced runtime.