A Harmony Composition-Inspired Tensor Modalization Method for Near-Field IRS Channel Estimation

Intelligent reflecting surfaces (IRSs) are poised to revolutionize next-generation wireless communication systems by enhancing channel quality and spectrum efficiency through advanced wave manipulation. However, extremely large-scale IRS {(XL-IRS)} deployments face significant challenges in channel estimation due to multiplicative path loss and near-field (NF) effects, where spherical wavefronts couple distance and angle parameters. Existing polar-domain codebook-based compressive sensing methods for NF channel estimation suffer from low accuracy and high complexity, caused by the need for high-resolution grids of both distance and angle parameters. To address this, we propose a harmonic processing-inspired channel estimation framework for NF {XL-IRS} systems by leveraging tensor modalization to decouple channel parameters. Drawing an analogy to musical harmonic analysis, our approach decomposes the high-dimensional NF channel tensor into independent factor matrices, modeled as ``chords," representing distance and angle parameters. Through harmonic analysis-inspired distance parameter decoupling, we design a compact, distance-dependent codebook that enables high-resolution NF channel parameter estimation. This approach significantly reduces the codebook size compared to polar-domain methods. {Then, we} derive the Cramér-Rao lower bound (CRLB) to evaluate the estimators. Finally, simulation results show an 8.5 dB improvement in normalized mean square error (NMSE) compared to conventional methods, underscoring its low complexity and high accuracy.

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

Accurate cascaded channel state information is pivotal for extremely large-scale intelligent reflecting surfaces (XL-IRS) in next-generation wireless networks. However, the large XL-IRS aperture induces spherical wavefront propagation due to near-field (NF) effects, complicating cascaded channel estimation. Conventional dictionary-based methods suffer from cumulative quantization errors and high complexity, especially in uniform planar array (UPA) systems. To address these issues, we first 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 structure leverages spatial characteristics, enabling independent estimation of factor matrices to improve 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 matrices are spanned by BS and NF IRS array responses. We then formulate a sparse core tensor minimization problem with tri-modal log-sum sparsity constraints to tackle the NP-hard challenge. Finally, the method is accelerated via higher-order singular value decomposition preprocessing, combined with majorization-minimization and a tailored tensor over-relaxation fast iterative shrinkage-thresholding technique. We derive the Cramér-Rao lower bound and conduct convergence analysis. Simulations show the proposed scheme achieves a 13.6 dB improvement in normalized mean square error over benchmarks with significantly reduced runtime.