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.