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

Wenzhou Cao, Yashuai Cao, Tiejun Lv, Mugen Peng

Abstract

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.

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

Abstract

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.
Paper Structure (16 sections, 68 equations, 10 figures, 1 table, 1 algorithm)

This paper contains 16 sections, 68 equations, 10 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Motivations and Contributions
  4. System Model
  5. Channel Model
  6. Observation Signal Tensor Model
  7. Off-Grid Tucker Decomposition-Based NF Cascaded Channel Estimation Framework
  8. Problem Formulation
  9. Cascaded Channel Recovery Algorithm
  10. Multi-Antenna User Scenario
  11. Algorithm Analysis
  12. Convergence Analysis
  13. Cramér-Rao Bound Analysis
  14. Complexity Analysis
  15. Simulation Results
  16. ...and 1 more sections

Figures (10)

  • Figure 1: NF XL-IRS-assisted communication systems.
  • Figure 2: Schematic diagram of the proposed NF IRS cascaded channel estimation algorithm based on Tucker decomposition: 1) Construct the cascaded channel and observation signal tensors; 2) Perform Tucker decomposition to formulate the objective function and apply an off-grid estimation approach to obtain the core tensor and factor matrices; 3) Based on the estimated core tensor and factor matrices, the estimated cascade channel is recovered.
  • Figure 3: Computational complexity comparison for different methods vs. dimension of the received signal.
  • Figure 4: Convergence behavior vs. SNR.
  • Figure 5: NMSE comparison for different algorithms. (a) UE-IRS distance of (5 m, 10 m). (b) UE-IRS distance of (10 m, 15 m).
  • ...and 5 more figures

Theorems & Definitions (2)

  • Remark 1
  • Remark 2