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Near-Field Sparse Bayesian Channel Estimation and Tracking for XL-IRS-Aided Wideband mmWave Systems

Xiaokun Tuo, Zijian Chen, Ming-Min Zhao, Changsheng You, Min-Jian Zhao

TL;DR

This work tackles CSI acquisition for XL-IRS aided wideband mmWave systems where near-field propagation and high-dimensional cascaded channels hinder estimation. It proposes TS-CET, a tensor-based sparse CET framework that employs a unified near-field channel model and hierarchical spatio-temporal priors to exploit 2D polar-domain block sparsity, 1D angular-delay clustering, and inter-frame temporal correlation. The algorithm combines tensor-based orthogonal matching pursuit for coarse estimation with a particle-based variational Bayesian inference and turbo-style message passing to obtain accurate marginal posteriors for channel gains, Doppler effects, and off-grid parameters, while minimizing pilot overhead. Simulation results show that TS-CET significantly improves NMSE over EM-OMP/FSBL baselines and achieves reliable tracking with as few as 6 pilots per tracking frame, highlighting its practical potential for 6G XL-IRS systems. The framework thus provides a principled, low-overhead approach to near-field CET that can adapt to dynamic user motion and sparse scattering in XL-IRS-aided networks.

Abstract

The rapid development of 6G systems demands advanced technologies to boost network capacity and spectral efficiency, particularly in the context of intelligent reflecting surfaces (IRS)-aided millimeter-wave (mmWave) communications. A key challenge here is obtaining accurate channel state information (CSI), especially with extremely large IRS (XL-IRS), due to near-field propagation, high-dimensional wideband cascaded channels, and the passive nature of the XL-IRS. In addition, most existing CSI acquisition methods fail to leverage the spatio-temporal sparsity inherent in the channel, resulting in suboptimal estimation performance. To address these challenges, we consider an XL-IRS-aided wideband multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system and propose an efficient channel estimation and tracking (CET) algorithm. Specifically, a unified near-field cascaded channel representation model is presented first, and a hierarchical spatio-temporal sparse prior is then constructed to capture two-dimensional (2D) block sparsity in the polar domain, one-dimensional (1D) clustered sparsity in the angle-delay domain, and temporal correlations across different channel estimation frames. Based on these priors, a tensor-based sparse CET (TS-CET) algorithm is proposed that integrates tensor-based orthogonal matching pursuit (OMP) with particle-based variational Bayesian inference (VBI) and message passing. Simulation results demonstrate that the TS-CET framework significantly improves the estimation accuracy and reduces the pilot overhead as compared to existing benchmark methods.

Near-Field Sparse Bayesian Channel Estimation and Tracking for XL-IRS-Aided Wideband mmWave Systems

TL;DR

This work tackles CSI acquisition for XL-IRS aided wideband mmWave systems where near-field propagation and high-dimensional cascaded channels hinder estimation. It proposes TS-CET, a tensor-based sparse CET framework that employs a unified near-field channel model and hierarchical spatio-temporal priors to exploit 2D polar-domain block sparsity, 1D angular-delay clustering, and inter-frame temporal correlation. The algorithm combines tensor-based orthogonal matching pursuit for coarse estimation with a particle-based variational Bayesian inference and turbo-style message passing to obtain accurate marginal posteriors for channel gains, Doppler effects, and off-grid parameters, while minimizing pilot overhead. Simulation results show that TS-CET significantly improves NMSE over EM-OMP/FSBL baselines and achieves reliable tracking with as few as 6 pilots per tracking frame, highlighting its practical potential for 6G XL-IRS systems. The framework thus provides a principled, low-overhead approach to near-field CET that can adapt to dynamic user motion and sparse scattering in XL-IRS-aided networks.

Abstract

The rapid development of 6G systems demands advanced technologies to boost network capacity and spectral efficiency, particularly in the context of intelligent reflecting surfaces (IRS)-aided millimeter-wave (mmWave) communications. A key challenge here is obtaining accurate channel state information (CSI), especially with extremely large IRS (XL-IRS), due to near-field propagation, high-dimensional wideband cascaded channels, and the passive nature of the XL-IRS. In addition, most existing CSI acquisition methods fail to leverage the spatio-temporal sparsity inherent in the channel, resulting in suboptimal estimation performance. To address these challenges, we consider an XL-IRS-aided wideband multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system and propose an efficient channel estimation and tracking (CET) algorithm. Specifically, a unified near-field cascaded channel representation model is presented first, and a hierarchical spatio-temporal sparse prior is then constructed to capture two-dimensional (2D) block sparsity in the polar domain, one-dimensional (1D) clustered sparsity in the angle-delay domain, and temporal correlations across different channel estimation frames. Based on these priors, a tensor-based sparse CET (TS-CET) algorithm is proposed that integrates tensor-based orthogonal matching pursuit (OMP) with particle-based variational Bayesian inference (VBI) and message passing. Simulation results demonstrate that the TS-CET framework significantly improves the estimation accuracy and reduces the pilot overhead as compared to existing benchmark methods.

Paper Structure

This paper contains 28 sections, 46 equations, 9 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Proposed Transmission Protocol
  3. System Model
  4. Transmission Protocol
  5. Channel Model
  6. Hierarchical Spatio-temporal Sparse Prior Model
  7. Polar-Angle-Delay Domain Sparse Representation of the Cascaded Channel
  8. Spatially Structured Sparse Probability Model for CE
  9. Probability Model for Channel Amplitude $\bm{\nu}$ and Phase $\bm{\omega}$
  10. Probability Model for Support Vector $\mathbf{s}$
  11. Probability Model for Support Vector $\mathbf{s}_R$
  12. Probability Model for Support Vectors $\mathbf{s}_U$ and $\mathbf{s}_K$
  13. Probability Model for DFO $f_d$ and Off-Grid Vectors $\bm{\Xi}$
  14. Temporally Dynamic Sparse Probability Model for CT
  15. Probability Model for Channel Amplitude $\bm{\nu}^{(2:T)}$ and Phase $\bm{\omega}^{(2:T)}$
  16. ...and 13 more sections

Figures (9)

  • Figure 1: System model of the considered XL-IRS-aided wideband mmWave system.
  • Figure 2: Transmission protocol.
  • Figure 3: Factor graphs of the 4-connected MRF (a) and the Markov chain (b). For clarity, only the factor nodes associated with the central variable node $s_{R,m}$ are plotted in the figure.
  • Figure 4: Flow chart of the proposed TS-CET algorithm.
  • Figure 5: Top-level diagram of the T-SPVBI method.
  • ...and 4 more figures