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Low-Complexity Channel Estimation for Internet of Vehicles AFDM Communications With Sparse Bayesian Learning

Xiangxiang Li, Haiyan Wang, Yao Ge, Xiaohong Shen, Miaowen Wen, Shun Zhang, Yong Liang Guan

TL;DR

This work addresses accurate AFDM channel estimation in high-mobility IoV scenarios by formulating the problem as sparse recovery on a virtual delay-Doppler grid and introducing Sparse Bayesian Learning (SBL) based off-grid estimators. The authors develop two off-grid solutions, GR-SBL with local grid refinement and GE-SBL with grid evolution via first-order approximation, and further reduce complexity through distributed schemes (D-GR-SBL and D-GE-SBL) that enable parallel processing. Simulation results show that GR-SBL delivers high precision with fine grid steps, while GE-SBL provides a better complexity-accuracy balance; distributed schemes achieve comparable performance with substantial latency reductions. Collectively, these methods enable reliable AFDM in doubly-dispersive channels for IoV while mitigating computational burdens, with potential impact on real-time vehicular communications and ISAC applications.

Abstract

Affine frequency division multiplexing (AFDM) has been considered as a promising waveform to enable high-reliable connectivity in the internet of vehicles. However, accurate channel estimation is critical and challenging to achieve the expected performance of the AFDM systems in doubly-dispersive channels. In this paper, we propose a sparse Bayesian learning (SBL) framework for AFDM systems and develop a dynamic grid update strategy with two off-grid channel estimation methods, i.e., grid-refinement SBL (GR-SBL) and grid-evolution SBL (GE-SBL) estimators. Specifically, the GR-SBL employs a localized grid refinement method and dynamically updates grid for a high-precision estimation. The GE-SBL estimator approximates the off-grid components via first-order linear approximation and enables gradual grid evolution for estimation accuracy enhancement. Furthermore, we develop a distributed computing scheme to decompose the large-dimensional channel estimation model into multiple manageable small-dimensional sub-models for complexity reduction of GR-SBL and GE-SBL, denoted as distributed GR-SBL (D-GR-SBL) and distributed GE-SBL (D-GE-SBL) estimators, which also support parallel processing to reduce the computational latency. Finally, simulation results demonstrate that the proposed channel estimators outperform existing competitive schemes. The GR-SBL estimator achieves high-precision estimation with fine step sizes at the cost of high complexity, while the GE-SBL estimator provides a better trade-off between performance and complexity. The proposed D-GR-SBL and D-GE-SBL estimators effectively reduce complexity and maintain comparable performance to GR-SBL and GE-SBL estimators, respectively.

Low-Complexity Channel Estimation for Internet of Vehicles AFDM Communications With Sparse Bayesian Learning

TL;DR

This work addresses accurate AFDM channel estimation in high-mobility IoV scenarios by formulating the problem as sparse recovery on a virtual delay-Doppler grid and introducing Sparse Bayesian Learning (SBL) based off-grid estimators. The authors develop two off-grid solutions, GR-SBL with local grid refinement and GE-SBL with grid evolution via first-order approximation, and further reduce complexity through distributed schemes (D-GR-SBL and D-GE-SBL) that enable parallel processing. Simulation results show that GR-SBL delivers high precision with fine grid steps, while GE-SBL provides a better complexity-accuracy balance; distributed schemes achieve comparable performance with substantial latency reductions. Collectively, these methods enable reliable AFDM in doubly-dispersive channels for IoV while mitigating computational burdens, with potential impact on real-time vehicular communications and ISAC applications.

Abstract

Affine frequency division multiplexing (AFDM) has been considered as a promising waveform to enable high-reliable connectivity in the internet of vehicles. However, accurate channel estimation is critical and challenging to achieve the expected performance of the AFDM systems in doubly-dispersive channels. In this paper, we propose a sparse Bayesian learning (SBL) framework for AFDM systems and develop a dynamic grid update strategy with two off-grid channel estimation methods, i.e., grid-refinement SBL (GR-SBL) and grid-evolution SBL (GE-SBL) estimators. Specifically, the GR-SBL employs a localized grid refinement method and dynamically updates grid for a high-precision estimation. The GE-SBL estimator approximates the off-grid components via first-order linear approximation and enables gradual grid evolution for estimation accuracy enhancement. Furthermore, we develop a distributed computing scheme to decompose the large-dimensional channel estimation model into multiple manageable small-dimensional sub-models for complexity reduction of GR-SBL and GE-SBL, denoted as distributed GR-SBL (D-GR-SBL) and distributed GE-SBL (D-GE-SBL) estimators, which also support parallel processing to reduce the computational latency. Finally, simulation results demonstrate that the proposed channel estimators outperform existing competitive schemes. The GR-SBL estimator achieves high-precision estimation with fine step sizes at the cost of high complexity, while the GE-SBL estimator provides a better trade-off between performance and complexity. The proposed D-GR-SBL and D-GE-SBL estimators effectively reduce complexity and maintain comparable performance to GR-SBL and GE-SBL estimators, respectively.

Paper Structure

This paper contains 11 sections, 2 theorems, 58 equations, 12 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. AFDM System Model
  3. Proposed Channel Estimation with Sparse Bayesian Learning
  4. Channel Estimation Model
  5. Sparse Bayesian Learning
  6. GR-SBL for Off-Grid Doppler Component Estimation
  7. GE-SBL for Off-Grid Doppler Component Estimation
  8. Genie Bound
  9. Proposed Low-Complexity Distributed Channel Estimation Scheme
  10. Simulation Results
  11. Conclusion

Key Result

Proposition 1

Based on 29, the logarithmic objective function ${\mathcal{L}} \left( \boldsymbol{\alpha}^{(t)}, \boldsymbol{\bar{S}}^{(t)}\right)$ can be further decoupled into the influence of $p$-th grid component $\mathcal{L} \left( \alpha_p^{(t)}, \bar{S}_p^{(t)} \right)$ and the influence of other grid compon where $\boldsymbol{\alpha}_{-p}^{(t)}$ denotes $\boldsymbol{\alpha}^{(t)}$ without the $p$-th eleme

Figures (12)

  • Figure 1: Pilot and data pattern for channel estimation in AFDM systems.
  • Figure 2: An example structure of virtual sampling grid $\boldsymbol{\bar{S}}$ with $\boldsymbol{\tilde{\ell}} = [0, 1]^{\text{T}}$ and $\boldsymbol{\tilde{k}} = [-1, 0, 1]^{\text{T}}$.
  • Figure 3: GR-SBL for off-grid Doppler component estimation.
  • Figure 4: GE-SBL for off-grid Doppler component estimation.
  • Figure 5: AFDM measurement matrix structure $\boldsymbol{\Phi} (\boldsymbol{\bar{S}})$ with five pilot symbols.
  • ...and 7 more figures

Theorems & Definitions (2)

  • Proposition 1
  • Proposition 2