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Tensor Train Decomposition-based Channel Estimation for MIMO-AFDM Systems with Fractional Delay and Doppler

Ruizhe Wang, Cunhua Pan, Hong Ren, Haisu Wu, Jiangzhou Wang

TL;DR

A channel estimation algorithm based on Vandermonde-structured tensor-train (TT) decomposition is developed that achieves superior communication performance relative to the existing schemes, while offering a computational speedup, reducing the execution time by an order of magnitude compared to the state-of-the-art iterative algorithms.

Abstract

Affine Frequency Division Multiplexing (AFDM) has emerged as a promising chirp-based multicarrier technology for high-speed communication systems. To fully exploit the diversity gain offered by AFDM, accurate channel estimation is essential. However, existing studies have mainly focused on the integer-delay-tap scenario and single-symbol pilot-based estimation. Since delay taps in practice are generally fractional, approximating them as integers not only degrades delay estimation accuracy but also severely affects Doppler frequency estimation. To address this problem, in this paper, we investigate channel estimation for multiple-input multiple-output (MIMO)-AFDM systems. A time-affine frequency (T-AF) domain pilot structure is proposed to exploit time-domain phase variations. By leveraging the rotational invariance property in the spatial and temporal domains, a channel estimation algorithm based on Vandermonde-structured tensor-train (TT) decomposition is developed. The proposed algorithm demonstrates superior computational efficiency compared with state-of-the-art parameter estimation methods. Moreover, diverging from current studies, we derive the global Ziv-Zakai bound (ZZB) as an alternative parameter estimation error lower bound to the Cramér-Rao bound (CRB). Numerical results show that the derived ZZB provides tighter global performance characterization and successfully captures the threshold phenomenon in mean square error (MSE) performance in the low-SNR regime. Furthermore, the proposed algorithm achieves superior communication performance relative to the existing schemes, while offering a computational speedup, reducing the execution time by an order of magnitude compared to the state-of-the-art iterative algorithms.

Tensor Train Decomposition-based Channel Estimation for MIMO-AFDM Systems with Fractional Delay and Doppler

TL;DR

A channel estimation algorithm based on Vandermonde-structured tensor-train (TT) decomposition is developed that achieves superior communication performance relative to the existing schemes, while offering a computational speedup, reducing the execution time by an order of magnitude compared to the state-of-the-art iterative algorithms.

Abstract

Affine Frequency Division Multiplexing (AFDM) has emerged as a promising chirp-based multicarrier technology for high-speed communication systems. To fully exploit the diversity gain offered by AFDM, accurate channel estimation is essential. However, existing studies have mainly focused on the integer-delay-tap scenario and single-symbol pilot-based estimation. Since delay taps in practice are generally fractional, approximating them as integers not only degrades delay estimation accuracy but also severely affects Doppler frequency estimation. To address this problem, in this paper, we investigate channel estimation for multiple-input multiple-output (MIMO)-AFDM systems. A time-affine frequency (T-AF) domain pilot structure is proposed to exploit time-domain phase variations. By leveraging the rotational invariance property in the spatial and temporal domains, a channel estimation algorithm based on Vandermonde-structured tensor-train (TT) decomposition is developed. The proposed algorithm demonstrates superior computational efficiency compared with state-of-the-art parameter estimation methods. Moreover, diverging from current studies, we derive the global Ziv-Zakai bound (ZZB) as an alternative parameter estimation error lower bound to the Cramér-Rao bound (CRB). Numerical results show that the derived ZZB provides tighter global performance characterization and successfully captures the threshold phenomenon in mean square error (MSE) performance in the low-SNR regime. Furthermore, the proposed algorithm achieves superior communication performance relative to the existing schemes, while offering a computational speedup, reducing the execution time by an order of magnitude compared to the state-of-the-art iterative algorithms.
Paper Structure (16 sections, 65 equations, 11 figures, 1 table, 1 algorithm)

This paper contains 16 sections, 65 equations, 11 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. MIMO-AFDM System Model
  3. Pilot Structure Design And Channel Estimation Algorithm
  4. Proposed T-AF Embedded Pilot Structure
  5. Proposed Tensor Train based Channel Estimation Method
  6. Factor Matrices Retrieval
  7. Channel Parameters Estimation
  8. Complexity Analysis
  9. ZZB Anaysis
  10. Simulation Results
  11. Channel Parameters Estimate Performance
  12. Communication Performance Comparison with Existing Methods
  13. Versus OTFS and OFDM
  14. Conclusion
  15. Proof of Theorem 1
  16. ...and 1 more sections

Figures (11)

  • Figure 1: An example of MIMO-AFDM systems.
  • Figure 2: Proposed time-affine frequency domain embedded pilot structure.
  • Figure 3: The MSEs performance versus SNR.
  • Figure 4: The NMSE performance versus SNR.
  • Figure 5: The BER performance versus SNR for different order QAM modulations.
  • ...and 6 more figures