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

2026-03-10

AI Summary

This work addresses the performance degradation in existing MIMO-AFDM channel estimation methods, which typically assume integer delay taps and thus fail to accurately model the fractional delays and Doppler shifts commonly present in practical channels. To overcome this limitation, the paper proposes a time–affine frequency-domain pilot structure and introduces, for the first time, a tensor train (TT) decomposition-based channel estimation algorithm leveraging space–time rotational invariance, yielding a Vandermonde-structured TT formulation that enables efficient joint estimation of fractional delays and Doppler shifts. Furthermore, the authors derive the Ziv–Zakai bound (ZZB) as a new benchmark for performance evaluation in the low-SNR regime, surpassing the limitations of the conventional Cramér–Rao bound (CRB). The proposed algorithm achieves an order-of-magnitude speedup over existing iterative methods while maintaining superior communication performance, and the ZZB provides a tighter characterization of the mean-square error’s threshold effect at low SNR.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Matrix & Tensor Methods
• Intelligent Robots: State Estimation

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

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.

Problem

• Channel Estimation
• MIMO-AFDM
• Fractional Delay
• Doppler
• Tensor Train Decomposition

Innovation

• Tensor Train Decomposition
• MIMO-AFDM
• Fractional Delay and Doppler
• Ziv-Zakai Bound
• Vandermonde Structure