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

TL;DR

This paper introduces a tensor train decomposition-based channel estimation method for MIMO-AFDM systems that effectively handles fractional delays and Doppler effects, improving accuracy and computational efficiency.

Contribution

It proposes a novel channel estimation algorithm using Vandermonde-structured tensor-train decomposition and derives a tighter performance bound, addressing fractional delay challenges in AFDM systems.

Findings

The proposed method outperforms existing schemes in accuracy and speed.

ZZB provides a tighter bound than CRB in low-SNR regimes.

Algorithm achieves an order of magnitude faster execution time.

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 Cram\'{e}r-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.