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.

翻译：仿射频分复用（AFDM）作为一种基于线性调频信号的多载波技术，已成为高速通信系统的重要候选方案。为充分利用AFDM提供的分集增益，精确的信道估计至关重要。然而，现有研究主要关注整数延迟抽头场景和单符号导频估计。由于实际中的延迟抽头通常为分数，将其近似为整数不仅会降低延迟估计精度，还会严重影响多普勒频率估计。针对这一问题，本文研究了多输入多输出（MIMO）-AFDM系统的信道估计。我们提出了一种时-仿射频（T-AF）域导频结构，以利用时域相位变化。通过利用空间域和时间域的旋转不变性，开发了一种基于范德蒙德结构张量列（TT）分解的信道估计算法。与最先进的参数估计方法相比，该算法展现出更高的计算效率。此外，与现有研究不同，我们推导了全局Ziv-Zakai界（ZZB）作为Cramér-Rao界（CRB）之外的参数估计误差下界。数值结果表明，所推导的ZZB提供了更紧致的全局性能表征，并成功捕捉了低信噪比（SNR）区域下均方误差（MSE）性能的阈值现象。同时，与现有方案相比，所提出的算法实现了更优的通信性能，并在计算速度上展现出优势——与最先进的迭代算法相比，执行时间降低了一个数量级。