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)已成为高速通信系统中一种具有前景的基于啁啾波的多载波技术。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，现有研究主要集中于整数时延抽头场景及基于单符号导频的估计方法。由于实际中的时延抽头通常为分数值，将其近似为整数不仅会降低时延估计精度，还会严重影响多普勒频率估计。为解决该问题，本文研究了多输入多输出(MIMO)-AFDM系统的信道估计。提出了一种时域-仿射频域导频结构以利用时域相位变化特性。通过利用空域和时域的旋转不变性，开发了一种基于范德蒙结构张量链分解的信道估计算法。与现有参数估计方法相比，所提算法展现出更优的计算效率。此外，不同于当前研究，本文推导了全局Ziv-Zakai界作为克拉美-罗界的替代参数估计误差下界。数值结果表明，所推导的ZZB能提供更紧致的全局性能表征，并成功捕捉了低信噪比区域均方误差性能中的阈值现象。进一步地，所提算法相对于现有方案实现了更优的通信性能，同时提供计算加速，与现有迭代算法相比执行时间降低了一个数量级。