On the heels of orthogonal time frequency space (OTFS) modulation, the recently discovered affine frequency division multiplexing (AFDM) is a promising waveform for the sixth-generation wireless network. In this paper, we study the widely-used embedded pilot-aided (EPA) channel estimation in multiple-input multiple-output AFDM (MIMO-AFDM) system with fractional Doppler shifts. We first formulate the vectorized input-output relationship of MIMO-AFDM, and theoretically prove that MIMO-AFDM can achieve full diversity in doubly selective channels. Then we illustrate the implementation of EPA channel estimation in MIMO-AFDM and unveil that serious inter-Doppler interference (IDoI) occurs if we try to estimate the channel gain, delay shift, and Doppler shift of each propagation path. To address this issue, the diagonal reconstructability of AFDM subchannel matrix is studied and a low-complexity embedded pilot-aided diagonal reconstruction (EPA-DR) channel estimation scheme is proposed. The EPA-DR scheme calculates the AFDM effective channel matrix directly without estimating the three channel parameters, eliminating the severe IDoI inherently. Since the effective channel matrix is necessary for MIMO-AFDM receive processing, we believe this is an important step to bring AFDM towards practical communication systems. Finally, we investigate the orthogonal resource allocation of affine frequency division multiple access (AFDMA) system. Simulation results validate the effectiveness of the proposed EPA-DR scheme.

翻译：继正交时频空间（OTFS）调制之后，最新发现的仿射频分复用（AFDM）技术成为第六代无线网络的一种有前途的波形。本文研究了存在分数多普勒频移的多输入多输出-仿射频分复用（MIMO-AFDM）系统中广泛使用的嵌入式导频辅助（EPA）信道估计方法。我们首先建立MIMO-AFDM的向量化输入输出关系，并从理论上证明MIMO-AFDM在双选择性信道中能够实现全分集增益。随后阐述了EPA信道估计在MIMO-AFDM中的实现过程，并揭示出在尝试估计每条传播路径的信道增益、时延偏移和多普勒频移时会出现严重的多普勒间干扰（IDoI）。为解决该问题，本文研究了AFDM子信道矩阵的对角重构特性，并提出了一种低复杂度的嵌入式导频辅助对角重构（EPA-DR）信道估计方案。该方案无需估计三个信道参数即可直接计算AFDM有效信道矩阵，从而从根本上消除了严重的多普勒间干扰。由于有效信道矩阵是MIMO-AFDM接收处理的关键，我们认为这项研究对推动AFDM走向实用通信系统具有重要意义。最后，我们探讨了仿射频分多址（AFDMA）系统的正交资源分配问题。仿真结果验证了所提EPA-DR方案的有效性。