The impact of both multiplicative and additive hardware impairments (HWIs) on multiple-input multiple-output affine frequency division multiplexing (MIMO-AFDM) systems is investigated. For small-scale MIMO-AFDM systems, a tight bit error rate (BER) upper bound associated with the maximum likelihood (ML) detector is derived. By contrast, for large-scale systems, a closed-form BER approximation associated with the linear minimum mean squared error (LMMSE) detector is presented, including realistic imperfect channel estimation scenarios. Our first key observation is that the full diversity order of a hardware-impaired AFDM system remains unaffected, which is a unique advantage. Furthermore, our analysis shows that 1) the BER results derived accurately predict the simulated ML performance in moderate-to-high signal-to-noise ratios (SNRs), while the theoretical BER curve of the LMMSE detector closely matches that of the Monte-Carlo based one. 2) MIMO-AFDM is more resilient to multiplicative distortions, such as phase noise and carrier frequency offset, compared to its orthogonal frequency division multiplexing (OFDM) counterparts. This is attributed to its inherent chirp signal characteristics; 3) MIMO-AFDM consistently achieves superior BER performance compared to conventional MIMO-OFDM systems under the same additive HWI conditions, as well as different velocity values. The latter is because MIMO-AFDM is also resilient to the additional inter-carrier interference (ICI) imposed by the nonlinear distortions of additive HWIs. In a nutshell, compared to OFDM, AFDM demonstrates stronger ICI resilience and achieves the maximum full diversity attainable gain even under HWIs, thanks to its intrinsic chirp signalling structure as well as to the beneficial spreading effect of the discrete affine Fourier transform.

翻译：本文研究了乘性与加性硬件损伤对多输入多输出仿射频分复用系统的影响。针对小规模 MIMO-AFDM 系统，推导了与最大似然检测器相关的误码率紧致上界。相比之下，针对大规模系统，给出了与线性最小均方误差检测器相关的闭式误码率近似，包括实际非理想信道估计场景。我们的第一个关键发现是，受硬件损伤的 AFDM 系统的全分集阶数保持不变，这是一个独特优势。此外，分析表明：1）所推导的误码率结果能准确预测中高信噪比下仿真 ML 性能，而 LMMSE 检测器的理论误码率曲线与基于蒙特卡罗仿真的结果高度吻合；2）与正交频分复用系统相比，MIMO-AFDM 对相位噪声和载波频率偏移等乘性失真具有更强的鲁棒性，这归因于其固有的线性调频信号特性；3）在相同加性硬件损伤条件及不同速度值下，MIMO-AFDM 始终比传统 MIMO-OFDM 系统获得更优的误码率性能。后者是因为 MIMO-AFDM 对加性硬件损伤非线性失真引入的额外载波间干扰同样具有抵抗能力。简而言之，得益于其内在的线性调频信号结构以及离散仿射傅里叶变换的有益扩展效应，与 OFDM 相比，AFDM 展现出更强的 ICI 鲁棒性，即使在硬件损伤条件下也能实现可达的最大全分集增益。