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：研究了乘性和加性硬件损伤（HWI）对多输入多输出仿射频分复用（MIMO-AFDM）系统的影响。针对小规模MIMO-AFDM系统，推导了与最大似然（ML）检测器相关的紧密误码率（BER）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（LMMSE）检测器相关的闭合形式BER近似，涵盖了实际存在的不完美信道估计场景。我们的首个关键发现是：存在硬件损伤的AFDM系统的满分集阶数保持不变，这是一个独特的优势。此外，分析表明：1）所推导的BER结果能在中高信噪比（SNR）下准确预测模拟ML性能，而LMMSE检测器的理论BER曲线与基于蒙特卡洛的曲线紧密吻合；2）与正交频分复用（OFDM）系统相比，MIMO-AFDM对乘性失真（如相位噪声和载波频率偏移）具有更强的鲁棒性，这归因于其固有的啁啾信号特性；3）在相同加性HWI条件及不同速度值下，MIMO-AFDM始终优于传统MIMO-OFDM系统，实现更优的BER性能。后者是因为MIMO-AFDM对加性HWI引起的额外子载波间干扰（ICI）同样具有鲁棒性。简而言之，与OFDM相比，AFDM凭借其内在的啁啾信号结构及离散仿射傅里叶变换的有益扩频效应，即使在硬件损伤下也能展现更强的ICI鲁棒性并实现最大的满分集增益。