Affine frequency division multiplexing (AFDM) is a strong candidate for the sixth-generation wireless network thanks to its strong resilience to delay-Doppler spreads. In this letter, we investigate the error performance of coded AFDM systems in doubly selective channels. We first study the conditional pairwise-error probability (PEP) of AFDM system and derive its conditional coding gain. Then, we show that there is a fundamental trade-off between the diversity gain and the coding gain of AFDM system, namely the coding gain declines with a descending speed with respect to the number of separable paths, while the diversity gain increases linearly. Moreover, we propose a near-optimal turbo decoder based on the sum-product algorithm for coded AFDM systems to improve its error performance. Simulation results verify our analyses and the effectiveness of the proposed turbo decoder, showing that AFDM outperforms orthogonal frequency division multiplexing (OFDM) and orthogonal time frequency space (OTFS) in both coded and uncoded cases over high-mobility channels.

翻译：仿射频率分复用（AFDM）凭借其对时延-多普勒扩展的强鲁棒性，成为第六代无线网络的有力候选技术。本文研究了编码AFDM系统在双选择性信道中的差错性能。我们首先分析了AFDM系统的条件成对差错概率（PEP）并推导其条件编码增益。进而发现AFDM系统的分集增益与编码增益存在基本权衡关系：编码增益随可分离路径数增加呈递减速度下降，而分集增益呈线性增长。此外，我们提出了一种基于和积算法的近最优Turbo译码器以提升编码AFDM系统的差错性能。仿真结果验证了理论分析及所提Turbo译码器的有效性，表明在高移动性信道中，AFDM在编码与未编码场景下均优于正交频分复用（OFDM）和正交时频空（OTFS）系统。