The performance of different probabilistic amplitude shaping (PAS) techniques in the nonlinear regime is investigated, highlighting its dependence on the PAS block length and the interaction with carrier phase recovery (CPR). Different PAS implementations are considered, based on different distribution matching (DM) techniques-namely, sphere shaping, shell mapping with different number of shells, and constant composition DM-and amplitude-to-symbol maps. When CPR is not included, PAS with optimal block length provides a nonlinear shaping gain with respect to a linearly optimized PAS (with infinite block length); among the considered DM techniques, the largest gain is obtained with sphere shaping. On the other hand, the nonlinear shaping gain becomes smaller, or completely vanishes, when CPR is included, meaning that in this case all the considered implementations achieve a similar performance for a sufficiently long block length. Similar results are obtained in different link configurations (1x180km, 15x80km, and 27x80km single-mode-fiber links), and also including laser phase noise, except when in-line dispersion compensation is used. Furthermore, we define a new metric, the nonlinear phase noise (NPN) metric, which is based on the frequency resolved logarithmic perturbation models and explains the interaction of CPR and PAS. We show that the NPN metric is highly correlated with the performance of the system. Our results suggest that, in general, the optimization of PAS in the nonlinear regime should always account for the presence of a CPR algorithm. In this case, the reduction of the rate loss (obtained by using sphere shaping and increasing the DM block length) turns out to be more important than the mitigation of the nonlinear phase noise (obtained by using constant-energy DMs and reducing the block length), the latter being already granted by the CPR algorithm.

翻译：针对不同概率幅度整形（PAS）技术在非线性区域内的性能进行了研究，重点揭示了其对PAS块长度的依赖性以及与载波相位恢复（CPR）的交互作用。基于不同的分布匹配（DM）技术——即球形整形、不同壳数的壳映射以及恒定成分DM——和幅度-符号映射，考虑了多种PAS实现方案。当未包含CPR时，具有最优块长度的PAS相对于线性优化的PAS（无限块长度）可提供非线性整形增益；在所考虑的DM技术中，球形整形获得了最大增益。另一方面，当包含CPR时，非线性整形增益减小甚至完全消失，这意味着在此情况下，对于足够长的块长度，所有考虑的实现方案性能相似。在不同链路配置（1×180km、15×80km和27×80km单模光纤链路）中，以及在包含激光相位噪声的情况下（使用在线色散补偿时除外），得到了类似的结果。此外，我们定义了一个新指标——非线性相位噪声（NPN）指标，该指标基于频率分辨的对数微扰模型，并解释了CPR与PAS的交互作用。研究表明，NPN指标与系统性能高度相关。我们的结果表明，通常而言，在非线性区域内优化PAS时，应始终考虑CPR算法的存在。在此情况下，降低速率损失（通过使用球形整形和增加DM块长度实现）比减轻非线性相位噪声（通过使用恒定能量DM和减小块长度实现）更为重要，后者已由CPR算法保障。