As the demand for higher data throughput in coherent optical communication systems increases, we need to find ways to increase capacity in existing and future optical communication links. To address the demand for higher spectral efficiencies, we apply end-to-end optimization for joint geometric and probabilistic constellation shaping in the presence of Wiener phase noise and carrier phase estimation. Our approach follows state-of-the-art bitwise auto-encoders, which require a differentiable implementation of all operations between transmitter and receiver, including the DSP algorithms. In this work, we show how to modify the ubiquitous blind phase search (BPS) algorithm, a popular carrier phase estimation algorithm, to make it differentiable and include it in the end-to-end constellation shaping. By leveraging joint geometric and probabilistic constellation shaping, we are able to obtain a robust and pilot-free modulation scheme improving the performance of 64-ary communication systems by at least 0.1bit/symbol compared to square QAM constellations with neural demappers and by 0.05 bit/symbol compared to previously presented approaches applying only geometric constellation shaping.

翻译：随着相干光通信系统对更高数据吞吐量的需求日益增长，我们需要探索在现有及未来光通信链路中提升容量的方法。为满足更高频谱效率的要求，本文在存在维纳相位噪声和载波相位估计的情况下，采用端到端优化实现联合几何与概率星座成形。我们的方法遵循最先进的逐比特自编码器架构，要求发射机与接收机之间所有操作（包括数字信号处理算法）均能实现可微分实现。本研究展示了如何改进普适的盲相位搜索（BPS）算法（一种常用载波相位估计算法），使其具有可微分特性，并将其纳入端到端星座成形框架。通过联合几何与概率星座成形，我们获得了稳健且无需导频的调制方案，相比采用神经解映射器的方形QAM星座，该方案使64进制通信系统的性能至少提升0.1比特/符号，相较于仅应用几何星座成形的既有方法，性能提升达0.05比特/符号。