We propose Four-Dimensional (4D) energy limit enumerative sphere shaping (ESS) of $M$-QAM signaling to minimize rate loss and improve the transmission performance over non-linear WDM optical-fiber systems. Simulation results show that the proposed scheme outperforms the conventional ESS by $0.19$~bit/4D-symbol in achievable information rate over a $205$-km single-span link and a WDM transmission of five polarization-division-multiplexed channels with $400$-Gbit/s net rate per channel. We also study the achieved performance over several shaping block lengths and show that the achieved gains do not scale well over multi-span systems.

翻译：我们提出了一种基于$M$-QAM信号的四维能量限制枚举球形整形方案，以最小化速率损失并提升非线性波分复用光纤系统的传输性能。仿真结果表明，在205公里单跨链路及每信道净速率400吉比特/秒的五信道偏振复用波分复用传输系统中，所提方案在可达信息速率上相比传统球形整形提升0.19比特/四维符号。我们还研究了不同整形块长度下的性能表现，结果表明在多跨系统中该增益的扩展性有限。