Recently, neural network (NN) nonlinear equalizers which are expected to reduce computational complexity have attracted attention as fiber nonlinear compensation methods for coherent optical transmission systems. However, these fiber nonlinear compensation methods have problems that training of NN is not easy for long-distance transmission systems because of accumulated phase noise. In this letter, we propose a training method of NN nonlinear equalizer using the target outputs including phase noise which is produced by received signals. The phase noise is estimated by the inverse modulation of received signals and filtering. The estimated phase noise is added to transmitter signals, and the target outputs are obtained. The target outputs allow training of NN in long-distance coherent optical transmission systems. Since the NN trained by this proposed method compensates only for fiber nonlinearities, the phase locked loop (PLL) is placed after the NN to compensate for phase noise. The performances are evaluated by the simulation of 32 Gbaud 16QAM 4000 km long-distance coherent optical transmission. These results indicate that the proposed training method is effective in training NN nonlinear equalizer in long-distance coherent optical transmission in the presence of phase noise.

中文翻译：

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长距离相干光传输系统中的神经网络非线性均衡器

最近，作为用于相干光传输系统的光纤非线性补偿方法，期望减少计算复杂性的神经网络（NN）非线性均衡器引起了人们的关注。然而，这些光纤非线性补偿方法存在的问题是，由于累积的相位噪声，对于长距离传输系统而言，NN的训练不容易。在这封信中，我们提出了一种使用目标输出（包括由接收信号产生的相位噪声）的NN非线性均衡器的训练方法。通过接收信号的逆调制和滤波来估计相位噪声。估计的相位噪声被添加到发射机信号中，并获得目标输出。目标输出允许在长距离相干光传输系统中训练NN。由于通过此方法训练的神经网络仅补偿光纤的非线性，因此将锁相环（PLL）放置在神经网络之后以补偿相位噪声。通过对32 Gbaud 16QAM 4000 km长距离相干光传输的仿真来评估性能。这些结果表明，所提出的训练方法对于在相位噪声存在下的长距离相干光传输中的NN非线性均衡器的训练是有效的。