Abstract

Derived from the regular perturbation treatment of the nonlinear Schrödinger equation, a machine learning-based scheme to mitigate the intra-channel optical fiber nonlinearity is proposed. Referred to as the perturbation theory-aided (PA) learned digital back propagation (LDBP), the proposed scheme constructs a deep neural network (DNN) in a way similar to the split-step Fourier method: linear and nonlinear operations alternate. Inspired by the perturbation analysis, the intra-channel cross phase modulation term is conveniently represented by matrix operations in the DNN. The introduction of this term in each nonlinear operation considerably improves the performance, as well as enables the flexibility of PA-LDBP by adjusting the numbers of spans per step. The proposed scheme is evaluated by numerical simulations of a single-carrier optical fiber communication system operating at 32 Gbaud with 64-quadrature amplitude modulation and 20 × 80 km transmission distance. The results show that the proposed scheme achieves approximately 1 dB, 1.2 dB, 1.2 dB, and 0.5 dB performance gain in terms of ${\it Q}$ factor over LDBP, when the numbers of spans per step are 1, 2, 4, and 10, respectively. Two methods are proposed to reduce the complexity of PA-LDBP, i.e., pruning the number of perturbation coefficients and chromatic dispersion compensation in the frequency domain for multi-span per step cases. Investigation of the performance and complexity suggests that PA-LDBP attains improved performance gains with reduced complexity when compared to LDBP in the cases of 4 and 10 spans per step.

Joint intra and inter-channel nonlinear compensation scheme based on improved learned digital back propagation for WDM systems

Xinyu Chi, Chenglin Bai, Fan Yang, Qi Qi, Ruohui Zhang, Hengying Xu, Lishan Yang, Wanxiang Bi, Tianchi Chen, and Shunchang Bai
Opt. Express 32(4) 5095-5116 (2024)

Learning-based digital back propagation to compensate for fiber nonlinearity considering self-phase and cross-phase modulation for wavelength-division multiplexed systems

Takashi Inoue, Ryosuke Matsumoto, and Shu Namiki
Opt. Express 30(9) 14851-14872 (2022)

Correlated digital back propagation based on perturbation theory

Xiaojun Liang and Shiva Kumar
Opt. Express 23(11) 14655-14665 (2015)

Inverse regular perturbation with ML-assisted phasor correction for fiber nonlinearity compensation

Hubert Dzieciol, Toshiaki Koike-Akino, Ye Wang, and Kieran Parsons
Opt. Lett. 47(14) 3471-3474 (2022)

Equalization in dispersion-managed systems using learned digital back-propagation

Mohannad Abu-romoh, Nelson Costa, Yves Jaouën, Antonio Napoli, João Pedro, Bernhard Spinnler, and Mansoor Yousefi
Opt. Continuum 2(10) 2088-2105 (2023)