Perturbation Theory-Aided Learned Digital Back-Propagation Scheme for Optical Fiber Nonlinearity Compensation

Derived from the regular perturbation treatment of the nonlinear Schrodinger\nequation, a machine learning-based scheme to mitigate the intra-channel optical\nfiber nonlinearity is proposed. Referred to as the perturbation theory-aided\n(PA) learned digital back-propagation (LDBP), the proposed scheme constructs a\ndeep neural network (DNN) in a way similar to the split-step Fourier method:\nlinear and nonlinear operations alternate. Inspired by the perturbation\nanalysis, the intra-channel cross-phase modulation term is conveniently\nrepresented by matrix operations in the DNN. The introduction of this term in\neach nonlinear operation considerably improves the performance, as well as\nenables the flexibility of PA-LDBP by adjusting the numbers of spans per step.\nThe proposed scheme is evaluated by numerical simulations of a single carrier\noptical fiber communication system operating at 32 Gbaud with 64-quadrature\namplitude modulation and 20*80 km transmission distance. The results show that\nthe proposed scheme achieves approximately 3.5 dB, 1.8 dB, 1.4 dB, and 0.5 dB\nperformance gain in terms of Q2 factor over the linear compensation, when the\nnumbers of spans per step are 1, 2, 4, and 10, respectively. Two methods are\nproposed to reduce the complexity of PALDBP, i.e., pruning the number of\nperturbation coefficients and chromatic dispersion compensation in the\nfrequency domain for multi-span per step cases. Investigation of the\nperformance and complexity suggests that PA-LDBP attains improved performance\ngains with reduced complexity when compared to LDBP in the cases of 4 and 10\nspans per step.\n