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ML-Enhanced Digital Backpropagation for Long-Reach Single-Span Systems

Dario Cellini, Stella Civelli, Marco Secondini

TL;DR

This work addresses the high computational burden of digital backpropagation (DBP) in coherent optical systems by proposing Learned ESSFM (L-ESSFM), an ML-driven, parameterized variant of the FFT-based enhanced SSFM (ESSFM). L-ESSFM treats each backpropagation step as a layer in a deep neural network, jointly optimizing the step lengths $L_i$ and nonlinear phase rotation filter (NLPR) coefficients $oldsymbol{c}_i$ across all steps, with FFT-based linear and nonlinear operations and overlap-and-save. Offline training on blocks of i.i.d. complex Gaussian symbols enables these parameters to be learned, resulting in real-time complexity that matches CB-ESSFM for a single band. In a 5×93 GBd WDM system over a 170 km single-span link, L-ESSFM with four steps provides about 0.8 dB gain over electronic dispersion compensation at $172 \, RM/2D$, while requiring only a fraction of the RM/2D compared with ESSFM and far less complexity than LDBP, demonstrating a favorable accuracy–complexity trade-off and potential for extension to long-haul systems and subband processing.

Abstract

We propose a digital backpropagation method that employs machine-learning-aided joint optimization of dispersion step lengths and nonlinear phase rotation filters within an FFT-based enhanced split-step Fourier structure, achieving improved accuracy at low computational complexity.

ML-Enhanced Digital Backpropagation for Long-Reach Single-Span Systems

TL;DR

This work addresses the high computational burden of digital backpropagation (DBP) in coherent optical systems by proposing Learned ESSFM (L-ESSFM), an ML-driven, parameterized variant of the FFT-based enhanced SSFM (ESSFM). L-ESSFM treats each backpropagation step as a layer in a deep neural network, jointly optimizing the step lengths and nonlinear phase rotation filter (NLPR) coefficients across all steps, with FFT-based linear and nonlinear operations and overlap-and-save. Offline training on blocks of i.i.d. complex Gaussian symbols enables these parameters to be learned, resulting in real-time complexity that matches CB-ESSFM for a single band. In a 5×93 GBd WDM system over a 170 km single-span link, L-ESSFM with four steps provides about 0.8 dB gain over electronic dispersion compensation at , while requiring only a fraction of the RM/2D compared with ESSFM and far less complexity than LDBP, demonstrating a favorable accuracy–complexity trade-off and potential for extension to long-haul systems and subband processing.

Abstract

We propose a digital backpropagation method that employs machine-learning-aided joint optimization of dispersion step lengths and nonlinear phase rotation filters within an FFT-based enhanced split-step Fourier structure, achieving improved accuracy at low computational complexity.
Paper Structure (4 sections, 1 figure)

This paper contains 4 sections, 1 figure.

Table of Contents

  1. Introduction
  2. Learned ESSFM
  3. System setup and performance
  4. Conclusions

Figures (1)

  • Figure 1: (a) L-ESSFM architecture with the learnable parameters in red; (b) system performance vs. complexity in real multiplications per 2D symbol.