Learned Volterra Models for Nonlinearity Equalisation in Optical Networks

Abstract

Digital equalisation of fibre-based nonlinear impairments in optical transmission systems remains commercially unavailable, mainly due to the high computational complexity of existing algorithms. Machine learning has recently revolutionised the field, enabling lowcomplexity schemes and introducing a range of approaches, from black-box methods to model-driven schemes. While black-box schemes are effective, they lack interpretability, require extensive training data and rely on heuristic designs. In contrast, model-driven schemes, such as learned digital backpropagation (LDBP), integrate signal propagation principles into the equaliser architecture, providing a framework that can be more easily understood and optimised. Although LDBP has achieved significant performance improvements and cost reductions, its sequential computations lead to high processing latency. For high-speed applications, the architecture of Volterra series models is an attractive alternative due to their inherent parallelisation capabilities. In particular, the third-order inverse Volterra series transfer function (IVSTF) model, while having known accuracy limitations that hinder its applicability, features a fully parallel structure with untapped potential as the basis of model-driven schemes.

This thesis presents a learned Volterra-based framework to mitigate nonlinear impairments, providing an alternative to LDBP. For single-channel transmission, we present a time-domain equaliser enabled by machine learning and based on simplifying the IVSTF.
The scheme achieves equivalent performance to LDBP with comparable computational effort. For wavelength-division multiplexed (WDM) systems, three multiple-input-multiple-output (MIMO) equalisation architectures for mitigating interchannel impairments are introduced. Their design and training were enabled by a purpose-built computational framework. Efficient MIMO equalisation is achieved, which has not been demonstrated before with the IVSTF architecture. The proposed models demonstrate robust improvements over chromatic dispersion compensation. A comprehensive performance and cost analysis identifies the model with the best trade-off, and the interpretability of our approach is demonstrated through the examination of the learned parameters. Our analysis and results can be used as guidelines for designing learned multi-channel equalisers for WDM systems.

Date of Award	Dec 2024
Original language	English
Awarding Institution	Aston University
Supervisor	Stylianos Sygletos (Supervisor), Andrew Ellis (Supervisor) & Sonia Boscolo (Supervisor)