Machine Learning For Performance Improvement of Long-Haul End-to-End Optical Transmission Systems

The thesis focuses on addressing the challenges faced by optical fiber networks in keeping up with the growing demand for data transfer, especially with the advent of 5G/6G and the Internet of Things (IoT). The rapid expansion in data transfer requirements highlights the limitations of current optical fiber networks and the necessity for improvements in data encoding techniques, spectrumutilization, and signal clarity over long distances. The thesis contributes to this field by developing new methods for applying the Nonlinear Fourier Transform (NFT) to continuous signals, improving signal processing algorithms, and using Machine learning (ML) to understand complex patterns and make data-driven decisions to optimize optical communication systems. The work is divided into two primary sections. The first section delves into advanced NFT techniques, including their application in optical fiber channel modeling for single and dualpolarization systems, signal processing with a sliding window technique combined with NFT, exploring solitonic components in optical signals, and the use of neural networks for NFT to work with noisy signals. The second section is dedicated to the role of ML in optimizing optical communication systems, discussing the new High-Performance COMmunication library (Hp-Com) framework for simulating optical channels, the use of Gradient Boosting for nonlinear equalization, studying received symbol distributions using the GaussianMixtureModel, and summarizing findings with insights for future research. The thesis outlines the creation of innovative techniques to improve optical fiber systems, thus aiding the continued development of the digital world by handling the ever-increasing demands for data transmission

Nonlinear Spectrum of Conventional OFDM and WDM Return-to-Zero Signals in Nonlinear Channel

The nonlinear Schrödinger equation (NLSE) is often used as a master path-average model for fiber-optic links to analyze fundamental properties of such nonlinear communication channels. Transmission of a signal in nonlinear channels is conceptually different from linear communications. We use here the NLSE channel model to explain and illustrate some new unusual features introduced by nonlinearity. In general, NLSE describes the co-existence of dispersive (continuous) waves and localized (here in time) waves: soliton pulses. The nonlinear Fourier transform method allows one to compute for any given temporal signal the so-called nonlinear spectrum that defines both continuous spectrum (analog to conventional Fourier spectral presentation) and solitonic components. Nonlinear spectrum remains invariant during signal evolution in the NLSE channel. We examine conventional orthogonal frequency-division multiplexing (OFDM) and wavelength-division multiplexing (WDM) return-to-zero signals and demonstrate that both signals at certain power levels have soliton component. We would like to stress that this effect is completely different from the soliton communications studied in the past. Applying Zakharov-Shabat spectral problem to a single WDM or OFDM symbol with multiple sub-carriers, we quantify the effect of statistical occurrence of discrete eigenvalues in such an information-bearing optical signal. Moreover, we observe that at signal powers optimal for transmission, an OFDM symbol with high probability has a soliton component

Computing continuous nonlinear Fourier spectrum of optical signal with artificial neural networks

In this work, we demonstrate that the high-accuracy computation of the continuous nonlinear spectrum can be performed by using artificial neural networks. We propose the artificial neural network (NN) architecture that can efficiently perform the nonlinear Fourier (NF) optical signal processing. The NN consists of sequential convolution layers and fully connected output layers. This NN predicts only one component of the continuous NF spectrum, such that two identical NNs have to be used to predict the real and imaginary parts of the reflection coefficient. To train the NN, we precomputed 94035 optical signals. 9403 signals were used for validation and excluded from training. The final value of the relative error for the entire validation dataset was less than 0.3%. Our findings highlight the fundamental possibility of using the NNs to analyze and process complex optical signals when the conventional algorithms can fail to deliver an acceptable result

Soliton content in the standard optical OFDM signal

The nonlinear Schrödinger equation (NLSE) is often used as a master path-average model for fiber-optic transmission lines. In general, the NLSE describes the co-existence of dispersive waves and soliton pulses. The propagation of a signal in such a nonlinear channel is conceptually different from linear systems. We demonstrate here that the conventional orthogonal frequency-division multiplexing (OFDM) input optical signal at powers typical for modern communication systems might have soliton components statistically created by the random process corresponding to the information content. Applying the Zakharov–Shabat spectral problem to a single OFDM symbol with multiple subcarriers, we quantify the effect of the statistical soliton occurrence in such an information-bearing optical signal. Moreover, we observe that at signal powers optimal for transmission, an OFDM symbol incorporates multiple solitons with high probability. The considered optical communication example is relevant to a more general physical problem of the generation of coherent structures from noise

Phase computation for the finite-genus solutions to the focusing nonlinear Schrödinger equation using convolutional neural networks

We develop a method for retrieving a set of parameters of a quasi-periodic finite-genus (finite-gap) solution to the focusing nonlinear Schrödinger (NLS) equation, given the solution evaluated on a finite spatial interval for a fixed time. These parameters (named “phases”) enter the jump matrices in the Riemann-Hilbert (RH) problem representation of finite-genus solutions. First, we detail the existing theory for retrieving the phases for periodic finite-genus solutions. Then, we introduce our method applicable to the quasi-periodic solutions. The method is based on utilizing convolutional neural networks optimized by means of the Bayesian optimization technique to identify the best set of network hyperparameters. To train the neural network, we use the discrete datasets obtained in an inverse manner: for a fixed main spectrum (the endpoints of arcs constituting the contour for the associated RH problem) and a random set of modal phases, we generate the corresponding discretized profile in space via the solution of the RH problem, and these resulting pairs – the phase set and the corresponding discretized solution in a finite interval of space domain – are then employed in training. The method’s functionality is then verified on an independent dataset, demonstrating our method’s satisfactory performance and generalization ability

Neural networks for computing and denoising the continuous nonlinear Fourier spectrum in focusing nonlinear Schrödinger equation

We combine the nonlinear Fourier transform (NFT) signal processing with machine learning methods for solving the direct spectral problem associated with the nonlinear Schrödinger equation. The latter is one of the core nonlinear science models emerging in a range of applications. Our focus is on the unexplored problem of computing the continuous nonlinear Fourier spectrum associated with decaying profiles, using a specially-structured deep neural network which we coined NFT-Net. The Bayesian optimisation is utilised to find the optimal neural network architecture. The benefits of using the NFT-Net as compared to the conventional numerical NFT methods becomes evident when we deal with noise-corrupted signals, where the neural networks-based processing results in effective noise suppression. This advantage becomes more pronounced when the noise level is sufficiently high, and we train the neural network on the noise-corrupted field profiles. The maximum restoration quality corresponds to the case where the signal-to-noise ratio of the training data coincides with that of the validation signals. Finally, we also demonstrate that the NFT b-coefficient important for optical communication applications can be recovered with high accuracy and denoised by the neural network with the same architecture

Influence of the Cross-Link Density on the Rate of Crystallization of Poly(ε-Caprolactone)

Cross-linked poly(ε-caprolactone) (PCL) is a smart biocompatible polymer exhibiting two-way shape memory effect. PCL samples with different cross-link density were synthesized by heating the polymer with various amounts of radical initiator benzoyl peroxide (BPO). Non-isothermal crystallization kinetics was characterized by means of conventional differential scanning calorimetry (DSC) and fast scanning calorimetry (FSC). The latter technique was used to obtain the dependence of the degree of crystallinity on the preceding cooling rate by following the enthalpies of melting for each sample. It is shown that the cooling rate required to keep the cooled sample amorphous decreases with increasing cross-link density, i.e., crystallization process slows down monotonically. Covalent bonds between polymer chains impede the crystallization process. Consequently, FSC can be used as a rather quick and low sample consuming method to estimate the degree of cross-linking of PCL samples

Crystal Nucleation and Growth in Cross-Linked Poly(ε-caprolactone) (PCL)

The crystal nucleation and overall crystallization kinetics of cross-linked poly(ε-caprolactone) was studied experimentally by fast scanning calorimetry in a wide temperature range. With an increasing degree of cross-linking, both the nucleation and crystallization half-times increase. Concurrently, the glass transition range shifts to higher temperatures. In contrast, the temperatures of the maximum nucleation and the overall crystallization rates remain the same, independent of the degree of cross-linking. The cold crystallization peak temperature generally increases as a function of heating rate, reaching an asymptotic value near the temperature of the maximum growth rate. A theoretical interpretation of these results is given in terms of classical nucleation theory. In addition, it is shown that the average distance between the nearest cross-links is smaller than the estimated lamellae thickness, which indicates the inclusion of cross-links in the crystalline phase of the polymer

Multi-Task Learning to Enhance Generalizability of Neural Network Equalizers in Coherent Optical Systems

<p>For the first time, multi-task learning is proposed to improve the flexibility of NN-based equalizers in coherent systems. A "single" NN-based equalizer improves Q-factor by up to 4 dB compared to CDC, without re-training, even with variations in launch power, symbol rate, or transmission distance.</p&gt