On nonlinear Fourier transform-based fibre-optic communication systems for periodic signals

As the demand for information rate grows on a daily basis, new ways of improving the efficiency of fibre-optic communication systems, the backbone of the global data network,are highly anticipated. Nonlinear Fourier transform (NFT) is one of the newly emerged techniques showing promising results in recent studies both in simulation and experiment. Along this path, this method has shown its potential to overcome some difficulties of the fibre-optic communication regarding nonlinear distortions, especially the crosstalk between the user’s bands in wavelength division multiplexing (WDM) systems. NFT-based systems, however, in the conventional, widely considered case of vanishing boundary signals, have exhibited some drawbacks related to the computational complexity and spectral efficiency. Both problems are the direct consequences of large signal duration ensued from the vanishing boundary condition. Considering periodic solutions to the nonlinear Schrödinger equation is among attempts to solve this problem. It helps to decrease the processing window at the receiver and gives full control over the communication-related parameters of the signal. Periodic NFT (PNFT) can also be implemented through fast numerical methods which makes it yet more appealing. In this thesis, a general framework to implement PNFT in fibre-optic communication systems is proposed. As the most challenging part of such a system, the inverse transformation stage is particularly taken attention to, and a few ways to perform it are put forward. From the simplest signals with analytically known nonlinear spectrum to a complete periodic solution with arbitrary, finite number of degrees of freedom, several system configurations are conferred and evaluated in terms of their performance. Common measures such as bit error rate, quality factor and mutual information are considered in scrutinising the systems.Based on simulation results, we conclude that the PNFT can, in fact, improve the mutual information by overcoming some shortcomings of the vanishing boundary NFT

Noise-Resistant Optical Implementation of Analogue Neural Networks

Analogue artificial neural networks are widely considered as promising computational models that more closely imitate the information processing capabilities of the human brain compared to digital neural networks. The significant computation power and the much reduced power consumption per operation make the analogue implementation of neural networks very attractive. There is an active research on artificial neural networks (ANNs) implementation using both analogue photonic and electronic hardware [1] – [4] . However, compared to digital realisations the conventional analogue systems are more sensitive to the noise that is inevitably present in practical implementations [2] , [3] . Noise properties in ANNs have been studied both in the electronic and photonic domains. However, photonic ANNs are much less investigated compared to the electronic implementations, for which some training techniques have been proposed to enhance ANNs robustness against noise [1] , [4]

Communication System Using Periodic Nonlinear Fourier Transform Based on Riemann-Hilbert Problem

In a communication system based on periodic nonlinear Fourier transform, we apply the associated Riemann-Hilbert problem to modulate the nonlinear spectrum of the signal and study the performance and achievable mutual informatio

Full-spectrum periodic nonlinear Fourier transform optical communication through solving the Riemann-Hilbert problem

In this article, for the first time, a full-spectrum periodic nonlinear Fourier transform (NFT)-based communication system with the inverse transformation at the transmitter performed by using the solution of Riemann-Hilbert problem (RHP), is proposed and studied. The entire control over the nonlinear spectrum rendered by our technique, where we operate with two qualitatively different components of this spectrum represented, correspondingly, in terms of the main spectrum and the phases, allows us to design a time-domain signal tailored to the characteristics of the transmission channel. In the heart of our system is the RHP-based signal processing utilised to generate the time-domain signal from the modulated nonlinear spectrum. This type of NFT processing leads to a computational complexity that scales linearly with the number of time-domain samples, and we can process signal samples in parallel. In this article, we suggest the way of getting an exactly periodic signal through the correctly formulated RHP, and present evidence of the analogy between band-limited (in ordinary Fourier sense) signals and finite-band (in RHP sense) signals. Also, for the first time, we explain how to modulate the phases of individual periodic nonlinear modes. The performance of our transmission system is evaluated through numerical simulations in terms of bit error rate and Q$^2$-factor dependencies on the transmission distance and power, and the results demonstrate the good potential of the approach

Communication system based on periodic nonlinear Fourier transform with exact inverse transformation

By performing the exact inverse transformation, a periodic solution to channel model is constructed and used in an NFT-based communication system. The achievable mutual information is calculated using the non-uniform probability distribution for transmitted symbols for different link lengths

Optical communication based on the periodic nonlinear Fourier transform signal processing

In this work we introduce the periodic nonlinear Fourier transform (PNFT) and propose a proof-of-concept communication system based on it by using a simple waveform with known nonlinear spectrum (NS). We study the performance (addressing the bit-error-rate (BER), as a function of the propagation distance) of the transmission system based on the use of the PNFT processing method and show the benefits of the latter approach. By analysing our simulation results for the system with lumped amplification, we demonstrate the decent potential of the new processing method

Machine learning for performance improvement of periodic NFT-based communication system

We compare performance of several machine learning methods, including support vector machine, k-nearest neighbours, k-means clustering, and Gaussian mixture model, used for increasing transmission reach in the optical communication system based on the periodic nonlinear Fourier transform signal processin

Combining nonlinear Fourier transform and neural network-based processing in optical communications

We propose a method to improve the performance of the nonlinear Fourier transform (NFT)-based optical transmission system by applying the neural network post-processing of the nonlinear spectrum at the receiver. We demonstrate through numerical modeling about one order of magnitude bit error rate improvement and compare this method with machine learning processing based on the classification of the received symbols. The proposed approach also offers a way to improve numerical accuracy of the inverse NFT; therefore, it can find a range of applications beyond optical communications

Unsupervised and supervised machine learning for performance improvement of NFT optical transmission

We apply both the unsupervised and supervised machine learning (ML) methods, in particular, the k-means clustering and support vector machine (SVM) to improve the performance of the optical communication system based on the nonlinear Fourier transform (NFT). The NFT system employs the continuous NFT spectrum part to carry data up to 1000 km using the 16-QAM OFDM modulation. We classify the performance of the system in terms of BER versus signal power dependence. We show that the NFT system performance can be improved considerably by means of the ML techniques and that the more advanced SVM method typically outperforms the k-means clustering