Morteza Kamalian-Kopae

Machine learning methods, including artificial neural networks, used for mitigation of nonlinear transmission impairments in ultra-long-haul and long-haul unmanaged fibre-optic links feature high complexity due to the accumulated dispersion resulting into large channel memory. Combination of the all-optical dispersion management techniques reducing effective channel memory and low-complexity digital post-processing potentially can offer an attractive trade-off between performance, complexity and costs (or power consumption). This paper demonstrates a feasibility of substantial complexity reduction of machine learning-based channel equalisation in dispersion-managed transmission with acceptable system performance.

Many modern applications of the artificial neural networks ensue large number of layers making traditional digital implementations increasingly complex. Optical neural networks offer parallel processing at high bandwidth, but have the challenge of noise accumulation. We propose here a new type of neural networks using stochastic resonances as an inherent part of the architecture and demonstrate a possibility of significant reduction of the required number of neurons for a given performance accuracy. We also show that such a neural network is more robust against the impact of noise.

Using a multi-layer perceptron to equalise the residual nonlinearity from the transmission of PDM 28 Gbaud 64QAM over 400km of SSMF employing midlink optical phase conjugation, we demonstrate 12-fold reduction in the BER.

We evaluate improvement in the performance of the optical transmission systems operating with the continuous nonlinear Fourier spectrum by the artificial neural network equalisers installed at the receiver end. We propose here a novel equaliser designs based on bidirectional long short-term memory (BLSTM) gated recurrent neural network and compare their performance with the equaliser based on several fully connected layers. The proposed approach accounts for the correlations between different nonlinear spectral components. The application of BLSTM equaliser leads to a 16x improvement in terms of bit-error rate (BER) compared to the non-equalised case. The proposed equaliser makes it possible to reach the data rate of 170 Gbit/s for one polarisation conventional nonlinear Fourier transform (NFT) based system at 1000 km distance. We show that our new BLSTM equalisers significantly outperform the previously proposed scheme based on a feed-forward fully connected neural network. Moreover, we demonstrate that by adding a 1D convolutional layer for the data pre-processing before BLSTM recurrent layers, we can further enhance the performance of the BLSTM equaliser, reaching 23x BER improvement for the 170 Gbit/s system over 1000 km, staying below the 7% forward error correction hard decision threshold (HD-FEC).

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.

Modern high-power lasers exhibit a rich diversity of nonlinear dynamics, often featuring nontrivial co-existence of linear dispersive waves and coherent structures. While the classical Fourier method adequately describes extended dispersive waves, the analysis of time-localised and/or non-stationary signals call for more nuanced approaches. Yet, mathematical methods that can be used for simultaneous characterisation of localized and extended fields are not yet well developed. Here, we demonstrate how the Nonlinear Fourier transform (NFT) based on the Zakharov-Shabat spectral problem can be applied as a signal processing tool for representation and analysis of coherent structures embedded into dispersive radiation. We use full-field, real-time experimental measurements of mode-locked pulses to compute the nonlinear pulse spectra. For the classification of lasing regimes, we present the concept of eigenvalue probability distributions. We present two field normalisation approaches, and show the NFT can yield an effective model of the laser radiation under appropriate signal normalisation conditions.

Fulfilling the requirements of 5G NR, the 5 ^th generation mobile network equipped with advanced features such as network MIMO and multi-user diversity, new and more advanced fronthaul design is needed. Analog radio over fiber has been proposed to provide high bandwidth signals with simple receiver architecture from the baseband unit to the remote radio heads. At such a high data rate, fiber distortions, i.e. chromatic dispersion, become significant and need to be compensated. Here we study applying a simple optical filter implemented by means of fiber Bragg grating technique and evaluate its performance for various scenarios through numerical simulations. It is evident from the observed results that the proposed approach is effective in increasing the reach and providing reliable communication with simple implementation.

Nonlinear Fourier transform (NFT) has shown its potential to overcome some challenges of nonlinear signal distortions in fibre-optic communications ystems [1]. However, there is yet so much unknown about fundamental properties and traits of a communication based on NFT. One of the most important aspects of an optical communication system is its robustness against the inevitable amplified spontaneous emission (ASE) noise coming from optical amplifiers. The ASE noise not only contaminates the signal as it does for all systems, but it also has a special detrimental effect on NFT-based systems; destroying the very basic concept of integrability of the nonlinear Schrodinger equation (NLSE). Moreover, this noise, undergoing a nonlinear transformation, i.e. "direct NFT" is dependent on the signal power. There are initial studies to model the noise in the nonlinear Fourier domain and some approximations for particular cases of modulation such as discrete spectrum-only or continuous spectrum-only modulations are available [2–3]. The limited extent of the mentioned studies makes it difficult to use them in order to design an optimum receiver — the primary engineering purpose of analysing the noise properties. On the other hand, machine learning-based techniques to study the noise characteristics in fibre-optic communication have been tried and promising results are already obtained [4]. Machine learning (ML) can also be used to find the impact of noise and alleviate the extent of its perturbation. In particular, in an NFT-based system, where data is mapped on the discrete spectrum (DS) of a signal, at the receiver, the calculated DS contains some spurious elements which are the result of the noise. These points are usually filtered out considered to be void of useful information about the transmitted signal. However, the correlation between these points and the main elements of the DS points that there is mutual information which can be used in order to improve the detection performance at the receiver. In this work, we use a simple Neural Network (NN) to back-propagate the received DS of a signal in a periodic NFT-based communication system. As shown in Fig1. a, drawn from a 64-QAM constellation, each symbol is mapped on the DS of a periodic signal as described in [5,6]. Performing the exact inverse transformation, a signal with the given DS is constructed and sent to a noisy link with 11 spans of 80 km length standard SMF. At the receiver, the DS is calculated and even the out-of-band components are passed to the NN-based equaliser. All data from the calculated DS is used as the input feature vector to our 2-layer (10 neurons each) NN. Raman amplification is used and assumed to provide perfect power loss compensation along the span.