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.
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.Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
The deployment of artificial neural networks-based optical channel equalizers on edge-computing devices is critically important for the next generation of optical communication systems. However, this is a highly challenging problem, mainly due to the computational complexity of the artificial neural networks (NNs) required for the efficient equalization of nonlinear optical channels with large memory. To implement the NN-based optical channel equalizer in hardware, a substantial complexity reduction is needed, while keeping an acceptable performance level. In this work, we address this problem by applying pruning and quantization techniques to an NN-based optical channel equalizer. We use an exemplary NN architecture, the multi-layer perceptron (MLP), and address its complexity reduction for the 30 GBd 1000 km transmission over a standard single-mode fiber. We demonstrate that it is feasible to reduce the equalizer’s memory by up to 87.12%, and its complexity by up to 91.5%, without noticeable performance degradation. In addition to this, we accurately define the computational complexity of a compressed NN-based equalizer in the digital signal processing (DSP) sense and examine the impact of using different CPU and GPU settings on power consumption and latency for the compressed equalizer. We also verify the developed technique experimentally, using two standard edge-computing hardware units: Raspberry Pi 4 and Nvidia Jetson Nano.
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