Convolutional long short-term memory neural network equalizer for nonlinear Fourier transform-based optical transmission systems

Neural network-aided receivers for soliton communication impaired by solitonic interaction

In this paper, different neural network-based methods are proposed to improve the achievable information rate in amplitude-modulated soliton communication systems. The proposed methods use simulated data to learn effective soliton detection by suppressing nonlinear impairments beyond amplifier noise, including intrinsic inter-soliton interaction, Gordon-Haus effect-induced timing jitter, and their combined impact. We first present a comprehensive study of these nonlinear impairments based on numerical simulations. Then, two neural network designs are developed based on a regression network and a classifier. We estimate the achievable information rates of the proposed learning-based soliton detection schemes as well as two model-based benchmark schemes, including the nonlinear Fourier transform eigenvalue estimation and continuous spectrum-aided eigenvalue estimation schemes. Our results demonstrate that both learning-based designs lead to substantial performance gains when compared to the benchmark schemes. Importantly, we highlight that exploiting the channel memory, introduced by solitonic interactions, can yield additional gains in the achievable information rate. Through a comparative analysis of the two neural network designs, we establish that the classifier design exhibits superior adaptability to interaction impairment and is more suitable for symbol detection tasks in the context of the investigated scenarios.

Autoencoder assisted subcarrier optimization for nonlinear frequency division multiplexing

Nonlinear frequency division multiplexing (NFDM) is a novel optical communication technique that can achieve nonlinear free transmission. However, current design of NFDM is analogous to orthogonal frequency division multiplexing (OFDM), where sinc function is utilized as subcarriers, which may not be optimal for nonlinear spectrums. In this paper, we propose an auto-encoder (AE) assisted subcarrier optimization scheme for dual-polarized (DP) NFDM systems. Numerical verifications show that our scheme can improve the Q-factor by 1.54 dB and 0.62 dB compared to sinc subcarrier and linear minimum mean square error (LMMSE) equalization, respectively, in a 960 km transmission scenario. We also analyze the characteristics of the optimized subcarriers and discuss how they enhance the performance. Furthermore, we demonstrate the robustness of the optimized subcarriers to different modulation formats, transmission distances and bandwidth. Our work provides a new idea in subcarrier design for NFDM.

Frequency offset estimation for nonlinear frequency division multiplexing with continuous spectrum modulation

Carrier frequency offset (CFO) estimation is very important for the optical fiber communications and has been studied widely in linear coherent systems, while only a few works have been reported for nonlinear Fourier transform (NFT) based systems. In continuous spectrum (CS) modulation nonlinear frequency division multiplexing (CS-NFDM) systems, frequency offset (FO) has a great influence on its performance, requiring an improved frequency offset estimation (FOE) method. We found that the oversampling rate R0 adopted in NFDM to ensure the accuracy of the NFT and inverse NFT (INFT) calculations, would cause the estimation accuracy of the traditional FFT-FOE method to decrease by R0 times. Moreover, CS-NFDM signals with higher baud rate require more subcarriers and then result in an oversampling factor greater than 16. This makes the traditional FFT-FOE method be ineffective to use the common training sequence (TS) overhead to meet the FOE error requirement of CS-NFDM system. Therefore, a modified FOE method based on FFT assisted by TS and autocorrelation has been proposed. The theoretical analysis and simulation results show that the proposed method is applicable to CS-NFDM system, no matter what modulation format is used. For 512 subcarriers, with a high rate of 70GBaud and the TS length of 8192, the proposed method can obtain a minimum FO estimation error about 0.1 MHz, which is better than the other two typical FFT-FOE and Schmidl & Cox methods. In addition, the proposed method can save at least 87.5% and 50% overhead. Thus, the proposed method has obvious improvement for CS-NFDM system with requiring high oversampling rate.

One-Day-Ahead Solar Irradiation and Windspeed Forecasting with Advanced Deep Learning Techniques

In recent years, demand for electric energy has steadily increased; therefore, the integration of renewable energy sources (RES) at a large scale into power systems is a major concern. Wind and solar energy are among the most widely used alternative sources of energy. However, there is intense variability both in solar irradiation and even more in windspeed, which causes solar and wind power generation to fluctuate highly. As a result, the penetration of RES technologies into electricity networks is a difficult task. Therefore, more accurate solar irradiation and windspeed one-day-ahead forecasting is crucial for safe and reliable operation of electrical systems, the management of RES power plants, and the supply of high-quality electric power at the lowest possible cost. Clouds’ influence on solar irradiation forecasting, data categorization per month for successive years due to the similarity of patterns of solar irradiation per month during the year, and relative seasonal similarity of windspeed patterns have not been taken into consideration in previous work. In this study, three deep learning techniques, i.e., multi-head CNN, multi-channel CNN, and encoder–decoder LSTM, were adopted for medium-term windspeed and solar irradiance forecasting based on a real-time measurement dataset and were compared with two well-known conventional methods, i.e., RegARMA and NARX. Utilization of a walk-forward validation forecast strategy was combined, firstly with a recursive multistep forecast strategy and secondly with a multiple-output forecast strategy, using a specific cloud index introduced for the first time. Moreover, the similarity of patterns of solar irradiation per month during the year and the relative seasonal similarity of windspeed patterns in a timeseries measurements dataset for several successive years demonstrates that they contribute to very high one-day-ahead windspeed and solar irradiation forecasting performance.

Serial and parallel convolutional neural network schemes for NFDM signals

Two conceptual convolutional neural network (CNN) schemes are proposed, developed and analysed for directly decoding nonlinear frequency division multiplexing (NFDM) signals with hardware implementation taken into consideration. A serial network scheme with a small network size is designed for small user applications, and a parallel network scheme with high speed is designed for places such as data centres. The work aimed at showing the potential of using CNN for practical NFDM-based fibre optic communication. In the numerical demonstrations, the serial network only occupies 0.5 MB of memory space while the parallel network occupies 128 MB of memory but allows parallel computing. Both network schemes were trained with simulated data and reached more than 99.9% accuracy.

Computer-automated design of mode-locked fiber lasers

We automate the mode-locked fiber laser design process using a modified genetic algorithm and an intuitive optimization loss function to control highly accurate polarization-resolved simulations of laser start-up dynamics without user interaction. We reconstruct both the cavity designs and output pulse characteristics of experimentally demonstrated Yb-fiber all-normal dispersion, dispersion-managed, and wavelength-tuneable all-anomalous dispersion Tm-fiber femtosecond lasers with exceptional accuracy using minimal prior knowledge, and show that our method can be used to predict new cavity designs and novel mode locking states that meet target pulse requirements. Our approach is directly applicable to a broad range of mode locking regimes, wavelengths, pulse energies, and repetition rates, requires no training or knowledge of the loss function gradients, and is scalable for use on supercomputers and inexpensive desktop computers.

81-GHz W-band 60-Gbps 64-QAM wireless transmission based on a dual-GRU equalizer

We propose a dual gated recurrent unit neural network based on nonlinear equalizer (dual-GRU NLE) for radio-over-fiber (ROF) communication systems. The dual equalization scheme is mainly based upon GRU algorithm, which can be trained via two steps including I-GRU and Q-GRU. By using the dual-GRU equalizer, 60-Gbps 64-QAM signal generation and transmission over 10-km SMF and 1.2-m wireless link at 81-GHz can be achieved. For the digital signal processing (DSP) at receiver, comparison between CMMA equalizer, Volterra equalizer, and dual-GRU equalizer are demonstrated. The results indicate that the proposed dual-GRU NLE significantly mitigates the nonlinear distortions. The dual-GRU equalizer has a better BER performance in receiver sensitivity than the traditional CMMA and Volterra equalizer. At the expense of large complexity, an improvement of receiver sensitivity can be achieved as much as 1 dB compared with Volterra equalizer at the BER of 2×10^-2. To the best of our knowledge, this is the first time to propose a novel dual-GRU equalizer, which is promising for the development in millimeter-wave photonics for B5G applications and beyond.

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.