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.

Improvement for a full-spectrum modulated nonlinear frequency division multiplexing transmission system.

Nonlinear frequency division multiplexing (NFDM), as a possible technique to overcome the limit imposed by Kerr nonlinearity in conventional coherent optical communication systems, has attracted widespread attention in the communication community in recent years. In order to fully utilize the available degrees of freedom in the nonlinear spectrum, this paper focuses on the full-spectrum (FS) modulated NFDM system. First, we maximize the data rate of discrete spectrum (DS) by optimizing the distribution of eigenvalues in DS part of FS. Then through introducing the probabilistic shaping (PS) into the FS system, and combined with linear minimum mean square (LMMSE) estimators, a 1120 km transmission with BER below the hard decision forward error correction (HD-FEC) threshold at 112 Gbps is achieved, where 128 subcarriers with PS-64QAM are used in the continuous spectrum (CS) and 13 eigenvalues with 64QAM are adopted in the discrete spectrum (DS). The achievable data rate is about 12% higher than that of pure CS modulation. Our work achieves the current FS NFDM system with the largest number of multiplexed eigenvalues, and provides a way to improve the performance of FS systems.

Nonlinear frequency domain PMD modeling and equalization for nonlinear frequency division multiplexing transmission.

Polarization mode dispersion (PMD) is one of the fundamental properties of a standard single-mode fiber. It affects the propagating signals and degrades the performance of high-speed optical fiber communication systems. PMD also gives an effect on the nonlinear spectra or scattering data in nonlinear frequency division multiplexing (NFDM) systems. However, PMD is usually described in the linear frequency domain, and there are few investigations about the influence of PMD in the nonlinear frequency domain (NFD). An NFD-PMD model is needed to understand the impact of PMD in the NFD. In this work, using a linear approximation method, we first propose an NFD-PMD model and verify its effectiveness. With the guide of the NFD-PMD model, a blind NFD-PMD equalization scheme is designed. The simulation results indicate that the proposed NFD-PMD equalization scheme has better performance than the training sequence method based on linear frequency domain equalization.

Probabilistic shaping and neural network-based optimization for a nonlinear frequency division multiplexing system.

A joint scheme introducing probabilistic shaping (PS) at the transmitter and utilizing a neural network (NN) equalizer at the receiver is proposed to improve the performance of the b-modulated nonlinear frequency division multiplexing (NFDM) system. Through a numerical simulation, we demonstrate that PS plays a leading role for low launch power case, which improves the performance of the system effectively, while the NN equalizer's superiority appears in a high launch power region, whose main role is to weaken the correlation among subcarriers for improving system performance. The proposed scheme would enlighten the optimum modulation and detection schemes of the NFDM system.

Robust neural network receiver for multiple-eigenvalue modulated nonlinear frequency division multiplexing system.

Nonlinear frequency division multiplexing (NFDM) has been shown to be promising in overcoming the fiber Kerr nonlinearity limit. In multiple-eigenvalue modulated NFDM systems, the transmission capacity increases with the number of modulated eigenvalues. However, as the number of modulated eigenvalues increases, the complexities of the signal waveform and the nonlinear Fourier transform (NFT) algorithm for demodulation increase dramatically as well, while the accuracy drops significantly. Meanwhile, impairments such as amplifier spontaneous emission noise and phase noise in practical channels would perturb the eigenvalues and the corresponding nonlinear spectra during transmission. Coupled with an increase in the modulation format order, it is difficult for NFT algorithm-based receivers to recover information. To enable the use of multiple-eigenvalue modulated NFDM systems, we propose an innovative receiver based on regression neural networks (NNs), which can demodulate information correctly for both single- and dual-polarization NFDM systems. The results show that it has strong robustness and has a certain tolerance to the impairments of communication systems. In the contrast that the poor demodulation performance of the NFT and the Euclidean minimum distance (MD) receivers for multi-eigenvalue modulated NFDM systems, our proposed NN receiver can achieve low bit error rate with 2 GBaud 16QAM modulation over 1,000 km transmission in four-eigenvalue modulated single-polarization NFDM systems. The performance of three receivers (NFT, MD and NN) in a two-eigenvalue modulated NFDM system are also compared, the NN receiver shows the best performance and appears more suitable for higher-order modulation formats.

Nonlinear-frequency-packing nonlinear frequency division multiplexing transmission.

A nonlinear frequency division multiplexing (NFDM) transmission system, designed specifically for nonlinear fiber channel, has the potential to overcome the nonlinear Shannon capacity limit. However, the spectral efficiency (SE) of the current proven NFDM transmission systems is still lower than that of the analogous orthogonal frequency division multiplexing system. It is extremely necessary to explore effective modulation scheme for the aim of increasing the SE of NFDM system. In this study, we first propose the nonlinear-frequency-packing nonlinear frequency division multiplexing (NFP-NFDM) transmission system. In NFP-NFDM, the spacing of nonlinear subcarriers is squeezed and more nonlinear subcarriers can be packed, but the inter carrier interference (ICI) is introduced. The method of NFP in nonlinear Fourier domain is carefully designed to reduce the complexity of ICI cancellation. Through numerical simulation, we illustrate the feasibility of NFP-NFDM transmission, and higher SE in NFP-NFDM than that of NFDM system is also demonstrated. The upper bound of the normalized SE for NFP-NFDM is estimated, which is higher than that of current NFDM system. Besides, we find out that the NFP scheme may have the advantage of reducing the signal-noise interaction in fiber transmission scenario, which indicates there may be a better way to load the data into the nonlinear Fourier domain.