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We demonstrate, for the first time, a record 113 Gb/s (spectral efficiency of 2.8 bits/s/Hz) full-spectrum modulated nonlinear frequency division transmission system with 256 nonlinear subcarriers for continuous spectrum and 11 eigenvalues for discrete spectrum.

We elaborately design a full-spectrum modulated NFDM system with b-scheme. A 1120km transmission with BER < 3.8 × 10−3 at 103.75 Gbps is achieved through geometric shaping (GS) and linear minimum mean square error (LMMSE) estimator.

A combination scheme of 4D-2A8PSK modulation with neural network receiver is proposed to improve the performance of the discrete spectra modulated nonlinear frequency division multiplexing systems. The transmission distance extends from 1000km to 2100km.

The parameters in the waveform shaping stage of the transmitter are critical to the performance of the NFDM system. By designing and optimizing these parameters, the performance of the NFDM system can be effectively improved. © 2021 The Author(s)

We introduce probabilistic shaping at the transmitter and apply neural network spectrum equalizer at the receiver in 64-QAM NFDM system. The proposed scheme possesses higher mutual information and further transmission distance. © 2020 The Author(s)

A nonlinear Fourier domain PMD impairment model is first proposed and verified. It can help to better understand the effects of PMD, and provide guidance for the design of corresponding equalization scheme. © 2020 The Author(s)

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.