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

Abstract

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.

Neural networks for computing the continuous nonlinear Fourier spectrum in focusing nonlinear Schrodinger equation: NFT-Net

“…Finally, we note that the problem of recovering a few solitons from a given pulse utilizing NN has been studied in 31,43,44,67 . However, the NN architectures used in these works are much more simple as far as we need to identify and denoise just several solitonic parameters, while in our work we recovered 1024 complex numbers representing the continuous NF spectrum.…”

“…In the other approach, the NFT operation at the receiver is entirely replaced by the NN element. It has been shown that this approach, indeed, results in a considerable improvement of the NFT-based transmission system functioning 31,43,44 . But, despite the benefits rendered by such a NN utilisation, the NNs emulating the NFT operation have so far been mostly used in the NFDM systems operating with solitons only, and the NN structure used there was relatively simple.…”

“…When the solitons are absent, as it is in the case considered, the full NF spectrum corresponding to a given finite-extent signal can be equivalently represented by either the reflection coefficient or by the b-coefficient, see more in Methods. Finally, we note that for the NFDM based on the discrete NF spectrum [29][30][31] , the achieved data rates have been noticeably lower than those for the modulation of continuous NF spectrum, see the comparison in [12, Fig. 1], and we do not address the computation of solitonic parameters in our research.…”

Eigenvalue-Domain Neural Network Demodulator for Eigenvalue-Modulated Signal

“…To facilitate improvement in the received power margin, use of an additional decision process based on the Euclidian minimum distance (MD) has been demonstrated [16]. In addition, machine learning-based demodulation methods for eigenvalue modulation, such as classification [17]- [20] and equalization [21], [22], have been investigated in recent years. Demodulation methods based on time-domain (TD) artificial neural networks (ANNs) for quadrature phase shift keying (QPSK) modulation of spectral amplitudes with two eigenvalues and on-off encoding of four-eigenvalue modulation have been proposed [17], [18].…”

Signal Processing Techniques for Optical Transmission Based on Eigenvalue Communication

“…Since neural networks have gained increased interest for optical communication systems [25,26], they are also a promising candidate for equalizing NFT-based communication [27,28]. Eigenvalue communication systems, where the receiver is based on a neural network only, have been proposed in [29,30], which is a very effective alternative to the standard NFT approach.…”