A survey on fiber nonlinearity compensation for 400 Gbps and beyond optical communication systems

Optical communication systems represent the backbone of modern communication networks. Since their deployment, different fiber technologies have been used to deal with optical fiber impairments such as dispersion-shifted fibers and dispersion-compensation fibers. In recent years, thanks to the introduction of coherent detection based systems, fiber impairments can be mitigated using digital signal processing (DSP) algorithms. Coherent systems are used in the current 100 Gbps wavelength-division multiplexing (WDM) standard technology. They allow the increase of spectral efficiency by using multi-level modulation formats, and are combined with DSP techniques to combat the linear fiber distortions. In addition to linear impairments, the next generation 400 Gbps/1 Tbps WDM systems are also more affected by the fiber nonlinearity due to the Kerr effect. At high input power, the fiber nonlinear effects become more important and their compensation is required to improve the transmission performance. Several approaches have been proposed to deal with the fiber nonlinearity. In this paper, after a brief description of the Kerr-induced nonlinear effects, a survey on the fiber nonlinearity compensation (NLC) techniques is provided. We focus on the well-known NLC techniques and discuss their performance, as well as their implementation and complexity. An extension of the inter-subcarrier nonlinear interference canceler approach is also proposed. A performance evaluation of the well-known NLC techniques and the proposed approach is provided in the context of Nyquist and super-Nyquist superchannel systems.Comment: Accepted in the IEEE Communications Surveys and Tutorial

Harnessing machine learning for fiber-induced nonlinearity mitigation in long-haul coherent optical OFDM

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).Coherent optical orthogonal frequency division multiplexing (CO-OFDM) has attracted a lot of interest in optical fiber communications due to its simplified digital signal processing (DSP) units, high spectral-efficiency, flexibility, and tolerance to linear impairments. However, CO-OFDM’s high peak-to-average power ratio imposes high vulnerability to fiber-induced non-linearities. DSP-based machine learning has been considered as a promising approach for fiber non-linearity compensation without sacrificing computational complexity. In this paper, we review the existing machine learning approaches for CO-OFDM in a common framework and review the progress in this area with a focus on practical aspects and comparison with benchmark DSP solutions.Peer reviewe

Digital signal processing for fiber nonlinearities [Invited]

This paper reviews digital signal processing techniques that compensate, mitigate, and exploit fiber nonlinearities in coherent optical fiber transmission systems

Multichannel Nonlinear Equalization in Coherent WDM Systems based on Bi-directional Recurrent Neural Networks

Kerr nonlinearity in the form of self- and cross-phase modulation imposes a fundamental limitation to the capacity of wavelength division multiplexed (WDM) optical communication systems. Digital back-propagation (DBP), that requires solving the inverse-propagating nonlinear Schr\"odinger equation (NLSE), is a widely adopted technique for the mitigation of impairments induced by Kerr nonlinearity. However, multi-channel DBP is too complex to be implemented commercially in WDM systems. Recurrent neural networks (RNNs) have been recently exploited for nonlinear signal processing in the context of optical communications. In this work, we propose multi-channel equalization through a bidirectional vanilla recurrent neural network (bi-VRNN) in order to improve the performance of the single-channel bi-VRNN algorithm in the transmission of WDM M-QAM signals. We compare the proposed digital algorithm to full-field DBP and to the single channel bi-RNN in order to reveal its merits with respect to both performance and complexity. We finally provide experimental verification through a QPSK metro link, showcasing over 2.5 dB optical signal-to-noise ratio (OSNR) gain and up to 43% complexity reduction with respect to the single-channel RNN and the DBP.Comment: 9 page

Comparison of Nonlinear Compensation Techniques for 400-Gb/s Coherent Multi-Band OFDM Super-Channels

The last few years, many studies have been published on the 3rd-order inverse Volterra series transfer function nonlinear equalizer (IVSTF-NLE) in long-haul optical communication systems. Nonetheless, no experimental work has been published on investigating the potential of the 3rd-order IVSTF-NLE for the compensation of Kerr nonlinearities in a long-haul wavelength division multiplexing (WDM) system consisting of high-bit rate super-channels, as high as 400 Gb/s. In this paper, we study experimentally the performance of a 3rd-order IVSTF-NLE in a coherent optical WDM system, with a central, 400-Gb/s, 4-band, dual-polarization (DP), 16-ary quadrature amplitude modulation (QAM) orthogonal frequency division multiplexing (OFDM) super-channel. We compare its performance against the performance of the digital back-propagation split-step Fourier (DBP-SSF) method for the compensation of nonlinearities after 10 × 100 km of ITU-T G.652 standard single mode fiber (SSMF). In the second part of this paper, we compare, via Monte Carlo simulations, the performance of the 3rd-order IVSTF-NLE and the DBP-SSF method, in terms of reach extension and computational complexity, after propagation through ITU-T G.652 SSMF and a ITU-T G.655 large effective area fiber (LEAF). By means of both experimental evaluation and simulations, we show that, in the presence of strong nonlinear effects, the 3rd-order IVSTF-NLE, which uses a single step per span, performs similarly with the two-steps-per-span DBP-SSF, whereas the eight-steps-per-span DBP-SSF is only marginally better but at the vast expense of computational complexity

Advanced DSP Techniques for High-Capacity and Energy-Efficient Optical Fiber Communications

The rapid proliferation of the Internet has been driving communication networks closer and closer to their limits, while available bandwidth is disappearing due to an ever-increasing network load. Over the past decade, optical fiber communication technology has increased per fiber data rate from 10 Tb/s to exceeding 10 Pb/s. The major explosion came after the maturity of coherent detection and advanced digital signal processing (DSP). DSP has played a critical role in accommodating channel impairments mitigation, enabling advanced modulation formats for spectral efficiency transmission and realizing flexible bandwidth. This book aims to explore novel, advanced DSP techniques to enable multi-Tb/s/channel optical transmission to address pressing bandwidth and power-efficiency demands. It provides state-of-the-art advances and future perspectives of DSP as well

Perturbative Machine Learning Technique for Nonlinear Impairments Compensation in WDM Systems

We propose a perturbation-based receiver-side machine-learning equalizer for inter- and intra-channel nonlinearity compensation in WDM systems. We show 1.6 dB and 0.6 dB Q2 -factor improvement compared with linear equalization and DBP respectively for 1000km transmission of 3×128Gbit/s DP-16QAM signal

Equalização digital para sistemas de transmissão ópticos coerentes

This thesis focus on the digital equalization of fiber impairments for coherent optical transmission systems. New efficient and low-complexity equalization and mitigation techniques that counteract fiber nonlinear impairments are proposed and the tradeoff between performance and complexity is numerically assessed and experimentally demonstrated in metro and long-haul 400G superchannels-based transmission systems. Digital backpropagation (DBP) based on low-complexity split-step Fourier method and Volterra series nonlinear equalizers are experimentally assessed in an uniform superchannel system. In contrast with standard DBP methods, these techniques prove to be able to be implemented with larger step-sizes, consequently requiring a reduced number of multiplications, and still achieve a significant reach extension over linear equalization techniques. Moreover, given its structure, the complexity of the proposed Volterra-based DBP approach can be easily adjusted by changing the nonlinear filter dimension according to the system requirements, thus providing a higher flexibility to the nonlinear equalization block. A frequency-hybrid superchannel envisioning near-future flexible networks is then proposed as a way to increase the system bit-rate granularity. The problematic of the power-ratio between superchannel carriers is addressed and optimized for linear and nonlinear operation regimes using three distinct FEC paradigms. Applying a single FEC to the entire superchannel has a simpler implementation and is found to be a more robust approach, tolerating larger uncertainties on the system parameters optimization. We also investigate the performance gain provided by the application of different DBP techniques in frequency-hybrid superchannel systems, and its implications on the optimum power-ratio. It is shown that the application of DBP can be restricted to the carrier transporting the higher cardinality QAM format, since the DBP benefit on the other carriers is negligible, which might bring a substantially complexity reduction of the DBP technique applied to the superchannel.A presente tese foca-se na equalização digital das distorções da fibra para sistemas óticos de transmissão coerente. São propostas novas técnicas eficientes e de baixa complexidade para a equalização e mitigação das distorções não lineares da fibra, e o compromisso entre desempenho e complexidade é testado numericamente e demonstrado experimental em sistemas de transmissão metro e longa distância baseados em supercanais 400G. A propagação digital inversa baseada no método de split-step Fourier e equalizadores não lineares de séries de Volterra de baixa complexidade são testadas experimentalmente num sistema baseado em supercanais uniformes. Ao contrário dos métodos convencionais utilizados, estas técnicas podem ser implementadas utilizando menos interações e ainda extender o alcance do sistema face às técnicas de equalização linear. Para além disso, a complexidade do método baseado em Volterra pode ser facilmente ajustada alterando a dimensão do filtro não linear de acordo com os requisitos do sistema, concedendo assim maior flexibilidade ao bloco de equalização não linear. Tendo em vista as futuras redes flexı́veis, um supercanal hı́brido na frequência é proposto de modo a aumentar a granularidade da taxa de transmissão do sistema. A problemática da relação de potência entre as portadoras do supercanal é abordada e optimizada em regimes de operação linear e não linear utilizando paradigmas diferentes de códigos correctores de erros. A aplicação de um único código corrector de erros à totalidade do supercanal mostra ser a abordagem mais robusta, tolerando maiores incertezas na optimização dos parâmetros do sistema. O ganho de desempenho dado pela aplicação de diferentes técnicas de propagação digital inversa em sistemas de supercanais hı́bridos na frequência é tamém analizado, assim como as suas implicações na relação óptima de potência. Mostra-se que esta pode ser restringida à portadora que transporta o formato de modulação de ordem mais elevada, uma vez que o benefı́cio trazido pelas restantes portadotas é negligenciável, permitindo reduzir significativamente a complexidade do algoritmo aplicado.Programa Doutoral em Telecomunicaçõe

Phase-sensitive amplifiers for nonlinearity impairment mitigation in optical fiber transmission links

The fundamental limitations in fiber-optic communication are caused by optical amplifier noise and the nonlinear response of the optical fibers. The quantum-limited noise figure of erbium-doped fiber amplifiers (EDFAs) or any phase-insensitive amplifier is 3 dB. However, the noise added by the amplification can be reduced using phase-sensitive amplifiers (PSAs), whose quantum-limited noise figure is 0 dB. PSAs can also compensate for the nonlinear distortions from the optical transmission fiber in the copier-PSA implementation. At the transmitter, a copier which is nothing but a phase-insensitive amplifier, is used to create a conjugated copy of the signal. The signal and idler are then copropagated in the fiber link, experiencing correlated nonlinear distortions. The nonlinear distortions are reduced by the all-optical coherent superposition of the signal and idler in the PSA.In this work, an investigation is made for the nonlinearity mitigation using the PSAs, by calculating the residual nonlinear distortion after the coherent superposition in a copier-PSA link. The nonlinearity mitigation efficiency in PSA links is studied with respect to modulation formats, symbol rates and number of wavelength channels. The effectiveness of nonlinearity mitigation is found to increase with higher-order modulation formats. However, the efficiency of nonlinearity mitigation decreases with increasing number of wavelength channels and increasing symbol rate resulting in larger residual nonlinear distortions. A modified Volterra nonlinear equalizer (VNLE) is implemented to reduce the residual nonlinear distortions after PSAs in single- and multi-channel PSA links. Cross-phase modulation mitigation using PSAs is also demonstrated