Nonlinear Signal-noise Interactions Research Articles

Performance Evaluation of Digital Back-Propagation in the Presence of Power Excursion

An accurate power map is mandatory to evaluate the performance of optical fiber transmissions in the nonlinear transmission region. In this letter, we discuss the performance variation in dispersion unmanaged fiber links due to power excursions, overarching the fiber nonlinearity that imposes a fundamental limit on the capacity of optical fiber transmissions. After using digital back-propagation (DBP) in optical fiber transmissions, the performance degradation due to power excursions shows different characteristics, depending on the location of the power excursion. Further, due to the cascading effect of the nonlinear signal-noise interaction (NSNI), the power excursion on the latter spans exerts a greater impact than that on the front spans. We implement a polarization-multiplexed 16-QAM over 12 spans of standard single-mode fiber (SSMF) experiment. The experimental results verify our theoretical analyses that the received SNRs after DBP can be sensitive to the power excursion and its location.

A Machine Learning-Based Detection Technique for Optical Fiber Nonlinearity Mitigation

We investigate the performance of a machine learning classification technique, called the Parzen window, to mitigate the fiber nonlinearity in the context of dispersion managed and dispersion unmanaged systems. The technique is applied for detection at the receiver side, and deals with the non-Gaussian nonlinear effects by designing improved decision boundaries. We also propose a two-stage mitigation technique using digital back propagation and Parzen window for dispersion unmanaged systems. In this case, digital back propagation compensates for the deterministic nonlinearity and the Parzen window deals with the stochastic nonlinear signal-noise interactions, which are not taken into account by digital back propagation. A performance improvement up to 0:4 dB in terms of Q factor is observed.

Noise Analysis of Zero-Forcing Nonlinear Equalizers for Coherent WDM Systems

We explore the fundamental limits on the achievable information rate (AIR) of fiber-optic coherent transmission systems equipped with ideal zero-forcing nonlinear equalizer (ZFNLE). In the absence of amplifier noise, the ZFNLE forces the nonlinear signal-signal distortions to zero. If amplifier noise is included in the analysis, the equalization performance is severely limited by the nonlinear interactions between signal and noise both in fiber and inside the nonlinear equalizers. We build upon our previously developed theory of nonlinear signal-noise interactions, and compute the AIR due to ZFNLE for a variety of system parameters.

Closed-form solutions for nonlinear Shannon limit due to Kerr effect in optical fibre transmissions with digital backpropagation

Abstract Among various fibre nonlinearity compensation schemes, digital backpropagation (DBP) is considered a benchmark because it can eliminate all deterministic linear and nonlinear impairments. The so-called nonlinear Shannon limit in optical fibre transmissions with DBP origins from nondeterministic effects, mainly nonlinear signal–noise interaction (NSNI) via the Kerr effect. Previous analysis of the nonlinear transmission performance is generally based on an assumption of weak NSNI. In this paper, we extend the theoretical analysis to the strong NSNI. We analyse the accumulation of NSNI along the whole fibre link and derive closed-form expressions of SNR and other important parameters. Subsequently, we verify our theoretical analysis in simulation and show that our expression still provides a good prediction well beyond the SNR peak, where the nonlinear phase shift is much larger than unity and the NSNI is strong. Our solutions provide more accurate amendments to the established ones, and we extend them to optical fibre transmission systems with polarization-multiplexing, wavelength-division multiplexing and finite transceiver noise.

Improved Lower Bounds on Mutual Information Accounting for Nonlinear Signal–Noise Interaction

In fiber-optic communications, evaluation of mutual information (MI) is still an open issue due to the unavailability of an exact and mathematically tractable channel model. Traditionally, lower bounds on MI are computed by approximating the (original) channel with an auxiliary forward channel. In this paper, lower bounds are computed using an auxiliary backward channel, which has not been previously considered in the context of fiber-optic communications. Distributions obtained through two variations of the stochastic digital backpropagation (SDBP) algorithm are used as auxiliary backward channels and these bounds are compared with bounds obtained through the conventional digital backpropagation (DBP). Through simulations, higher information rates were achieved with SDBP, {which can be explained by the ability of SDBP to account for nonlinear signal--noise interactions

NSNI Mitigation in Bi-Directional Raman Amplified Unrepeatered System Using Split-DBP

The nonlinear signal–noise interaction (NSNI) is analyzed in the bi-directional Raman amplified unrepeatered system with digital back-propagation (DBP) algorithm. When the DBP is applied at the receiver side, because in the DBP process the spontaneous Raman scattering is not dealt with, extra NSNI occurs, and because of the high power in the system, the extra NSNI is severe. By adopting split-DBP, the interaction of noise and signal in the high-power region could be avoided. Thus, the extra NSNI was mitigated and the performance was improved. The performance of split-DBP algorithm in such a system was investigated through simulations and experiments, using a single-channel 300-km bi-directional Raman amplified unrepeatered system. The simulations were carried out with 16 QAM modulation and the modulation rates were 32 GBd and 10 GBd. The results showed that the split-DBP can deliver 0.8-dB Q 2-factor improvement for the case of 32 GBd and 1.3 dB for the case of 10 GBd, compared to the traditional DBP. The impact of the nonlinear transform function of modulator and power profile mismatch on the performance of split-DBP is discussed through the simulation, which is critical to the practical implementation of split-DBP. An experimental demonstration of the split-DBP with 10 GBd 16 QAM modulation was carried out. The experimental results presented a 1.2-dB Q 2-factor improvement of the signal due to split-DBP.

Nonlinear Signal–Noise Interaction in Optical Links With Nonlinear Equalization

We investigate nonlinear signal–noise interaction (NSNI) in dispersion uncompensated links by means of the enhanced Gaussian noise (EGN) model. We include a first-order perturbative description of digital backpropagation (DBP) in the EGN model, thus accounting for NSNI not just along the optical link but even inside DBP. Thanks to the EGN model, we are able to evaluate the impact of NSNI in a setup with 133 channels, thus filling the entire bandwidth of erbium-doped fiber amplifiers. We discuss the main implications of NSNI showing that it mainly impacts the part of the nonlinear interference variance predicted by the Gaussian noise model. A simple formula to extend noiseless results to the realistic case with NSNI is proposed. Finally, the reduced efficiency of DBP in presence of NSNI is investigated and discussed.

Stochastic Digital Backpropagation

In this paper, we propose a novel detector for single-channel long-haul coherent optical communications, termed stochastic digital backpropagation (SDBP), which takes into account noise from the optical amplifiers in addition to handling deterministic linear and nonlinear impairments. We discuss the design approach behind this detector, which is based on the maximum a posteriori (MAP) principle. As closed-form expressions of the MAP detector are not tractable for coherent optical transmission, we employ the framework of Bayesian graphical models, which allows a numerical evaluation of the proposed detector. Through simulations, we observe that by accounting for nonlinear signal-noise interactions, we achieve a significant improvement in system reach with SDBP over digital backpropagation (DBP) for systems with periodic inline optical dispersion compensation. In uncompensated links with high symbol rates, the performance difference in terms of system reach for SDBP over DBP is small. In the absence of noise, the proposed detector is equivalent to the well-known DBP detector.

Theoretical modeling of dispersion uncompensated CO-OFDM transmission with coarse-step DBP based intra-channel nonlinearity compensation

In this paper, we derive an accurate analytical expression for evaluating the transmission performance of dispersion uncompensated coherent optical OFDM (CO-OFDM) systems with intra-channel fiber nonlinearity mitigation based on coarse-step digital back propagation (CS-DBP). This theoretical model is substantiated through numerical simulations for the polarization-division multiplexed (PDM) 16-QAM systems with various DBP step size and processing bandwidth. After 1000km dispersion uncompensated SSMF transmissions, the maximum Q factor discrepancy between simulation and analytical results is only 0.62dB, showing quite good evaluation accuracy. In addition to the theoretically modeling and numerically substantiations, the impacts of ASE and nonlinear signal–noise interaction (NSNI) on CS-DBP are also investigated. It is found that, unlike ideal DBP with fine enough processing step size, the influence of NSNI on 25GHz dispersion uncompensated CO-OFDM transmissions with commonly used CS-DBP can be negligible. Moreover, our results also show that the influence of ASE on the optimum nonlinear compensation factor is only noticeable for very small launch power levels where the system performance would still not be impacted.

Nonlinear signal-noise interactions in dispersion managed coherent PM-QPSK systems in the presence of PMD

Considering the polarization mode dispersion(PMD), the transmission penalty induced by nonlinear signal-noise interactions (NSNI) between the amplified spontaneous emission noise (ASE) and the information signal is investigated numerically for 40(100)G dispersion-managed(DM) polarization-multiplexed quadrature phase-shift keying (PM-QPSK) systems. We show that for single-channel PM-QPSK systems, PMD is helpful to reduce the NSNI-induced penalty. For multi-channel PM-QPSK system, however, the NSNI-induced nonlinear penalty is significantly enhanced by PMD, especially at low bit-rate. Our results show that due to the NSNI, the reduction of allowed input power that gives 1-dB Q penalty after 1600-km nonlinear transmission will increase from 1dB without PMD to 3.7dB with PMD for 42.8-Gbit/s coherent return-to-zero (RZ)-PM-QPSK systems.

Impact of nonlinear signal-noise interactions on symbol-aligned and -interleaved formats in dispersion managed coherent PM-QPSK systems

Using numerical simulations, the impact of nonlinear signal-noise interactions (NSNI) between the amplified spontaneous emission noise (ASE) and the information signal on polarization-multiplexed quadrature phase-shift keying (PM-QPSK) systems at 42.8 (112)-Gbit/s is investigated over dispersion-managed (DM) link. Both symbol-aligned and symbol-interleaved formats are considered and compared. We find that for symbol-aligned PM-QPSK systems, the impact of NSNI on system performance seems rather weak due to the strong inter-channel cross-polarization modulation (XPolM). However, when the symbol-interleaved format is used, in which the XPolM is suppressed significantly, the system performance is seriously degraded by NSNI, especially at low bit-rate. Results of 1000-km transmission employing standard single-mode fiber (SSMF) over DM link show that for 42.8-Gbit/s coherent PM-QPSK systems, the nonlinear threshold (NLT) will decrease from 5.8dBm to 0.6dBm due to the nonlinear signal-noise interactions when symbol-interleaved RZ format is used.

Nonlinear signal–noise interactions in dispersion-managed links with various modulation formats

Purpose of this paper is to highlight the principles of the nonlinear signal–noise interaction (NSNI) in dispersion-managed long-haul optical links and provide a quantitative understanding of the system parameters for which NSNI sets the nonlinear performance of the most popular intensity and phase modulation formats, namely on–off keying, differential binary and quadrature phase-shift keying and coherent quadrature phase-shift keying.