Nonlinearity Mitigation in WDM Systems: Models, Strategies, and Achievable Rates

After reviewing models and mitigation strategies for interchannel nonlinear interference (NLI), we focus on the frequency-resolved logarithmic perturbation model to study the coherence properties of NLI. Based on this study, we devise an NLI mitigation strategy which exploits the synergic effect of phase and polarization noise compensation (PPN) and subcarrier multiplexing with symbol-rate optimization. This synergy persists even for high-order modulation alphabets and Gaussian symbols. A particle method for the computation of the resulting achievable information rate and spectral efficiency (SE) is presented and employed to lower-bound the channel capacity. The dependence of the SE on the link length, amplifier spacing, and presence or absence of inline dispersion compensation is studied. Single-polarization and dual-polarization scenarios with either independent or joint processing of the two polarizations are considered. Numerical results show that, in links with ideal distributed amplification, an SE gain of about 1 bit/s/Hz/polarization can be obtained (or, in alternative, the system reach can be doubled at a given SE) with respect to single-carrier systems without PPN mitigation. The gain is lower with lumped amplification, increases with the number of spans, decreases with the span length, and is further reduced by in-line dispersion compensation. For instance, considering a dispersion-unmanaged link with lumped amplification and an amplifier spacing of 60 km, the SE after 80 spans can be be increased from 4.5 to 4.8 bit/s/Hz/polarization, or the reach raised up to 100 spans (+25%) for a fixed SE.Comment: Submitted to Journal of Lightwave Technolog

Scope and Limitations of the Nonlinear Shannon Limit

The concept and significance of the so called nonlinear Shannon limit are reviewed and their relation to the channel capacity is analyzed from an information theory point of view. It is shown that this is a limit (if at all) holding only for conventional detection strategies. Indeed, it should only be considered as a limit to the information rate that can be achieved with a given modulation/detection scheme. By virtue of some simple examples and theoretical results, it is also shown that, using the same approximated models commonly adopted for deriving the nonlinear Shannon limit, the information rate can be arbitrarily increased by increasing the input power. To this aim, the validity of some popular approximations to the output distribution is also examined to show that their application outside the scope for which they were devised can lead to pitfalls. To the best of our belief, the existence of a true nonlinear Shannon limit has still not been demonstrated, and the problem of determining the channel capacity of a fiber-optic system in the presence of Kerr nonlinearities is still an open issue

Digital nonlinearity compensation in high-capacity optical communication systems considering signal spectral broadening effect

Nyquist-spaced transmission and digital signal processing have proved effective in maximising the spectral efficiency and reach of optical communication systems. In these systems, Kerr nonlinearity determines the performance limits, and leads to spectral broadening of the signals propagating in the fibre. Although digital nonlinearity compensation was validated to be promising for mitigating Kerr nonlinearities, the impact of spectral broadening on nonlinearity compensation has never been quantified. In this paper, the performance of multi-channel digital back-propagation (MC-DBP) for compensating fibre nonlinearities in Nyquist-spaced optical communication systems is investigated, when the effect of signal spectral broadening is considered. It is found that accounting for the spectral broadening effect is crucial for achieving the best performance of DBP in both single-channel and multi-channel communication systems, independent of modulation formats used. For multi-channel systems, the degradation of DBP performance due to neglecting the spectral broadening effect in the compensation is more significant for outer channels. Our work also quantified the minimum bandwidths of optical receivers and signal processing devices to ensure the optimal compensation of deterministic nonlinear distortions

Modelling non-linear interference in non-periodic and disaggregated optical network segments

We investigate the generation of nonlinear interference (NLI) within two disaggregated transmission scenarios, each considering a chain of three distinct optical line systems that contain fibers with different dispersion values, with 400G-ZR+ 64 GBd transmission simulated using the split-step Fourier method. Firstly, by separating the NLI into its main constituents: the self- and cross-phase modulations, we investigate the impact of accumulated dispersion upon NLI generation and compensate for the coherent accumulation of the former to produce a model that is fully spectrally and spatially separable, including for alien wavelengths. Considering ideal and optimized in-line amplification, we calculate the amplified spontaneous emission noise and combine this value with the recovered NLI to obtain the generalized signal-to-noise ratio. We show that this disaggregated model provides accurate and conservative results for both transmission scenarios, showing that abstracting these signals with a Gaussian noise approximation always results in a conservative prediction, even for non-uniform fiber dispersion scenarios

Nonlinear Interference Generation in Wideband and Disaggregated Optical Network Architectures

L'abstract è presente nell'allegato / the abstract is in the attachmen

Capacity Analysis and Receiver Design in the Presence of Fiber Nonlinearity

The majority of today\u27s global Internet traffic is conveyed through optical fibers. The ever-increasing data demands have pushed the optical systems to evolve from using regenerators and direct-direction receivers to a coherent multi-wavelength network. Future services like cloud computing and virtual reality will demand more bandwidth, so much so that the so called capacity-crunch is anticipated to happen in near future. Therefore, studying the capacity of the optical system is needed to better understanding and utilizing the existing fiber network.The characterization of the capacity of the dispersive and nonlinear optical fiber described by the nonlinear Schr{\"o}dinger equation is an open problem. There are a number of lower bounds on the capacity which are mainly obtained based on the mismatched decoding principle or by analyzing simplified channels. These lower bounds either fall to zero at high powers or saturate. The question whether the fiber-optical capacity has the same behavior as the lower bounds at high power is still open. Indeed, the only known upper bound increases with the power unboundedly. In this thesis, we first study how the fiber nonlinear distortion is modeled in some simplified channels and what is the influence of the simplifying assumptions on the capacity. To do so, the capacity of three different memoryless simplified models of the fiber-optical channel are studied. The results show that in the high-power regime the capacities of these models grow with different pre-logs, which indicates the profound impact of the simplifying assumptions on the capacity of these channels. Next, we turn our attention to demodulation and detection processes in the presence of fiber nonlinearity. We study a two-user memoryless network. It is shown that by deploying a nonlinearity-tailored demodulator, the performance improves substantially compared with matched filtering and sampling. In the absence of dispersion, we show that with the new receiver, unlike with matched filtering and sampling, arbitrarily low bit error rates can be achieved. Furthermore, we show via simulations that performance improvements can be obtained also for a low-dispersion fiber.Then, we study the performance of three different dispersion compensation methods in the presence of inter-channel nonlinear interference. The best performance, in terms of achievable information rate, is obtained by a link with inline per-channel dispersion compensation combined with a receiver that compensates for inter-channel nonlinearities. Finally, the capacity analysis is performed for short-reach noncoherent channel, where the source of nonlinearity is not the fiber but a square-law receiver. Capacity bounds are established in the presence of optical and thermal noises. Using these bounds we show that optical amplification is beneficial at low signal-to-noise ratios (SNRs), and detrimental at high SNRs. We quantify the SNR regime for each case for a wide range of channel parameters

Calculation of Mutual Information for Partially Coherent Gaussian Channels with Applications to Fiber Optics

The mutual information between a complex-valued channel input and its complex-valued output is decomposed into four parts based on polar coordinates: an amplitude term, a phase term, and two mixed terms. Numerical results for the additive white Gaussian noise (AWGN) channel with various inputs show that, at high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the mixed terms. For the AWGN channel with a Gaussian input, analytical expressions are derived for high SNR. The decomposition method is applied to partially coherent channels and a property of such channels called "spectral loss" is developed. Spectral loss occurs in nonlinear fiber-optic channels and it may be one effect that needs to be taken into account to explain the behavior of the capacity of nonlinear fiber-optic channels presented in recent studies.Comment: 30 pages, 9 figures, accepted for publication in IEEE Transactions on Information Theor

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