We consider the communication channel given by a fiber optical transmission line. We develop a method to perturbatively calculate the information capacity of a nonlinear channel, given the corresponding evolution equation. Using this technique, we compute the decrease of the channel capacity to the leading order in the perturbative parameter for fiber optics communication systems.

https://arxiv.org/pdf/physics/0007033.pdf

The Channel Capacity of a Fiber Optics Communication System: perturbation theory

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 Gb/s wavelength-division multiplexing (WDM) standard technology. They allow the increase of spectral efficiency by using multilevel modulation formats, and are combined with DSP techniques to combat linear fiber distortions. In addition to linear impairments, the next generation 400 Gb/s and 1 Tb/s WDM systems are also more affected by the fiber nonlinearity due to the Kerr effect. At high input powers, 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 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.

A Survey on Fiber Nonlinearity Compensation for 400 Gb/s and Beyond Optical Communication Systems

From first-order perturbation theory, we derive the autocorrelation function of the nonlinear interference in coherent optical links We show that the fundamental assumptions of the Gaussian noise (GN) model regarding stationary Gaussian statistics of the transmitted signal can be removed for a more complete model accounting for the fine details of the cyclostationary modulation format We first give an intuitive presentation of the theory, and then provide a formal mathematical treatment based on symbol cumulants and discuss its key assumptions and limitations The proposed model includes dual polarization effects, wavelength-division multiplexing and the nonlinear signal to amplified spontaneous emission noise interaction along the line, thus neglecting only the impact of four-wave mixing

/pdf/a-time-domain-extended-gaussian-noise-model-17lrkxb674.pdf

A Time-Domain Extended Gaussian Noise Model

Previous investigations have revealed that the impairments of the cross-phase modulation (XPM) in dense wavelength-division multiplexing (DWDM) systems include two aspects: the XPM-induced phase noise and the XPM-induced polarization scattering. Such XPM phenomena are strongly dependent on the transmission system configurations and are nonintuitive. In this paper, a simple fiber model is proposed to facilitate the determination of XPM effects. By employing this model, the phase noise and polarization scattering are calculated based on the system configurations and the time-consuming computation by the split step Fourier method is avoided. The proposed model is verified by the dual polarization quadrature phase-shift keying coherent DWDM experiments and simulations in terms of the variance and autocorrelations of phase noise and polarization crosstalk as well as their dependence on relative polarization states and the overall Q-impairment. The proposed model helps deeper analysis of XPM phenomena, and eventually, leads to development of various XPM mitigation methods through transmission system design and coherent receiver DSP.

Simple Fiber Model for Determination of XPM Effects

We describe in detail the recently proposed four-dimensional modulation format family based on 2-ary amplitude 8-ary phase-shift keying (2A8PSK), supporting spectral efficiencies of 5, 6, and 7 bits/symbol. These formats nicely fill the spectral efficiency gap between the dual-polarization (DP) quadrature PSK (QPSK) and DP 16-ary quadrature-amplitude modulation (16QAM), with excellent linear and nonlinear performance. Since these modulation formats just use different parity bit expressions in the same constellation, similar digital signal processing can be seamlessly used for different spectral efficiency. A series of nonlinear transmission simulation results shows that this modulation format family outperforms the conventional modulation formats at the corresponding spectral efficiency. We also investigate the adaptive equalizer for these modulation formats.

Nonlinearity-Tolerant Four-Dimensional 2A8PSK Family for 5–7 Bits/Symbol Spectral Efficiency

Starting from a model of random nonlinear polarization rotations for the effect of cross-polarization modulation in DWDM systems, we derive the mean distribution of the time-dependent polarization states at an arbitrary location within an optical link. We show that this distribution is fully parameterized by the degree of polarization of the particular wavelength channel, and we derive expressions to approximate this parameter for general optical links consisting of multiple optically amplified and dispersion-compensated spans, as well as related power thresholds. From the analytical expressions we derive a method to significantly reduce the detrimental effects.

/pdf/a-statistical-treatment-of-cross-polarization-modulation-in-28kockofg9.pdf

A Statistical Treatment of Cross-Polarization Modulation in DWDM Systems

We show theoretically and with the aid of computer simulations that the nonlinear depolarization induced by cross-polarization modulation leads to crosstalk between the polarization-division multiplex (PolDM) subchannels during their demultiplexing. This additive crosstalk can be approximated as additive Gaussian noise, and we derive expressions to estimate its variance. It can lead to significant penalties of up to several decibels for PolDM transmission and must be properly accounted for. We also show why time-interleaving both subchannels can significantly reduce these penalties.

Cross-Polarization Modulation in Polarization-Division Multiplex Transmission

Fiber nonlinearities in WDM systems using linear electronic dispersion precompensation are studied at high bit rates. In contrast to 10 Gb/s systems, only a small performance degradation due to nonlinearities was found at 40 Gb/s.

Fibre nonlinearities in 10 and 40 Gb/s electronically dispersion precompensated WDM transmission

Solutions to transmit 100 gigabit Ethernet signals (GbE) over hundred or more kilometers are discussed. An overview of experimental ges 100 Gb/s ETDM approaches is given and the suitability of various modulation formats is evaluated.

100 Gigabit Ethernet Transmission - Physical Layer Issues

We show how cross-polarization modulation and its associated signal depolarization can cause significant penalties in polarization-division multiplexed systems. We then explore the concept of degrees of freedom of a system to analyze the statistics of this impairment.

http://www.marcuswinter.de/media/publications/ecoc2010/Th.10.E.3.pdf

Marcus Winter

Papers

A Statistical Treatment of Cross-Polarization Modulation in DWDM Systems

Cross-Polarization Modulation in Polarization-Division Multiplex Transmission

Fibre nonlinearities in 10 and 40 Gb/s electronically dispersion precompensated WDM transmission

100 Gigabit Ethernet Transmission - Physical Layer Issues

Polarization-multiplexed transmission system outage due to nonlinearity-lnduced depolarization