Periodic Dispersion Compensation Research Articles

How to Increase the Achievable Information Rate by Per-Channel Dispersion Compensation

Deploying periodic inline chromatic dispersion compensation enables reducing the complexity of the digital back propagation (DBP) algorithm. However, compared with nondispersion-managed (NDM) links, dispersion-managed (DM) ones suffer a stronger cross-phase modulation (XPM). Utilizing per-channel dispersion-managed (CDM) links (e.g., using fiber Bragg grating) allows for a complexity reduction of DBP, while abating XPM compared to DM links. In this paper, we show for the first time that CDM links enable also a more effective XPM compensation compared to NDM ones, allowing a higher achievable information rate (AIR). This is explained by resorting to the frequency-resolved logarithmic perturbation model and showing that per-channel dispersion compensation increases the frequency correlation of the distortions induced by XPM over the channel bandwidth, making them more similar to a conventional phase noise. We compare the performance (in terms of the AIR) of a DM, an NDM, and a CDM link, considering two types of mismatched receivers: one neglects the XPM phase distortion and the other compensates for it. With the former, the CDM link is inferior to the NDM one due to an increased in-band signal--noise interaction. However, with the latter, a higher AIR is obtained with the CDM link than with the NDM one owing to a higher XPM frequency correlation. The DM link has the lowest AIR for both receivers because of a stronger XPM.

Optimization of the Capacity of a Fiber Communication Line with Nonlinear Memory

Channels with and without memory are compared using the simplest Gaussian noise distribution model. It is shown that both channels have similar dependences of the capacity on the average signal power. At the same time, the optimal input alphabet for the channel with memory changes. The applicability of the model with nonlinear memory to the QPSK communication line with a periodic dispersion compensation is demonstrated numerically.

Theoretical and numerical characterization of a 40 Gbps long-haul multi-channel transmission system with dispersion compensation

When updating the 10Gbps optical transmission system to 40Gbps, the main limits are chromatic dispersion, nonlinear effect, especially the interactions of dispersion and intra-channel nonlinearity. To optimize the performance of standard WDM in a 40Gbps four-channel transmission system, numerical simulations are carried out to compare three different dispersion compensation techniques (without compensation; periodic dispersion compensation at the front end; and dispensation compensation all at the end of the system by means of highly dispersed pulses) for chromatic dispersion on a terrestrial 40Gbps system. Both the loss and dispersion of the transmission fiber are periodically compensated, since two dispersive elements are placed at the input and the output ends of a compensation period. Due to the interplay between dispersion, nonlinearity and signal power, and the effect of dispersion on the pulse evolution, the pulse compress can be optimized and the system performance can be improved to compare with the system with either pre- or post-dispersion compensation. On comparing pre- and post-compensation methods, it is found that the latter is superior to the former. Further performance optimization includes how to properly match the EDFA power and length of the fiber.

Modified Nonlinear Decision Feedback Equalizer for Long-Haul Fiber-Optic Communications

In a long-haul optical fiber communication system, fiber attenuation, dispersion, and nonlinearity combined with nondeterministic noise from optical amplifiers used for periodic regeneration cause adverse effects on system performance. Several optical and electrical signal processing techniques have been proposed, and implemented to extract the transmitted data; some provide better performance than others, but at a cost of higher computational complexity. We present a modified nonlinear decision feedback equalizer designed for use in a legacy optical communication system with periodic dispersion compensation. The effects of noise and nonlinearity on the equalizer coefficients are investigated, and a suboptimal convergence algorithm to reduce such effects is proposed and verified. Our equalizer provides performance comparable to that obtained using digital backpropagation, while being computationally simpler, compensating linear and nonlinear physical impairment effects effectively even at high power levels where fiber nonlinearity is significant. Performance prediction of the designed DFE is also discussed, using a numerical method, with and without error propagation.

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.

Range of Influence and Impact of Physical Impairments in Long-Haul DWDM Systems

In long-haul dense wavelength-division multiplexing (DWDM) systems with periodic dispersion compensation and amplification, system performance is adversely affected by severe physical impairments due to fiber losses, dispersion and nonlinearity. Fiber modeling is a prerequisite for the development of physical impairment mitigation techniques to improve system performance. The distance between two interacting symbols in time and wavelength, i.e., the range of influence (RoI) of each physical impairment, plays an important role in the development of these mitigation techniques. In this paper, we use the Volterra series transfer function (VSTF) method to define impairment characteristic coefficients that capture intersymbol interference (ISI), self phase modulation (SPM), intrachannel cross phase modulation (IXPM), intrachannel four wave mixing (IFWM), cross phase modulation (XPM) and four wave mixing (FWM), to characterize the impact of these impairments individually on the system output. We then investigate the impact of system parameters, namely, duty cycle, spectral efficiency, frequency chirp, and span length, on the RoI for long-haul DWDM systems.

Pilot-based XPM nonlinearity compensator for CO-OFDM systems

We experimentally verify that pilot-based nonlinearity compensation is effective for mitigating XPM in CO-OFDM systems, if SPM is compensated first. A 6-dB increase in the nonlinear limit was produced by pilot-based XPM compensation after a single-step SPM compensator in a 400-km link with periodic dispersion compensation. In addition, we use numerical simulations to show that the required bandwidth of the guard-band around the pilot is almost independent of the bandwidth of the data-carrying sidebands. The optimal ratio of pilot to signal power also decreases for higher bandwidth OFDM signals. Therefore, the overhead associated with transmitting the pilot decreases as the bandwidth of the signal increases.

Mitigation of phase noise in dispersion compensated quasi-linear optical transmission systems: Analysis

We theoretically investigate the phase noise in quasi-linear optical transmission systems and study the mitigation of phase noise by properly choosing periodic dispersion compensation and amplification. Variational method is used to deduce the analytical formula for calculating the phase fluctuations of a Gaussian pulse. The analytical predictions are then checked against direct simulations by numerically solving the nonlinear Schrödinger equation. We find that stronger dispersion compensation maps can be used to reduce phase noise and it can be further mitigated by modifying the dispersion map appropriately. It is also found that shorter amplifier spacing yields lower phase noise. We also explore the effect of pre-, post- and bi-end dispersion compensation configurations on phase noise with full compensation and check the reduction of phase noise along the fiber link.

Impacts of dispersion maps on nonlinear distortion in distributed Raman amplified multi-span systems

The influences of dispersion maps on three major nonlinear effects (SPM, XPM and SRS) in distributed Raman amplified fiber transmission systems with periodic dispersion compensation are numerically investigated at identical nonlinear phase shift. The results show that compared with lumped amplification, distributed amplification tends to enhance the SPM/XPM induced penalties provided per span complete DC is used. However, these performance differences can be canceled out by means of optimal dispersion managements. Moreover, distributed Raman amplification can change the optimal dispersion maps for XPM effects. On the other hand, the impacts of SRS crosstalk are mainly determined by wavelength spacing and walk-off parameter, and the effects of dispersion management are quite limited. For a system with properly designed fiber dispersion characteristics, SRS induced waveform distortion can be well suppressed.

Numerical Study of Lumped Dispersion Compensation for 40-Gb/s Return-to-Zero Differential Phase-Shift Keying Transmission

Lumped dispersion compensation is numerically investigated for 40-Gb/s return-to-zero differential phase-shift-keying transmission. Using pseudorandom binary sequence lengths up to 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sup> -1, simulation results indicate that better long-distance transmission performance can be achieved using lumped dispersion compensation than using conventional periodic inline dispersion compensation. Improved performance is found to be a result of reduced nonlinear effects and the elimination of periodic accumulation of nonlinear effects. The lumped compensation scheme provides a simple, flexible, and potentially low-cost solution for transmission link design

Suppressing modulation instability in midway optical phase conjugation systems by using dispersion compensation

Modulation instability (MI) limits the transmission capacity of fiber systems using optical phase conjugation (OPC). A midway OPC system with periodic dispersion compensation (DC) where fiber parameters and the local path-averaged power are distributed symmetrically with respect to the position of OPC, is proposed to cope with the MI effect. The analytical solution for evaluating the effect of MI shows that the MI effect can be suppressed considerably in such an OPC system with a strong DC configuration. The improvement of the system performance is confirmed by numerical simulations.

Impact of the Fiber Type and Dispersion Management on the Performance of an NRZ 16&amp;lt;tex&amp;gt;$times$&amp;lt;/tex&amp;gt;40 Gb/s DWDM Transmission System

We examine the impact of the fiber type and dispersion management on the performance of a 16 /spl times/ 40 Gb/s dense wavelength-division-multiplexing nonreturn-to-zero transmission system. The transmission line is composed of G.652 or G.655 fiber with periodic dispersion compensation and hybrid Raman erbium-doped fiber amplifier amplification.

Impacts of SPM/XPM on Distributed Raman Amplified Multispan Systems at Identical Nonlinear Phase Shift

The influences of self-phase modulation (SPM) and cross-phase modulation (XPM) on Raman amplified multispan systems with periodic dispersion compensation (DC) are numerically investigated at identical nonlinear phase shift. The results show that compared with lumped amplification, distributed amplification tends to enhance the SPM/XPM-induced penalties provided per span complete DC is used. However, these performance differences can be canceled out by means of optimal dispersion managements. Useful guidelines for optimizing the dispersion maps of Raman amplified systems are demonstrated.

Minimization of the pulse's timing jitter in a dispersion-compensated WDM system

We address the problem of the collision-induced crosstalk between pulses in a dispersion-compensated WDM system composed of a periodic array of cells that include two or three fiber segments. Both the cross- and self-phase-modulation nonlinearities are taken into account. A semi-analytical approximation and direct simulations are used to calculate the frequency shift (FS) of colliding pulses, and to search for conditions which provide for minima of the FS and the temporal shift (TS), including the most promising possibility of minimizing both shifts simultaneously. Semi-analytical results, obtained by means of the perturbation theory, are in qualitative agreement with the numerical findings, especially in regimes near the optimum. In searching for the FS and TS minima, we investigate the effect of changing the initial width and chirp of the pulse, position of the amplifier within the dispersion–compensation period, group-velocity difference between the channels, allocation of the group-velocity-dispersion (GVD) inside the cell, and the average GVD. We conclude that a more sophisticated dispersion–compensation map, with three different local values of GVD, may be significantly more efficient than the one based on two different segments. A global FS minimum, with respect to the variation of all the parameters, is found.

Nonlinearity management in fiber transmission systems with hybrid amplification

Nonlinearity management in transmission lines with periodic dispersion compensation and hybrid Raman-Erbium doped fiber amplification is studied both analytically and numerically. Different transmission/compensating fiber pairs are considered, with particular focus on the SMF/DCF case.

Nonlinearity management in fibre links with distributed amplification

An approach to nonlinearity management in optical transmission lines with periodic dispersion compensation and distributed Raman amplification was presented. The optimization of a three-step dispersion map with forward and backward pumped distributed amplification was examined. The optimization was performed using the analytical solution obtained under the assumption of undepleted pumps and without inclusion of double Rayleigh Scattering (DRS), and by means of a full numerical approach accounting for all important effects. It was found that both procedures led to the same final solution.

Implementation of non-linearity management for Gaussian pulses in a fiber-optic link by means of second-harmonic-generating modules

We introduce a model for the non-linearity compensation (“management”), based on second-harmonic-generating [ χ (2)] elements, integrated with amplifiers, which are periodically inserted into a fiber-optic link. The link features the Kerr [ χ (3)] non-linearity, group-velocity dispersion (GVD), and loss. Simulations demonstrate that the system can directly provide for effective compensation of the fiber non-linearity for quasi-Gaussian pulses over the propagation distance z up to 10 fiber spans between the χ (2) modules, and the interaction between adjacent pulses does not manifest itself over the same propagation distance, provided that the separation between them is ≃5 widths of the pulse or more. The results are sensitive to the correct choice of the mismatch parameter in the χ (2) module, but not to variation of other parameters (for instance, peak power of the pulses). For larger values of z, distortion of the pulses commences under the action of GVD. This can be prevented by periodic dispersion compensation. Although the latter is not directly included into the model, it is demonstrated that the non-linearity and dispersion compensation can be implemented independently, as they take place at essentially different scales of z for typical NRZ pulses. Thus, the stable-transmission distance can be expanded much farther.

Numerical and experimental comparison of dispersion compensation techniques on different fibers

The authors carry out a numerical and experimental comparison between three different techniques for chromatic dispersion compensation on a terrestrial 40-Gb/s system. They are: periodic dispersion compensation at the amplifier places; the same but with initial prechirp; and dispersion compensation all at the end of the system by means of highly dispersed pulses. Numerical results are consistent with experimental ones and suggest the most convenient compensation technique with respect to fiber type (G.652 or G.655) and pulsewidth (3-10 ps).

The theory of optical communication lines with a short-scale dispersion management

We investigate, theoretically and numerically, properties of dispersion-managed (DM) solitons in fiber lines with the dispersion compensation period L much shorter than the amplification distance Za. We present the path-averaged theory of DM transmission lines with a short-scale management in the case of asymmetric maps. Applying a quasi-identical transformation, we demonstrate that the path-averaged dynamics in such systems can be described by an integrable model in some limits.

A simple design of a highly tolerable dispersion managed soliton system for trans-oceanic distance transmission

We present a design for a dispersion managed (DM) soliton system, which is based on two primary parameters; the dispersion compensation period (DCP), which is defined by the number of DSF spans between dispersion compensation fiber, and pulse width. We designed the optimum value of these two parameters to achieve the widest system margins for both repeater output power and signal wavelength for trans-oceanic distance transmission. We checked this analysis by experiments for both 10 and 20 Gb/s DM soliton systems having 53 km repeater spacing. Experimental results confirm the validity of proposed system design.