Intrachannel Nonlinear Effects Research Articles

Numerical Analysis of Dispersion Compensation Schemes for Pseudo-linear Transmission System

AbstractA pseudo-linear optical transmission system analytical model is built for the numerical analysis of dispersion compensation schemes. The system performance under the influence of intra-channel nonlinear effects and the initial pulse power is discussed for the data rates of 10, 40, 100 and 160 Gbit/s, respectively. We get the conclusion for the first time as we know the optimal dispersion compensation scheme for the optimal system performance is closely related to the system data rate and the proportion of the pre-dispersion compensation should be decreased while that of the post-dispersion compensation be increased with the increasing of system data rate. When the system data rate is higher than 160 Gbit/s, we can use the post-dispersion compensation scheme directly.

强色散管理准线性传输信道内非线性效应及其抑制研究

强色散管理准线性传输信道内非线性效应及其抑制研究

Performance Dependence on Channel Baud-Rate of PM-QPSK Systems Over Uncompensated Links

We investigated through simulation the performance of dense wavelength-division-multiplexing transmission systems based on polarization-multiplexed quadrature phase-shift keying over long-haul uncompensated links. We looked at three system configurations, whose per-channel Baud-rate was 14, 28, and 56 GBaud, respectively. Their total net capacity in the C-band (8 Tb/s) and net spectral efficiency (2 b/s/Hz) were exactly the same. We found that the systems long-haul performance is almost the same in the three cases, with the 56-GBaud configuration only slightly under-performing. By means of backward-propagation, we also found that the balance between intrachannel and interchannel nonlinear (NL) effects is completely different in the three cases, with 14-GBaud dominated by interchannel NL effects and 56-GBaud dominated by single-channel NL effects. We also show that, where possible to actually exploit backward-propagation, the 56-GBaud per channel system would outperform the lower Baud-rate configurations.

Influence of the Extinction Ratio on the Intrachannel Nonlinear Distortion of 40-Gb/s Return-to-Zero Transmission Systems Over Standard Fiber

The impact of the extinction ratio (ER) on the performance of a 40-Gb/s return-to-zero transmission system over standard single-mode fiber (SSMF) is presented. Several dispersion maps are analyzed in order to minimize the distortion due to the intrachannel nonlinear effects, namely, intrachannel cross-phase modulation and intrachannel four wave mixing (IFWM). The decrease of the ER until a specific value leads to an increase of the intensity distortion, which is mainly due to IFWM. As a consequence, two distinct transmission regimes are identified, depending on the input average power of each section and the ER of the optical signals. The first regime has previously been called the pseudolinear regime in the literature and occurs when high ERs are considered. The optimum dispersion map of this regime has a given optical precompensation and a total residual dispersion near zero. The second regime occurs with the decrease of the ER. Under such a circumstance, the optimum dispersion map obtained in the pseudolinear regime leads to significant degradation, which is mainly due to ghost pulses appearing in the symbol ldquo0.rdquo This effect can be reduced by a system with residual dispersion that is significantly different from zero, leading to a detected eye pattern with low degradation in the symbol ldquo0rdquo but high timing jitter, which limits the use of such signals in feasible transmission systems. We call this new regime pseudosolitonic as the intrachannel nonlinear effects are apparently reduced by the residual group velocity dispersion (as it is observed in the solitonic regime occurring at lower bit rates), but strong waveform degradation occurs along the SSMF transmission. The exact value of ER for which the change between the two transmission regimes is observed depends on the optical average power at the input of each section. A simple expression to predict the system conditions (namely, ER, input average power of each section, and number of sections) for which the transition between the two regimes occurs is proposed, and its validity is analyzed.

Optimization of Single-Sideband DCS-RZ Format for Long-Haul 43-Gb/s/channel Ultradense WDM Systems

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The optimization of the single-sideband (SSB) duobinary carrier-suppressed (DCS) return-to-zero (RZ) format for long-haul ultradense wavelength-division multiplexing (UDWDM) systems with a 43-Gb/s/channel and a channel spacing of 50 GHz is investigated numerically. It is shown that the optimized SSB-DCS-RZ format with an electrical transmitter bandwidth of 0.35 of the bit rate has about 1 dB of <formula formulatype="inline"><tex>$Q$</tex> </formula>-factor improvement relative to the conventional SSB-DCS-RZ format (an electrical transmitter bandwidth of 0.25 of the bit rate) due to the reduction of noise bandwidth, smaller linear crosstalk, and better tolerance to the intra-channel fiber nonlinear effects. No substantially different UDWDM system performance is observed when varying the duty cycle of the DCS-RZ signal with optimized SSB filters settings. The UDWDM transmission performance of SSB-DCS-RZ formats is compared with the bandwidth-limited (BL)-duobinary formats. It is shown that generally, the SSB-DCS-RZ formats have poorer <formula formulatype="inline"><tex>$Q$</tex></formula>-factor and tolerance to the total residual dispersion but much higher tolerance to the in-line dispersion compensation and intra-channel nonlinear effects than the BL-duobinary formats. </para>

Analysis and comparison of impairments in differential phase-shift keying and on-off keying transmission systems based on the error probability

The effect of nonlinear phase noise in dispersion-managed optical transmission systems is studied. The variance of the nonlinear phase noise in systems based on differential phase-shift keying (DPSK) in the presence of dispersion is examined analytically, and a semianalytical expression to calculate the error probability including intrachannel four-wave mixing, linear phase noise, and nonlinear phase noise for systems based on DPSK is derived. In addition, for the on-off keying (OOK) format, the formula for the error probability including amplified spontaneous emission noise and intrachannel nonlinear effects has been given. On the basis of the semianalytical expressions, we have compared the error probability of systems based on DPSK and OOK, and the results show that, to reach a given bit error rate of 10(-9) for a specific long-haul system, the difference between the signal-to-noise ratio required by the DPSK format and that required by the OOK format is around 6 dB for the launch power of 0 dBm, and the difference becomes larger as the launch power increases.

Electronic precompensation of intrachannel nonlinearities at 40 gb/s

Digital electronic precompensation of intrachannel nonlinearities is studied in a transmission system which consists of 100% dispersion-compensated spans. Different Mach-Zehnder-based transmitter structures are compared. Simulation results demonstrate that using a triple Mach-Zehnder modulator achieves effective compensation of intrachannel nonlinear effects at large launch powers

Noise-predictive BCJR equalization for suppression of intrachannel nonlinearities

An iterative equalization scheme for suppressing intrachannel nonlinearities in high-speed optical transmission systems operating at 40 Gb/s is presented. The proposed method employs a noise-predictive filter to mitigate the colored noise due to amplified spontaneous emission noise and optical filtering. The maximum a posteriori probability symbol detection implemented as the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm is employed to suppress the intrachannel nonlinear effects. Soft decision outputs provided by the noise-predictive BCJR equalizer are processed by an iterative low-density parity-check decoder

Rate 2/3 modulation code for suppression of intrachannel nonlinear effects in high-speed optical transmission

An efficient approach in suppressing of intrachannel nonlinear effects using modulation codes is proposed. Significant Q-factor improvement ranging from 7–13 dB depending on modulation format, extinction ratio and number of spans is demonstrated. The encoder design is described, and sliding window decoding logic is given.

Numerical discrimination of intrachannel cross-phase modulation and intrachannel four-wave mixing and their respective effect on 40 Gbit/s transmissions

We propose a numerical method to accurately discriminate the influence of the different intrachannel nonlinear effects occurring in 40 Gbit/s optical transmissions, following an analogy with methods used to discriminate WDM interchannel effects. In contrast to other studies showing the predominance of intrachannel cross-phase modulation when low-dispersion fibers are used, in our study intrachannel four-wave mixing is the most penalizing effect in all investigated cases.

Suppression of intrachannel nonlinear effects using pseudoternary constrained codes

In this paper, a novel approach for suppressing the intrachannel nonlinear effects using pseudoternary constrained codes is proposed. A significant Q-factor improvement of up to 9.75 dB is obtained. The eye opening penalty (EOP) is also significantly improved by more than 10.24 dB.

Constrained coding techniques for the suppression of intrachannel nonlinear effects in high-speed optical transmission

A problem of suppression of intrachannel nonlinearities through the use of constrained coding is considered. Three different techniques are proposed and compared with respect to their efficiency, namely 1) constrained coding; 2) combined constrained and error control coding; and 3) deliberate error insertion. Significant Q-factor improvement up to 16 dB depending on code rate and number of spans is demonstrated. A combined constrained-iterative forward error correction (FEC) scheme can operate in the presence of strong intrachannel nonlinearities when even advanced FEC schemes would be overwhelmed with errors. It provides a coding gain of 12.1 dB at a bit error rate (BER) of 10/sup -9/. Deliberate error insertion is an efficient approach to balance the encoder complexity and the achievable coding gain.

Unifying theory of compensation techniques for intrachannel nonlinear effects

We show a new graphical method to identify and create configurations yielding to nonlinearity compensation in a fiber transmission system. Method validity is shown with regards to different link configurations and different compensation techniques. It is demonstrated that a unifying principle can always be applied, because only one physical effect is involved, even if different practical arrangements are proposed. Disclosed method allows gaining physical insight and can be applied to derive new compensation techniques; two examples of configurations derived using the proposed technique are also reported.

Bit Pattern Length Dependence of Intrachannel Nonlinearities in Pseudolinear Transmission

A dependence of nonlinear transmission penalty on bit sequence length in pseudolinear transmission is demonstrated and studied. It is shown that, for a realistic dispersion map, bit sequence lengths incorporating tens of thousands of bits or more may become necessary to accurately capture the nonlinear transmission penalty due to intrachannel nonlinear effects, especially at low bit-error ratio (<10/sup -5/).

Intra-channel nonlinearity compensation with scaled translational symmetry

It is proposed and demonstrated that two fiber spans in a scaled translational symmetry could cancel out their intra-channel nonlinear effects to a large extent without using optical phase conjugation. Significant reduction of intra-channel nonlinear effects may be achieved in a long-distance transmission line consisting of multiple pairs of translationally symmetric spans. The results have been derived analytically from the nonlinear Schrödinger equation and verified by numerical simulations using commercial software.

Performance Analysis of Time–Polarization Multiplexed 40-Gb/s RZ-DPSK DWDM Transmission

The performance of return-to-zero differential phase-shift-keyed dense wavelength-division-multiplexing transmission with time-polarization multiplexing or interleaving is investigated. Polarization interleaving enables further reduction of nonlinear penalties, especially in high-bit-rate transmissions where intrachannel nonlinear effects dominate. We show numerically that transmission distance can be much increased with this scheme in a 40-Gb/s system. Polarization scattering resulting from polarization-mode dispersion and cross-phase modulation is also much reduced as compared to that in on-off keying systems, making it possible for effective polarization demultiplexing that may also reduce system cost.

Optical phase conjugation for intra-channel nonlinearity compensation in 40 Gbit∕s CSRZ pseudo-linear systems

The compensation of intra-channel nonlinear effects in a CSRZ 40 Gbit/s 32×100 km system using an LiNbO3 optical phase conjugator in a re-entrant, recirculating loop architecture, is experimentally demonstrated. Two decades of improvement in the bit error rate at 3200 km with phase conjugation has been achieved. Also, the performance of CSRZ and RZ-DPSK modulation formats at 3200 km with and without optical phase conjugation is compared.

Investigation of nonlinear distortion in 40-Gb/s transmission with higher order mode fiber dispersion compensators

The performance of 40-Gb/s transmission systems is limited by the nonlinearity of the transmission and dispersion compensating fibers, and hence, optimized dispersion map designs and signal formats are required to extend error-free transmission distances. In this paper, we describe systematic experiments and simulations of return-to-zero (RZ) and nonreturn-to-zero (NRZ) 40-Gb/s transmission over nonzero dispersion-shifted fiber using higher order mode fiber dispersion management devices. We compare the single channel transmission limits due to nonlinear distortion with dispersion compensators positioned at the start and end of each amplifier span (pre- and postcompensation) and show that the transmission distance of NRZ signals can be extended with the use of precompensation due to the reduced self-phase modulation in the transmission fiber. In contrast, the combination of precompensation and RZ format was found to give poor performance, and analysis shows that this is a result of intrachannel four-wave mixing. The best performance was obtained using an RZ signal format and postcompensated spans. The performance of wavelength-division multiplexing (WDM) signal transmission over the link was then investigated. The simultaneous transmission of multiple 40-Gb/s channels over long-distances was achieved, demonstrating broad-band compensation of the dispersion and dispersion-slope using higher order mode fiber. Results of experiments assessing cross-phase modulation between 40-Gb/s WDM channels spaced by 100 GHz are presented, and the penalties due to inter- and intrachannel nonlinear effects are compared.

Resonant intrachannel pulse interactions in dispersion-managed transmission systems

Nonlinear intrachannel interactions in a transmission system with strong periodic dispersion management are investigated. An analytical model that describes the fluctuation of the temporal position and amplitude of the main signal and ghost pulse generation at zero bits due to intrachannel crosstalk is developed. Intrachannel nonlinear effects are found to be a resonant process which is induced by periodic forcing due to lumped amplification assisted by temporal phase matching. Explicit formulae to estimate transmission impairments such as timing and amplitude jitter are provided based on the analytical model. The role of distributed amplification to suppress intrachannel nonlinear effects is also discussed. A more fundamental analytical framework which enables one to evaluate intrachannel crosstalk over a wide regime of system configurations is also presented.

Reduction of intrachannel nonlinear distortion in 40-Gb/s-based WDM transmission over standard fiber

Intrachannel cross-phase modulation and four-wave mixing in high-bit-rate WDM transmission systems employing standard single-mode fiber are investigated. The effects of imperfect third-order dispersion compensation are included in the study and analytical expressions giving optimum values of dispersion precompensation minimizing the distortion due to the intrachannel nonlinear effects are derived.