Dispersion-managed Link Research Articles

PMD tolerant transmission using multiple optical phase conjugators in the discretely amplified systems

Abstract In this paper, the impact of polarization mode dispersion (PMD) on system performance in coherent optical transmission assisted by optical phase conjugation (OPC) technique is numerically investigated for a 9-channel PM-4QAM system at 128Gbit/s. The OPC-aided transmission, amplified with lumped erbium doped fiber amplifier (EDFA), is a variation of the conventional dispersion-managed link, which is also called dispersion-inverted link. We demonstrate that introducing more OPCs along the link can partly suppress the PMD-induced impairments and thus improve the system performance significantly. Results of 960-km dispersion-managed transmission show that PMD effect will cause a performance penalty of 1.8 dB when using mid-link OPC (i.e., only 1-OPC), while this penalty will decrease to about 0.4 dB when employing 6-OPCs along the link. Comparing with conventional digital back-propagation (DBP) technique, a performance improvement of about 3.1 dB is observed with multi-OPCs when fiber PMD is equal to 0.1ps/ k m $\sqrt{km}$ .

Compensation of the Distorted WDM Signals by Symmetric Dispersion Map with Nonuniform Zero-Crossing Place of Accumulated Dispersion in Midway-OPC System

The nonlinear Kerr effect and chromatic dispersion are the fundamental causes of optical signal degradation in single-mode fiber (SMF) and erbium-doped fiber-amplification (EDFA)-based wavelength division multiplexing (WDM) transmission. Dispersion management combined with a midway optical phase conjugator among the technologies for compensating for such optical signal distortion is known to not be limited by the modulation format and multiplexing technology. Optimization of the dispersion map can partially alleviate the capacity and maximum transmission distance limitations of the SMF and EDFA system. In this paper, we propose various types of symmetric dispersion maps in which the position of zero-crossing place of the cumulative dispersion is not constant, and analyze the effect of each dispersion map configuration on 40 Gb/s × 24-channel WDM signal distortion compensation. When designed with the residual dispersion per span (RDPS) around 400 ps/nm, it is confirmed that most of the proposed dispersion maps are more effective in compensating the distorted WDM signal than conventional dispersion map. In particular, we confirm that, among the proposed dispersion maps, the dispersion map in which the RDPS is designed uniformly for all fiber spans can increase the power margin of WDM channel and expand the range of the total residual dispersion in the dispersion-managed link.

Performance Assessment of Joint Optical-Digital Nonlinearity Mitigation Schemes in Long-Haul Systems

The combined approach of optical and digital nonlinearity mitigation techniques have been shown to have an edge over the individual schemes, tackling their drawbacks and improving compensation capabilities. We demonstrated fiber-nonlinearity mitigation of 32 GBd single-polarization 16QAM signals transmitted over an 800-km dispersion-managed link using optical phase conjugation (OPC) and digital-domain neural networks (NN). Our implemented NN comprised a recurrent neural network (RNN), and a reservoir computing network (RCN). To further compensate for the penalty introduced by the design of OPC, we employed NN schemes in the digital signal processing and applied it to the signal after transmission in the OPC-assisted link. We present the results for optimizing the NN models for important hyper-parameters like the number of hidden layer neurons and the input vector size. The proposed joint approach achieves Q <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -factor improvements up to 1.8 dB while surpassing the improvements of the individual schemes. Our experiments indicate that the joint approach has the potential to reduce the overall complexity of NN architectures in terms of the size of the hidden layer and input vector.

Dispersion-Managed Link Configured with Repetitively Shaped Dispersion Maps and Embedded with Mid-span Spectral Inversion

Dispersion-Managed Link Configured with Repetitively Shaped Dispersion Maps and Embedded with Mid-span Spectral Inversion

MSSI-Based Dispersion-Managed Link Configured by Randomly-Distributed RDPS Only in Former Half Section

The weakness of the dispersion-managed link, which is combined with optical phase conjugation to compensate for optical signal distortion caused by chromatic dispersion and the nonlinear Kerr effect of the standard single mode fiber is, its limited structural flexibility. We propose a dispersion map that can simultaneously compensate for the distorted wavelength division multiplexed signal while increasing the configurational flexibility. Each residual dispersion per span (RDPS) in the former half of the proposed link is randomly determined, and in the latter half, the arrangement order of RDPS is the same as or inverted in the former half. We confirm that the dispersion maps in which the RDPS distribution pattern in the latter half is opposite to the arrangement order in the former half are more effective in compensation, and the compensation effect is better than in the dispersion map of the conventional scheme. The notable result of this study is that the flexibility can be increased by randomly arranging RDPS in the former half, and compensation improvement can be achieved by inversing the order of RDPS arrangement of the former half in the latter half, which makes the dispersion profile of each half link roughly symmetric with respect to the midway optical phase conjugator.

Fiber Nonlinearity Compensation: DBP Versus Link-Optimized OPC in Coherent Transmission

In this letter, we numerically compare the system performance of nonlinearity-compensated transmission based on digital back-propagation (DBP) and optical phase conjugation (OPC) technique in coherent transmission with lumped erbium doped fiber amplifiers (EDFAs). The tested transmission for DBP is a conventional dispersion-managed link, while it is an optimized design, the so-called dispersion inversion link for OPC-based system. Both of them have the same amount and type of fibers, and thus the same transmission reach. The numerical results show that DBP-aided systems have better performance for a shorter transmission reach while OPC technique presents its performance advantage when the transmission reach is increased. For a given transmission distance, the performance of OPC systems can further be improved by introducing additional OPCs. Results of 3840-km (<inline-formula> <tex-math notation="LaTeX">$48\times 80$ </tex-math></inline-formula>km) dispersion-managed transmission show that only mid-link OPC is enough to get similar performance with full-field DBP. By employing 6-OPCs in the links, the SNR of OPC-based system outperforms DBP by up to 1.9dB, while this SNR advantage will increase to 3dB after 5760-km (<inline-formula> <tex-math notation="LaTeX">$72\times 80$ </tex-math></inline-formula>km) transmission.

Fiber nonlinearity compensation using optical phase conjugation in dispersion-managed coherent transmission systems

Abstract In the discretely amplified transmission systems with erbium-doped fiber amplifiers, the system performance of nonlinearity-compensated optical transmission based on pre-dispersed spectral inversion (PSI) is investigated numerically. We find that PSI offers more significant performance improvement in dispersion-managed (DM) links than that in non-dispersion-managed (noDM) links. On the other hand, the DM link is more sensitive to the span offset from the center of the transmission link than noDM link. The performance difference between DM and noDM links is 1 dB if the span offset equals four spans in 20 × 90 km nonlinear transmission. Furthermore, we show that for the dispersion-managed transmission, in order to obtain the best system performance, the amount of pre-dispersion of the PSI, should be optimized over different dispersion maps.

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.

K-Nearest Neighbor Detector for Enhancing Performance of Optical Phase Conjugation System in the Presence of Nonlinear Phase Noise

Nonlinear phase noise (known as Gordon–Mollenauer phase noise) results from power fluctuations arising from amplified spontaneous-emission noise of the inline amplifier which is converted into phase fluctuations due to the self-phase modulation effect. It may severely impair the phase of optical signal, and would further degrade the performance of the long-haul optical transmission systems. The case can be compensated partially by mid-span optical phase conjugation(OPC). In this paper, an effective k-nearest neighbor (KNN) detector have been introduced to further improve the performance of OPC system by mitigating non-Gaussian impairments caused by nonlinear phase noise. The effectiveness is investigated in a 112-Gb/s 16QAM optical phase conjugation system with 800-km dispersion-managed link and 1280-km dispersion-shifted-fiber link. The results show that the effective and optimal KNN detector can enhance the overall performance of OPC system, even the asymmetric system.

Evaluating the Impact of QAM Constellation Subset Selection on the Achievable Information Rates of Multidimensional Formats in Fully Loaded Systems

An efficient procedure is presented for evaluating the performance of multidimensional modulation formats in terms of the achievable information rate (AIR). It allows the explicit properties of signal constellations to be captured and is applicable to fully loaded dense wavelength-division multiplexed transmission systems. The efficiency of the procedure facilitates formulating multidimensional quadrature amplitude modulation (QAM) constellation subset selection as a combinatorial optimization problem. The attained solutions for the quadrature phase shift keying (QPSK) 8D constellation subset selection suggest that a known 8D power and polarization balanced constellation (PPB constellation, 4 bits/8D symbol) and its different variations are the closest 8D QPSK subsets to the Shannon limit at 4 bits/8D symbol. 8D constellation subset selection of a QPSK constellation at 6 bits/8D symbol allows obtaining an 8D polarization balanced version of polarization-switched QPSK (PB-PS-QPSK). Using the proposed procedure, the performance of these constellations and their nonpolarization balanced counter parts, i.e., dual polarization binary phase shift keying (DP-BPSK) and PS-QPSK, is assessed in terms of the estimated AIR. The results exhibit good agreement with those of full system simulations for a single channel and five channels. Moreover, the impact of QAM constellation subset selection on the system performance is evaluated by comparing the reduction in information rate for a symbol rate of 35 Gbaud as a function of the number of channels. For 41 channels, the PPB constellation outperforms DP-BPSK by 2 Gb/s in information rate for a 12,000 km dispersion-managed (DM) link due to the improved linear and nonlinear constellation properties. Finally, PB-PS-QPSK enables an increase of 1.5 Gb/s in information rate compared to PS-QPSK for a 10,000 km DM link.

Performance Evaluation of a Silicon Waveguide for Phase Regeneration of a QPSK Signal

In this paper a silicon-on-insulator nanorib waveguide with reverse-biased p-i-n-junction is used to experimentally demonstrate phase-sensitive amplification based on four-wave mixing for the realization of an in-line four-level phase-regenerator. Phase regeneration of a 14-GBd quadrature phase-shift keying signal is demonstrated for the first time employing a silicon waveguide as phase sensitive amplifier. The regenerator is placed in a 1040-km dispersion-managed link and it is shown that phase noise accumulation in the transmission link can be reduced by the use of the in-line silicon-based phase-regeneration.

Higher-order interaction-induced effects between strong dispersion-managed solitons with dissimilar powers

We address one of the major penalties associated with the transmission of optical solitons in fiber-optic networks: the intrachannel interactions between pulses in a single channel strong dispersion-managed transmission link. We calculate the interaction length between sets of two and three pulses as a function of the ratio of dissimilar peak powers of interacting solitons by means of a variational approach to the generalized nonlinear Schrodinger equation describing the evolution of optical soliton pulses. We find a maximum of this colliding length for specific values of pulse energies. The effect of higher-order perturbation terms, such as third-order dispersion, Raman scattering, and self-steepening, shows an enhancement of the interaction distance in a broad range of dispersion difference values. We conclude that the transmission characteristics of soliton trains may be improved by means of using specific values of unequal energies and taking into account higher-order correction terms.

Nonlinearity Mitigation Using a Machine Learning Detector Based on &lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$k$ &lt;/tex-math&gt; &lt;/inline-formula&gt;-Nearest Neighbors

A powerful machine learning detector based on the k-nearest neighbors (KNN) algorithm is proposed to overcome system impairments. The zero-dispersion link (ZDL), dispersion managed link (DML), and dispersion unmanaged link (DUL) are considered. Meanwhile, an improved algorithm, the distance-weight KNN, is introduced, which outperforms the conventional maximum likelihood-post compensation approach. The numerical results show that KNN is feasible for overcoming various impairments, especially for non-Gaussian symmetric noise, such as laser phase noise and nonlinear phase noise in the ZDL or DML.

The Effects of the Number of Fiber Spans and Residual Dispersion per Span on the System Performance in Dispersion-Managed Optical Links Combined with Optical Phase Conjugation

The Effects of the Number of Fiber Spans and Residual Dispersion per Span on the System Performance in Dispersion-Managed Optical Links Combined with Optical Phase Conjugation

SMF 길이와 중계 구간 당 잉여 분산의 분포가 균일한 분산 제어 광전송 링크

SMF 길이와 중계 구간 당 잉여 분산의 분포가 균일한 분산 제어 광전송 링크

Impairment assessment of orthogonal frequency division multiplexing over dispersion-managed links in backbone and backhaul networks

The past decade has seen the phenomenal usage of orthogonal frequency division multiplexing (OFDM) in the wired as well as wireless communication domains, and it is also proposed in the literature as a future proof technique for the implementation of flexible resource allocation in cognitive optical networks. Fiber impairment assessment and adaptive compensation becomes critical in such implementations. A comprehensive analytical model for impairments in OFDM-based fiber links is developed. The proposed model includes the combined impact of laser phase fluctuations, fiber dispersion, self phase modulation, cross phase modulation, four-wave mixing, the nonlinear phase noise due to the interaction of amplified spontaneous emission with fiber nonlinearities, and the photodetector noises. The bit error rate expression for the proposed model is derived based on error vector magnitude estimation. The performance analysis of the proposed model is presented and compared for dispersion compensated and uncompensated backbone/backhaul links. The results suggest that OFDM would perform better for uncompensated links than the compensated links due to the negligible FWM effects and there is a need for flexible compensation. The proposed model can be employed in cognitive optical networks for accurate assessment of fiber-related impairments.

Stochastic Digital Backpropagation With Residual Memory Compensation

Stochastic digital backpropagation (SDBP) is an extension of digital backpropagation (DBP) and is based on the maximum a posteriori principle. SDBP takes into account noise from the optical amplifiers in addition to handling deterministic linear and nonlinear impairments. The decisions in SDBP are taken on a symbol-by-symbol (SBS) basis, ignoring any residual memory, which may be present due to non-optimal processing in SDBP. In this paper, we extend SDBP to account for memory between symbols. In particular, two different methods are proposed: a Viterbi algorithm (VA) and a decision directed approach. Symbol error rate (SER) for memory-based SDBP is significantly lower than the previously proposed SBS-SDBP. For inline dispersion-managed links, the VA-SDBP has up to 10 and 14 times lower SER than DBP for QPSK and 16-QAM, respectively.

Compensation characteristics of optical signal distortions in dispersion-managed optical links with randomly distributed RDPS

In high-capacity and long-haul optical communication systems, signal distortion is induced by the group velocity dispersion GVD and nonlinear Kerr effects of optical fibres. Different techniques to compensate for the signal distortion in the optical links, by using an optical phase conjugator OPC, have been proposed in the literature. However, compensation by the use of an OPC is limited by the asymmetry of the signal power. Dispersion management DM combined with an OPC is one of the various techniques for overcoming this drawback. The system performance improvement in these optical links has been reported; however, the fixed residual dispersion per span RDPS usually used in the optical links with an OPC and DM restricts flexible link configuration. In this paper, OPC links combined with DM of randomly distributed RDPS is proposed for implementing a flexible optical transmission network. We confirm that the proposed links are effective for our purpose, if the averaged RDPS of the fibre span was selected to be non-zero and low.

Non-midway 광 위상 공액기를 갖는 분산 제어 전송 링크를 통한 WDM 채널의 왜곡 보상

The implementation possibility of the flexible optical network configuration using the non-midway optical phase conjugator (OPC) in the dispersion-managed (DM) optical link for wavelength division multiplexed (WDM) transmission is demonstrated in this paper. It is confirmed that the implementation possibility of flexible link configuration is more increased, as number of fiber spans is more bigger and the residual dispersion per span (RDPS) is more large. It is also confirmed that the non-midway OPC link, in which RDPS of the latter half transmission section (after OPC) is decided by the averaged RDPS of the former half transmission section (before OPC), has more advantage for the flexible network configuration.

Qualitative Comparison of Kerr Nonlinearity Mitigation Schemes in a Dispersion-Managed Link for 4 × 28-GBd 16-QAM Signals

We present an experimental investigation of different Kerr nonlinearity mitigation schemes in a 2-span dispersion–compensated link of 160–km length for 4 × 28–GBd single–polarization 16–QAM signal transmission. We consider optical phase conjugation (OPC) based on mid–link spectral inversion, digital backpropagation (DBP), and transmission of phase-conjugated twin-waves with either digital coherent superposition (DCS) or all–optical coherent superposition employing phase–sensitive amplification (PSA). The experiments are performed in a single–channel and a wavelength-division multiplexing (WDM) scenario. For single–channel operation, phase-conjugated twin waves with DCS provided superior performance compared to all the other mitigation schemes with a maximum Q2–factor improvement of 1.7 dB compared to signal transmission without any nonlinearity mitigation. The DBP, however, showed a higher nonlinear threshold than all the other schemes in our experiments. In the WDM scenario, DBP showed worse performance than the other mitigation schemes whereas the DCS again provided a higher Q2–factor improvement than the other techniques with a maximum Q2–factor improvement of 1.9 dB. The PSA and the mid–link OPC showed similar nonlinearity mitigation performance both in single-channel and WDM scenarios.