Polarization Mode Dispersion Compensation Research Articles

Density-matrix-formalism based scheme for polarization mode dispersion monitoring and compensation in optical fiber communication systems

Density-matrix-formalism based scheme for polarization mode dispersion monitoring and compensation in optical fiber communication systems

Joint PMD Tracking and Nonlinearity Compensation With Deep Neural Networks

Overcoming fiber nonlinearity is one of the core challenges limiting the capacity of optical fiber communication systems. Machine learning based solutions such as learned digital backpropagation (LDBP) and the recently proposed deep convolutional recurrent neural network (DCRNN) have been shown to be effective for fiber nonlinearity compensation (NLC). Incorporating distributed compensation of polarization mode dispersion (PMD) within the learned models can improve their performance even further but at the same time, it also couples the compensation of nonlinearity and PMD. Consequently, it is important to consider the time variation of PMD for such a joint compensation scheme. In this paper, we investigate the impact of PMD drift on the DCRNN model with distributed compensation of PMD. We propose a transfer learning based selective training scheme to adapt the learned neural network model to changes in PMD. We demonstrate that fine-tuning only a small subset of weights as per the proposed method is sufficient for adapting the model to PMD drift. Using decision directed feedback for online learning, we track continuous PMD drift resulting from a time-varying rotation of the state of polarization (SOP). We show that transferring knowledge from a pre-trained base model using the proposed scheme significantly reduces the re-training efforts for different PMD realizations. Applying the hinge model for SOP rotation, our simulation results show that the learned models maintain their performance gains while tracking the PMD.

Complexity reduction over Bi-RNN-based nonlinearity mitigation in dual-pol fiber-optic communications via a CRNN-based approach

Bidirectional recurrent neural networks (bi-RNNs), in particular bidirectional long short term memory (bi-LSTM), bidirectional gated recurrent unit, and convolutional bi-LSTM models, have recently attracted attention for nonlinearity mitigation in fiber-optic communication. The recently adopted approaches based on these models, however, incur a high computational complexity which may impede their real-time functioning. In this paper, by addressing the sources of complexity in these methods, we propose a more efficient network architecture, where a convolutional neural network encoder and a unidirectional many-to-one vanilla RNN operate in tandem, each best capturing one set of channel impairments while compensating for the shortcomings of the other. We deploy this model in two different receiver configurations. In one, the neural network is placed after a linear equalization chain and is merely responsible for nonlinearity mitigation; in the other, the neural network is directly placed after the chromatic dispersion compensation and is responsible for joint nonlinearity and polarization mode dispersion compensation. For a 16-QAM 64 GBd dual-polarization optical transmission over 14×80km standard single-mode fiber, we demonstrate that the proposed hybrid model achieves the bit error probability of the state-of-the-art bi-RNN-based methods with greater than 50% lower complexity, in both receiver configurations.

Model-Based Machine Learning for Joint Digital Backpropagation and PMD Compensation

In this paper, we propose a model-based machine-learning approach for dual-polarization systems by parameterizing the split-step Fourier method for the Manakov-PMD equation. The resulting method combines hardware-friendly time-domain nonlinearity mitigation via the recently proposed learned digital backpropagation (LDBP) with distributed compensation of polarization-mode dispersion (PMD). We refer to the resulting approach as LDBP-PMD. We train LDBP-PMD on multiple PMD realizations and show that it converges within 1% of its peak dB performance after 428 training iterations on average, yielding a peak effective signal-to-noise ratio of only 0.30 dB below the PMD-free case. Similar to state-of-the-art lumped PMD compensation algorithms in practical systems, our approach does not assume any knowledge about the particular PMD realization along the link, nor any knowledge about the total accumulated PMD. This is a significant improvement compared to prior work on distributed PMD compensation, where knowledge about the accumulated PMD is typically assumed. We also compare different parameterization choices in terms of performance, complexity, and convergence behavior. Lastly, we demonstrate that the learned models can be successfully retrained after an abrupt change of the PMD realization along the fiber.

POLARIZATION MODE DISPERSION COMPENSATOR BASED ON ANISOTROPIC OPTICAL FIBER

Abstract. In this paper, a new method of polarization mode dispersion (PMD), which can significantly limit the speed and range of transmission of fiber optic transmission systems (FOTS), compensation was developed and analyzed. In contrast to the existing types of PMD compensators, in which the optical fiber is subjected to mechanical stresses to create a photoelastic anisotropy, in this work the use of alternative method of creating photoelasticity in optical fiber (OF) by creating a helical ordered rotation of the glass microstructure (ORMG) is proposed. The helical orientation of the microstructure of the OF glass is achieved by acting on the fiber in the process of manufacture (drawing), when it is in a hot state, electromagnetic field, the power lines of which are directed in a circle. I am not sure what this sentence is trying to say. The result is an asymmetry of the dielectric constant of the fiber glass material and therefore the anisotropy of the optical properties. When the optical signal propagates in such OF, there is a double refraction, which is the cause of artificial PMD in the compensator fiber. Compensation is achieved by performing the equality of the modulus and the sign-opposite between the linear path PMD and the PMD of the anisotropic OF with the ORMG. The expression of the calculation of the PMD of the compensator, which depends on the rotation step of the microstructure of the glass, the chemical composition of the OF, the length of the line, the width of the radiation spectrum and the wavelength of the optical signal, and the optical characteristics of the OF, is analyzed, as well as the spectral dependence of polarization mode dispersion for different chemical compositions of the OF. The expression of determining the length of the OF with the ORMG is presented to compensate for the set value of the PMD in the line. The results of the studies made it possible to determine the lengths of the segments of OF with ORMG, which will provide partial or complete compensation of PMD over a wide range of wavelengths and create passive compensators for dispersion.

Optical communication transmission systems improvement based on chromatic and polarization Mode dispersion compensation simulation management

Dispersion compensation technique is the most important issue in the optical communication system to overcome dispersion challenges. The current study focuses on a proposed compensation simulation model to handle not only chromatic dispersion (CD) but also polarization mode dispersion (PMD) simultaneously. The present compensation model is designed to analyze and simulate dispersion compensation technique which is based on deploying both fiber Bragg grating and emulator together till 250 km long of optical fiber. Signal to noise ratio (SNR), optical signal to noise ratio (OSNR), gain (G), noise figure (NF) and degree of polarization (DOP) are parameters that simulation depends on.

Performance Evaluation of 100 Gb/s WDM DP-QPSK Lightwave System with Reduced PMD Effects

In this paper, a coherent 100 Gb/s Wave Division Multiplexing (WDM)/Dual Polarization-Quadrature Phase Shift Keying (DP-QPSK) transceiver is proposed and optimized. The transmission of 40-channels has been achieved over 25×80 km of Standard Single Mode Fiber (SSMF) at 50-GHz channel spacing. A Digital Signal Processing (DSP) module has been implemented at the receiver for further system performance improvement. Simulation results have showed that the Polarization Mode Dispersion (PMD) effect have been efficiently compensated by 45 ps. The system has obtained a high Quality Factor (Q-Factor) for a wide range of input optical power from -10 dBm to 10 dBm with its maximum of 13.8 dB and has just decreased to 10.4 dB at 2000 km. The system has offered a high Degree of Polarization (DOP) of 0.9, indicating that the PMD compensation has been achieved remarkably. Furthermore, the proposed system has attained a spectral efficiency of 1-bits/s/Hz and the eye opening has improved significantly. It has been found out that the constellation diagrams have been distinguishable with very low data transmission errors and the received Radio Frequency (RF) signal has been strong with a very low level of noise.

Joint equalization scheme of ultra-fast RSOP and large PMD compensation in presence of residual chromatic dispersion.

Polarization demultiplexing is generally carried out by a multiple-input multiple-output (MIMO) based algorithm in polarization division multiplexing (PDM) coherent systems. However, in some extreme environments, the MIMO algorithm becomes inapplicable due to the ultra-fast rotation of the state of polarization (RSOP) and large polarization mode dispersion (PMD). In addition, the residual chromatic dispersion (RCD) is always present because of the mismatch of the compensated chromatic dispersion and real value induced in the optical fiber channel. According to the literature, the Kalman filter-based polarization demultiplexing algorithms possess very weak RCD tolerance. Faced with this dilemma, in this paper, a new Kalman filter structure is proposed, which can jointly compensate ultra-fast RSOP, large PMD and RCD. This Kalman filter structure enables the equalization of the RSOP in the time domain and compensation for RCD and PMD in the frequency domain. We verified the performance of the proposed Kalman scheme in the 28 Gbaud PDM-QPSK/16 QAM coherent system, with a comparison to constant modulus algorithm/multiple modulus algorithm (CMA/MMA). The simulation results confirm that, compared with CMA/MMA, the proposed Kalman scheme can provide a significant performance enhancement to cope with ultra-fast RSOP (up to 3 Mrad/s) and large PMD (more than 200 ps) with a large tolerance to RCD (over the range of ± 820 ps/nm in PDM-QPSK and ± 500 ps/nm in PDM-16 QAM).

The Impact of PMD on Single-Polarization Nonlinear Frequency Division Multiplexing

The impact of polarization mode dispersion (PMD) is studied on the single-polarization signal transmission over the continuous spectrum (CS) of a long-haul optical fiber link defined by nonlinear Fourier transform (NFT). It is shown that a linear all-order PMD compensation can reverse most of PMD effects in the temporal domain. However, due to the nonlinear interaction of the two polarization modes, the CS is distorted in the nonlinear spectral domain. Simulation results are presented, and a perturbation model is proposed based on the simulation results to describe the impact of PMD for different modulation formats and fiber parameters. It is demonstrated that, after linear PMD compensation, the residual polarization-dependent effects generate a constellation rotation and additional noise in the nonlinear spectral domain. The performance of NFT-based system in the presence of both PMD and amplifier noise is also studied. The results show that the effect of PMD is small provided that an efficient linear PMD compensation is performed in time domain.

Window-split structured frequency domain Kalman equalization scheme for large PMD and ultra-fast RSOP in an optical coherent PDM-QPSK system.

A window-split frequency domain Kalman scheme is proposed in this paper for the equalization of large polarization mode dispersion (PMD) and ultra-fast rotation of state-of-polarization (RSOP) which is an extreme environment due to the Kerr effect and the Faraday effect under the lightning strike near the fiber cables. In order to carry out the proposed Kalman scheme, we give a simplified and equivalent fiber channel model as a replacement for the general model of the polarization effect of the co-existence of PMD and RSOP. With this fiber channel model, we can conduct compensation for PMD in the frequency domain and tracking RSOP in time domain. A half analytical and half empirical theory for the initialization of the process and measurement noise covariance is also presented in theory and verified by the numerical simulation. The performance of the proposed Kalman scheme is checked in the 28Gbaud PDM-QPSK coherent system built on both simulation and experiment platforms. The simulation and experiment results confirm that compared with the generally used constant modulus algorithm (CMA), the proposed scheme provides excellent performance and stability to cope with large range DGD from 20ps to 200ps and RSOP from 200krad/s to 2Mrad/s, with less computational complexity.

Joint Scheme of Dynamic Polarization Demultiplexing and PMD Compensation Up To Second Order for Flexible Receivers

Polarization division multiplexing (PDM) doubles the bitrate of flexible transponders, whereas the joint effects of fast state of polarization (SOP) rotations, first-order polarization mode dispersion (PMD), and second-order PMD (SOPMD) would severely degrade the system performance. In this paper, we propose and experimentally validate a novel dynamic polarization demultiplexing scheme using extended Kalman filter (EKF) in digital signal processing of flexible receivers. The idea comes from two-stage PMD compensator in optical domain to perform SOP tracking and equalization of first-order PMD and SOPMD. After parameters optimization of EKF, the scheme can track up SOP rotations more than 35 times and 50 times faster than that of constant modulus algorithm (CMA) and CMA/multiple modulus algorithm (MMA), respectively. More importantly, when SOP keeps a fast rotation of 1.00, 10.00, or 20.02 Mrad/s, the system tolerances of first-order PMD and SOPMD that the joint scheme achieves are 28.57 ps and 793 ps2 for 28 GBaud PDM-QPSK at optical signal-to-noise rate (OSNR) of 17 dB, and 50 ps and 4836 ps2 for 10 GBaud PDM-16 quadratic-amplitude modulation (QAM) at OSNR of 23 dB, respectively. In addition, the proposed scheme has a fast convergence speed of about 50 symbols (equal to 5 ns). The calculation complexities of each symbol that the proposed scheme consumes are just about 44% of CMA for PDM-QPSK, and 31% of CMA/MMA for PDM-16 QAM.

PMD Emulator based on PZTs attached to pieces of an Hi-Bi fiber

In this paper we demonstrate the development of an adjustable and compact polarization mode dispersion (PMD) emulator device, based on piezoelectric actuators that squeezes a defined pieces of an Hi-Bi fiber. Using this device, the first and second order PMD (SOPMD) can be reproduced in a controlled and compact way, allowing its use as a reliable metrological reference for PMD compensators and for the study of several polarizations phenomena that can represent impairments to the high data transmission networks. This emulator was used to perform an analysis of the correlation between the PMD and SOPMD under different climate chamber temperature.

Compensation of chromatic and polarization mode dispersion in fiber-optic communication lines in microwave signals transmittion.

Methods of dispersion compensation in fiber-optic communication lines. A new proposed method of electronic dispersion compensation in the transmission of microwave signals through fiber-optic lines. Represents is proposed the results of experimental studies of this method.

Experimental demonstration of low-complexity fiber chromatic dispersion mitigation for reduced guard-interval OFDM coherent optical communication systems based on digital spectrum sub-band multiplexing.

We experimentally demonstrate a novel digital signal processing (DSP) structure for reduced guard-interval (RGI) OFDM coherent optical systems. The proposed concept is based on digitally slicing optical channel bandwidth into multiple spectrally disjoint sub-bands which are then processed in parallel. Each low bandwidth sub-band has a smaller delay-spread compared to a full-band signal. This enables compensation of both chromatic dispersion (CD) and polarization mode dispersion using a simple timing and one-tap-per-symbol frequency domain equalizer with a small cyclic prefix overhead. In terms of the DSP architecture, this allows for a highly efficient parallelization of DSP tasks performed over the received signal samples by deploying multiple processors running at a lower clock rate. It should be noted that this parallelization is performed in the frequency domain and it allows for flexible optical transceiver schemes. In addition, the resulting optical receiver is simplified due to the removal of the CD compensation equalizer compared to conventional RGI-OFDM systems. In this paper we experimentally demonstrate digital sub-banding of optical bandwidth. We test the system performance for different modulation formats (QPSK, 16QAM and 32QAM) over various transmission distances and optical launch powers using a 1.5% CP overhead in all scenarios. We also compare the proposed RGI-OFDM architecture performance against common single carrier modulation formats. At the same total data rate and signal bandwidth both systems have similar performance and transmission reach whereas the proposed method allows for a significant reduction of computational complexity due to removal of CD pre/post compensation equalizer.

Controlled and compact first- and second-order polarization mode dispersion emulator

In this article, the development of a controllable and compact polarization mode dispersion (PMD) emulator device, based on piezoelectric actuators, is presented. Using this device, the first- and second-order PMD is reproduced in a controlled and compact way, allowing its use as a reliable metrological reference for PMD compensators. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 57:765–769, 2015

Applying the data fusion method to evaluation of the performance of two control signals in monitoring polarization mode dispersion effects in fiber optic links

With increasing distance and bit rate in fiber optic links the effects of polarization mode dispersion (PMD) have been highlighted. Since PMD has a statistical nature, using a control signal that can provide accurate information to dynamically tune a PMD compensator is of great importance. In this paper, we apply the data fusion method with the aim of introducing a method that can be used to evaluate more accurately the performance of control signals before applying them in a PMD compensation system. Firstly, the minimum and average degree of polarization (DOPmin and DOPave respectively) as control signals in monitoring differential group delay (DGD) for a system including all-order PMD are calculated. Then, features including the amounts of sensitivity and ambiguity in DGD monitoring are calculated for NRZ data format as DGD to bit time (DGD/T) varies. It is shown that each of the control signals mentioned has both positive and negative features for efficient DGD monitoring. Therefore, in order to evaluate features concurrently and increase reliability, we employ data fusion to fuse features of each control signal, which makes evaluating and predicting the performance of control signals possible, before applying them in a real PMD compensation system. Finally, the reliability of the results obtained from data fusion is tested in a typical PMD compensator.

Adaptive Polarization Mode Dispersion Compensation with DPSO Algorithm

Dithering particle swarm optimization (DPSO) algorithm is introduced into adaptive polarization mode dispersion (PMD) compensation in optical communication system. The DPSO algorithm has the merits of rapid convergence to the global optimum, without being trapped in local sub-optima, and good robustness to noise. How to implement DPSO as a component of a control algorithm in adaptive polarization mode dispersion compensation is described. Performance comparisons between PSO and DPSO were carried out theoretically and experimentally.

A hollow waveguide Bragg reflector: A tunable platform for integrated photonics

Abstract Hollow waveguides are promising candidates for applications in sensing and high-power transmission. Flexible design and cost effective fabrication of hollow waveguides make it possible to realize integrated devices with small temperature dependence, tight control on optical confinement and tailorable characteristics. One of the potential applications of hollow waveguide is a tunable Bragg reflector, which can be used as building block for integrated photonics. In this review, integrated tunable Bragg reflector based on hollow-core optical waveguide is reviewed and presented; this Bragg reflector offers variable characteristics and design flexibility for applications in reconfigurable integrated photonic devices and circuits. Variety of tunable optical functions can be realized with on-chip Bragg reflector based on hollow waveguide, few of them are discussed in this review. Ultra-wide tuning in Bragg wavelength and on-chip polarization control can be realized using 3D hollow waveguide. A tapered 3D hollow waveguide Bragg reflector for an adjustable compensation of polarization mode dispersion (PMD) is then discussed. The utilization of a high-index contrast grating in hollow waveguide is demonstrated to reduce the polarization dependence and reflection-bandwidth. The polarization- and bandwidth control may be useful for realizing polarization insensitive devices and semiconductor lasers with ultra-wide tuning.

End-to-End Energy Modeling and Analysis of Long-Haul Coherent Transmission Systems

In this paper, we model and analyze the end-to-end energy consumption of 100-Gbps coherent long-haul transmission systems. In particular, we investigate the impact of forward error correction (FEC) on the end-to-end energy consumption. We compare the energy efficiency of commonly used modulation formats in 100-Gbps transmission, namely dual polarization-quadrature phase-shift-keying (DP-QPSK) and dual polarization-16-quadrature amplitude modulation (DP-16-QAM), for different transmission distance and input bit error rate. Our energy model includes consumption of transmitter, booster, link amplifier as well as receiver. Compared with previous digital signal processing models, we provide a very detailed model that not only includes all the significant functional blocks (such as timing and carrier recovery, chromatic and polarization mode dispersion compensation, and FEC), but also takes into account impact of the number of samples processed every clock cycle and of operations other than multiplications. We have found that receiver energy consumption dominates in transmission systems that use electronic dispersion compensation over long transmission distances. Our results show that for short transmission distances where hard-decision decoding is adequate for both modulation formats, DP-16-QAM is more energy efficient than DP-QPSK. However, as the transmission distance increases, the energy saving due to the low symbol rate of DP-16-QAM is offset by the energy consumption of soft-decision decoding. In this case, the two modulation formats have approximately similar energy consumption.

Monitoring FO-PMD and SO-PMD over Time with Respect to Environmental Conditions

Environmental conditions affect the birefringence of an optical fibre which in turn leads to fluctuations in its Polarization mode dispersion (PMD). Fluctuations in PMD make compensation for it in optical fibres very complicated. In this paper, fluctuations of first-order polarization mode dispersion (FO-PMD), FO-PMD coefficients and second-order polarization mode dispersion (SO-PMD) are monitored over time and also with respect to the environmental conditions. Long term measurements of FO-PMD have been done before by Mudau (2008) using the Generalized Interferometry Technique (GINTY) only. However, in this current study the FO-PMD coefficients and SO-PMD fluctuations were also monitored in addition to making a comparison between the measurements obtained using the Single-ended Dispersion Analyzer (FTB-5700) and the GINTY. These measurements were made on a 14.8 km long deployed aerial optical fibre that links St. Albans to Rockland transmission stations in Port Elizabeth, South Africa. The weather information was obtained from the Kestrel 4500 pocket weather tracker that was set up at St. Albans transmission station. So, for good PMD compensation, PMD should be monitored for a very long period of time or use an instrument that can accurately measure it even when the optical fibre is exposed to harsh environmental conditions.