Comparative investigations of DWDM transmission system with PMD for different orthogonally modulated signals at 80 Gb/s

Polarization mode dispersion (PMD) has become one of the major limiting factors for high‐bit‐rate optical transmission systems. This paper evaluates the performance of dense wavelength division multiplexed (DWDM) system with PMD at 80 Gb/s in the presence of Kerr‐nonlinear effects. Orthogonally modulated signals have been investigated and compared for tolerance against PMD in a DWDM transmission system with direct detection receivers. The optimized combinations of orthogonal polarization (OP) with carrier‐suppressed return‐to‐zero (CSRZ) and CSRZ differential‐phase‐shift‐keying signals are shown to improve PMD tolerance over high bit rates and long transmission lengths. Improved performance greater than 4 dB is observed for CSRZ modulated signal with OP because of less channel cross talk and reduced power transfer between adjacent bits over different PMD values. The numerical results demonstrate that our proposed orthogonally modulated signals perform better with lesser complex direct detection receivers. Copyright © 2015 John Wiley & Sons, Ltd.     

偏振模色散模拟器产生二阶PMD的理论研究

对基于保偏光纤（PMF）级联的偏振模色散模拟器（PMD emulator)产生的二阶PMD进行了数值模拟，结果表明，采用偏振控制器（PC）连接明显优于可旋转连接器（FC）连接，当级联段数N＝8时，PC连接的模拟器产生的二阶PMD与理论曲线基本符合；PMF的长度对PMD模拟器模拟二阶PMD并没有明显影响。     

On differential group-delay statistics for polarization-modedispersion emulators

We present a theoretical study on differential group-delay (DGD) statistics for common models of polarization-mode dispersion (PMD) emulators. Our study will show, for the first time to our knowledge, that the statistics for the length of the PMD vector will not necessarily behave as a system with three degrees of freedom when the number of sections in the PMD emulator is low. However, when the number of sections is large, i.e., 10 sections or more, the length of the PMD vector is well described with a system with three degrees of freedom     

Tracking and separation of time-varying principal states of polarization in optical fiber link for first-order PMD compensation and its filter-dependent performance

We propose a simple method for tracking and separating time-varying principal states of polarization (PSP) occurring in a fiber-optic transmission link with polarization mode dispersion (PMD) for use in PMD compensation. The proposed method uses as a feedback monitoring signal the bandpass-filtered RF power at bit-rate frequency for NRZ signal format. We demonstrated the operating principle of the method through theoretical simulation and experiment using an automatically adaptive PMD compensator employing a single polarization beam splitter (PBS). The effects of electrical filtering on the PSP tracking performance were also investigated by using three types of filters, i.e., a low-pass filter (LPF), a band-pass filter (BPF), and a high-pass filter (HPF). The simulation results showed that only a BPF centered at bit-rate frequency was found to allow for tracing and separation of two PSPs via PBS. The proposed method, when applied to a conventional PMD compensator that alternately controls a polarization controller and a delay line, enables separation of PSP control from differential-group-delay (DGD) control, thus allowing fast tracking of rapidly changing PSP in a PMD-impaired optical fiber link and reducing compensation time.     

Polarization mode dispersion compensation at 10, 20, and 40 Gb/swith various optical equalizers

Polarization mode dispersion (PMD), especially in “old” fibers, is considered harmful for installation and upgrading of trunk lines. An optical PMD equalizer should have several or many differential group delay (DGD) sections with polarization transformers in between which can endlessly transform any input polarization into a principal state of the following DGD section. The sections must practically have fixed DGDs unless there is only one section. The small-signal baseband transfer function for PMD, higher order PMD, and the necessary number of sections as well as their control by the output signals of an electrical filter bank in the receiver are also discussed in this context. Several PMD equalizers have been realized and successfully tested in transmission systems with bit rates of 10, 20, and 40 Gb/s. The systems operated stably with well-opened eye diagrams for DGDs ranging between 0 and 1.7 bit durations. Best performance is obtained from a distributed PMD equalizer with one piece of polarization-maintaining fiber twisted by 64 stepper motors. The principle can also be realized in LiNbO₃     

PMD penalties in long nonsoliton systems and the effect of inline filtering

We consider the polarization-mode dispersion (PMD) tolerance of long nonsoliton systems. We find that the effect of PMD in such systems is to derail the nonlinear evolution of the waveform from its PMD-free trajectory at an early stage of transmission, leading to extremely high penalties at the receiver end. It is shown that PMD affects the propagating bandwidth in a way that is strongly correlated with the received penalty. Use of inline optical filters is shown to be extremely efficient in reducing the penalties caused by PMD.     

Time and frequency domain characteristics of polarization-modedispersion emulators

We investigate both experimentally and theoretically a new technique to realistically emulate polarization-mode dispersion (PMD). We propose and demonstrate a PMD emulator using rotatable connectors between sections of polarization-maintaining fibers that generates an ensemble of high PMD fiber realizations by randomly rotating the connectors. It is shown that: (1) the DGD of this emulator is Maxwellian-distributed over an ensemble of fiber realizations at any fixed optical frequency; and (2) the frequency autocorrelation function of the PMD emulator resembles that in a real fiber when averaged over an ensemble of fiber realizations. A realistic autocorrelation function is required for proper emulation of higher order PMD and indicates the feasibility of using this emulator for wavelength-division-multiplexing (WDM) systems     

Numerical comparison between distributed and discrete amplificationin a point-to-point 40-Gb/s 40-WDM-Based transmission system with threedifferent modulation formats

We describe a detailed numerical investigation on the relative merits of gain flattened distributed Raman amplification (DRA) and discrete gain flattened amplifiers. We simulate a system with forty 40-Gb/s channels spaced at 100 GHz and compare the performance of three different modulation formats nonreturn-to-zero (NRZ), return-to-zero (RZ) and carrier-suppressed RZ (CS-RZ). Three types of amplifiers, multifrequency backward- and forward-pumped DRAs, and an idealized discrete gain flattened amplifier are examined for various signal powers and transmission distances. For the backward-pumped DRA, we also describe calculated tolerance limits imposed by incomplete dispersion slope compensation and polarization mode dispersion (PMD) level     

PSO-based Control Algorithm for Polarization Mode Dispersion Self-adaptive Compensation

Polarization mode dispersion（PMD） is considered to be the ultimate limitation in high-speed optical fiber communication systems. Establishing an effective control algorithm for adaptive PMD compensation is a challenging task, because PMD possesses the time-varying and statistical properties. The particle swarm optimization（PSO） algorithm is introduced into self-adaptive PMD compensation as feedback control algorithm. The experiment results show that PSO-based control algorithm has some unique features of rapid convergence to the global optimum without being trapped in local sub-optima and good robustness to noise in the optical fiber transmission line that has never been achieved in PMD compensation before.     

PSO2 based Control Algorithm for Polarization Mode Dispersion Self-adaptive Compensation

Polarization mode dispersion(PMD) is considered to be the ultimate limitation in high-speed optical fiber communication systems. Establishing an effective control algorithm for adaptive PMD compensation is a challenging task, because PMD possesses the time-varying and statistical properties. The particle swarm optimization(PSO) algorithm is introduced into self-adaptive PMD compensation as feedback control algorithm. The experiment results show that PSO2based control algorithm has some unique features of rapid convergence to the global optimum without being trapped in local sub-optima and good robustness to noise in the optical fiber transmission line that has never been achieved in PMD compensation before.     

The effects of PMD and PDL on the performance of OOK and DPSK systems

Using multiple importance sampling （MIS） technique, the optical communication system performance affected by polarization-mode dispersion （PMD） and polarization-dependent loss （PDL） is simulated numerically. The power penalties and system outage probabilities are obtained for optical communication systems with on-off keying （OOK） or differential phase shift keying （DPSK） modulation. The simulation results show that DPSK always performs better than OOK. When the system has moderate PDL （about 1.5 dB）, it is necessary to compensate effectively the fiber PMD in order to enhance the system tolerance to the PMD and PDL. However, the efficiency of PMD compensation will degrade rapidly when the PMD of the whole optical link drops into the low value.     

PMD-induced transmission penalties in polarization-multiplexed transmission

In this paper, we investigate for the first time chromatic dispersion and nonlinearity tolerances in the presence of polarization-mode dispersion (PMD) for polarization-multiplexed (POLMUX) 2 /spl times/ 10-Gb/s nonreturn-to-zero (NRZ) transmission. In polarization-multiplexing, the interaction between fiber nonlinearity and PMD can lower the nonlinear tolerance beyond the tolerances evident when considering both transmission penalties separately; the combined penalties are significantly worse than in the case for non-POLMUX transmission. In this paper, we show, through simulations comparing POLMUX with non-POMUX transmission in the presence of nonlinearity, a reduction of about a factor of three in PMD tolerance. In addition, we show that the dispersion tolerance of POLMUX transmission is severely limited in the presence of PMD. For example, a 40-ps differential group delay (DGD) with worst case coupling of the polarization channels into the fiber lowers the dispersion tolerance, resulting in a 1-dB eye-opening penalty (EOP), from 1200 to 450 ps/nm. We conclude that the interaction between PMD, chromatic dispersion, and nonlinearity leads to the worst signal impairments in POLMUX transmission and increases the effort of using polarization-multiplexing as a modulation format.     

System Outage Probability Due to PMD in High-Speed Optical OFDM Transmission

In this paper, closed-form analytical bounds on PMD-induced symbol error rate and outage probability in high-speed long-haul optical orthogonal frequency division multiplexed (OFDM) systems are derived, evaluated, and verified experimentally in order to assess the PMD tolerance of this modulation format. To obtain the analytical results, the PMD channel is modeled as a linear time-invariant system, whose end-to-end transfer function is used to upper-bound symbol error and outage probabilities in IM/DD optical OFDM transmission. The symbol error rate bounds predicted by the general analytical model are verified experimentally on a 10-Gb/s OFDM system with instantaneous DGD ranging between $Deltatau = 0$ and 120 ps . The outage probability bounds indicate that, if no RF guard bands are required, OFDM enables high-speed transmission with at least twice the PMD tolerance provided by an equivalent uncompensated OOK-based system at system outage probabilities $P_{{rm out, sys}}≪10^{-5}$ . If RF guard bands are required to mitigate effects of other distortions, it is shown that a penalty in the system PMD tolerance proportional to the intermediate RF subcarrier frequency, $f_{{rm RF}}$, is exerted. Consequently, a tolerance tradeoff exists in IM/DD OFDM systems, wherein $f_{rm RF}$ as well as baseband constellation size may be viewed as design parameters that can be optimized depending on specific system requirements.      

Novel C-IPDM Signal Format for Suppression of Polarization Mode Dispersion

A novel chirped intra-bit polarization diversity modulation (C-IPDM) signal format is proposed. The transmission performance of C-IPDM is compared to NRZ, RZ and the common IPDM in terms of the PMD tolerance by simulation in a 40 Gb/s system. The results show that the C-IPDM format can reduce the effects of second-order PMD significantly due to the chirping characteristic and the system Q-factor is increased especially in high PMD systems.     

Frequency and Duration of Communication System Outages Resulting From Polarization Mode Dispersion

In this paper, we employ measurements of transponder tolerance to both differential group delay (DGD) and second-order polarization mode dispersion (SOPMD) and of the temporal evolution of DGD and SOPMD in installed transmission systems to predict the influence of PMD on the rate and duration of PMD-induced system outages. An empirical 2-D random-walk model predicts that the outage rate and duration depends solely on the mean fiber DGD. We find that the step size of the random walk is nearly uncorrelated with the instantaneous value of the PMD. We then justify the assumptions of this procedure with a full numerical simulation and employ a biased Markov chain algorithm to generate highly accurate results for system outages where simplified models fail.      

Comparison of polarization mode dispersion emulators

We analyze polarization mode dispersion (PMD) emulators comprised of a small number of sections of polarization-maintaining fibers with polarization scattering at the beginning of each section. Unlike previously studied devices, these emulators allow the emulation of a whole ensemble of fibers. We derive an analytical expressions and determine two main criteria that characterize the quality of PMD emulation. The experimental results are in good agreement with the theoretical predictions     

Fast Time-Varying Dispersive Channel Estimation and Equalization for an 8-PSK Cellular System

In this paper, a novel channel-estimation scheme for an 8-PSK enhanced data rates for GSM evolution (EDGE) system with fast time-varying and frequency-selective fading channels is presented. Via a mathematical derivation and simulation results, the channel impulse response (CIR) of the fast fading channel is modeled as a linear function of time during a radio burst in the EDGE system. Therefore, a least-squares-based method is proposed along with the modified burst structure for time-varying channel estimation. Given that the pilot-symbol blocks are located at the front and the end of the data block, the LS-based method is able to estimate the parameters of the time-varying CIR accurately using a linear interpolation. The proposed time-varying estimation algorithm does not cause an error floor that existed in the adaptive algorithms due to a nonideal channel tracking. Besides, the time-varying CIR in the EDGE system is not in its minimum-phase form, as is required for low-complexity reduced-state equalization methods. In order to maintain a good system performance, a Cholesky-decomposition method is introduced in front of the reduced-state equalizer to transform the time-varying CIR into its minimum-phase equivalent form. Via simulation results, it is shown that the proposed algorithm is very well suited for the time-varying channel estimation and equalization, and a good bit-error-rate performance is achieved even at high Doppler frequencies up to 300 Hz with a low complexity.     

A Change of Perspective on Single- and Double-Stage Optical PMD Compensation

We present a rigorous investigation on how to optimize the degrees of freedom of optical polarization mode dispersion (PMD) compensators composed of differential group delay sections and polarization controllers, up to two stages. The analytical treatment relies on the extracted Jones matrices of the transmission and compensation fibers. The analysis of a single-stage compensator with two degrees of freedom (fixed DGD) is based on the maximization of the eye opening, as provided by the generalized Chen formula. The outage probability is quantified through a fast semi-analytical technique. It is shown how the benefits of single-stage compensation are strongly reduced and can lead to outage events, when certain critical input states of polarization are launched into transmission fibers with strong eigenmodes depolarization (i.e., strong higher order PMD). Focusing on such transmission fibers and input configurations, a novel algorithm is introduced for controlling a double-stage compensator with five degrees of freedom. The algorithm is based on an ideal equalization of the transmission fiber at half the bit-rate, realized resorting to spherical geometry. To this aim, we show that the first compensator stage must be a PMF fiber with very large DGD, equal to the bit period, in order to compensate the most critical configurations associated with outage events.      

Design,estimation and experimental validation of optical Polarization Mode Dispersion Compensator in 40 Gbit/s NRZ and RZ optical systems

Polarization Mode Dispersion (PMD) compensation has been a matter of investigation of several papers in literature. The proposed solutions belong basically to two large families: electronic compensators and optical compensators. Both PMD compensator schemes have advantages and disadvantages: electronic PMD compensators are usually simple to include in line-terminal, potentially low-cost, very fast, and FEC compatible but their development is strongly dependent on IC technology capability that at this time allows device developments up to the 10 Gbit/s bit rates area. Furthermore, they are strongly dependent on modulation formats, and they can operate only on a single channel. Conversely, optical compensators are independent of bit rate and modulation format and potentially they can compensate more channels simultaneously; their major drawbacks are the longer response time and the complexity in the feedback signal process within the control algorithm. In this paper we consider an optical Polarization Mode Dispersion Compensator (PMDC) that is simple to realize and easy to include at limited costs in each EDFA module (distributed compensation) as well as a single-stage front-end compensator. Numerical analysis of the PMDC and experimental results confirm the utility of the PMDC proposed and its capability in compensating DGD larger than 20 ps in NRZ and RZ 40 Gbit/s optical systems.     

Study on the PMD impairment of optical multilevel DPSK systems and its mitigation methods

We examine the polarization-mode dispersion (PMD) impairment of optical multilevel differential phase-shift keying systems, and also its mitigation method by comparing the electrical equalization technique and the receiver bandwidth optimization. Analysis has been carried out with 40-Gb/s systems experiencing 0/spl sim/60 ps of instantaneous differential group delay, corresponding up to 240%/80% of bit/symbol transmission rate. Results show considerable improvement in the PMD tolerance for return-to-zero format for the optimized receiver bandwidth either with or without the electrical equalization. For nonreturn-to-zero, the bandwidth optimization alone does not significantly improve the system's PMD tolerances.