Nonlinear Interference Research Articles

An extension to the enhanced Gaussian noise model in optical bus considering various links spectrum

Physical layer impairment modeling has considerably influenced optical networking in optimizing resource allocation for fulfilling a required quality of transmission. Among these impairments, the modeling of optical fiber non-linearity has enjoyed widespread applications by vendors and network operators, giving rise to the two well established Gaussian noise (GN) and enhanced Gaussian noise (EGN) models. In this work, we introduce an extension to the EGN model for a point-to-point bus transmission, where a demand is not typically routed over a single link. More specifically, we assume that a lightpath is routed over a bus and multiple interferers occasionally add and drop along the links, resulting in a mixture of coherent and incoherent non-linear propagation. We propose a mathematical formulation in the optical bus scenario, taking into account the spectrum variation of the links along the bus. To more accurately address their mutual statistical correlation in non-linear interference estimation, we make use of extra lightpath information. Along with presenting the new formulation, we modify the non-linear link function to include the spectrum variation of a lightpath links. The exploited optical bus topology is capable of approximating a real network lightpaths to enable design optimization of optical networks. Our numerical results show approximately 0.4 dB and 0.6 dB improvements versus the GN and EGN models in long bus scenarios with moderate number of channels and lightpaths, and around 0.3 dB minimum improvement.

Low complexity nonlinear detection for multiuser hybrid MIMO systems and performance analysis

This paper proposes an analytical framework and a system of distortion-aware receiver structures for single-carrier uplink hybrid beamforming-based multiple-input-multiple-output (MIMO) channels. Proposed single-user processing units cooperate at the base station (BS) in an iterative manner for multi-user symbol detection under hardware impairments. Firstly, in the proposed system, an iterative nonlinear interference cancellation (nIC) based on feedforward neural network (NN) modeling is developed to eliminate the nonlinear distortion effects of power amplifiers (PAs). Furthermore, depending on the fading pattern of the instantaneous channel, it is analytically shown that a large gain may be applied to the distortion signal during the equalization stage, which yields distortion amplification causing a significant decrease in the signal-to-distortion-plus-noise ratio (SDNR). A reduced complexity distortion aware detector, based on a bank of fractionally delayed iterative block decision feedback equalization (IB-DFE) receivers, is introduced to adjust the combiner weights for fractionally delayed IB-DFE outputs so that distortion power is minimized before detection. Consequently, multi-user detection capability is enhanced considerably. Secondly, an asymptotic SDNR analysis is performed. The theoretical analysis, verified via numerical evaluations, clearly shows that distortion amplification limits the achievable SDNR at the BS, and the proposed reduced complexity multi-user receiver architecture improves the BER performance by effectively mitigating this effect.

A Closed-Form Expression for the Gaussian Noise Model in the Presence of Inter-Channel Stimulated Raman Scattering Extended for Arbitrary Loss and Fibre Length

A closed-form formula for the nonlinear interference (NLI) estimation using the Gaussian noise (GN) model in the presence of inter-channel stimulated Raman scattering (ISRS) is derived. The formula enables accurate estimation of the NLI evolution along any portion of the fibre span together with arbitrary values of optical fibre losses. The formula also accounts for wavelength-dependent fibre parameters, variable modulation formats and launch power profiles. The formula is suitable for ultra-wideband (UWB) optical transmission systems and its accuracy is assessed for a system with 20 THz optical bandwidth over the entire S-, C-, and L- band through comparison with numerical integration of the ISRS GN model and split-step Fourier method (SSFM) simulations in point-to-point transmission and inline NLI estimation scenarios.

2.11 GHz all-fiber harmonic mode-locked laser based on highly nonlinear hybrid multimode interference saturable absorber

This paper proposes a harmonic mode-locked fiber laser based on a novel highly nonlinear hybrid multimode interference saturable absorber (SA). The hybrid multimode interference SA is integrated by tapered graded-index multimode fiber (TA-GIMF) and Bi2Te3. The numerical simulation results show that TA-GIMF can improve the stability of nonlinear multimode interference mode-locking by filtering higher-order transverse modes. In addition, the larger evanescent-wave fields generated by TA-GIMF are more beneficial to the light–matter interaction. By depositing Bi2Te3 on TA-GIMF, the nonlinear saturation absorption properties and nonlinear coefficients in the laser cavity are further improved. Based on the hybrid multimode interference SA, the repetition rate of the fiber laser reached 2.11 GHz, corresponding to the 30th harmonic of the fundamental repetition rate of 70.41 MHz. Our results are the highest repetition rate generated based on the NL-MMI effect and provide novel insights into implementing highly integrated, high repetition-rate mode-locked fiber lasers.

Frequency-domain nonlinear interference cancellation scheme with IQ imbalance in full-duplex systems

在全双工自干扰信道反射径较多的情况下, 针对已有时域自干扰对消方案复杂度高的问题, 提出了一种低复杂度的频域自干扰对消方案. 该方案以全双工零中频架构为基础, 综合考虑了IQ不平衡以及功放非线性对自干扰重建模型的影响, 优化了已有频域自干扰重建模型的准确度. 在此基础上, 利用正交化辅助的连续干扰对消技术实现了低复杂度的自干扰消除. 仿真分析表明, 所提方案相比已有的基于RLS算法的频域自干扰对消方案, 能够在存在IQ不平衡以及功放非线性的情况下实现几乎相同的自干扰对消性能, 但是降低了68.75%的复杂度.

GAWBS Noise in Digital Coherent Transmission

This paper presents recent progress on guided acoustic wave Brillouin scattering (GAWBS) noise in single-core fiber (SCF), multi-core fiber (MCF), and few-mode fiber (FMF). First, we describe theoretical analyses of GAWBS phase noise generated in these various types of fiber. By using three types of SCF, namely ultra-large area fiber (ULAF), standard single-mode fiber (SSMF), and dispersion-shifted fiber (DSF), we show that the GAWBS phase noise depends strongly on the effective core area A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> . We also describe the GAWBS phase noise in four-core fiber (4CF), where it is shown that GAWBS noise in the off-center core is quite different from that in SCF. Furthermore, we describe the GAWBS phase noise in FMF supporting two LP modes. Then, we compare the GAWBS noise powers induced in SCF, MCF, and FMF. Next, we describe experiments on GAWBS phase noise in various fibers, which agree well with the theory. We also measured and analyzed the GAWBS phase noise correlation between the cores in a 4CF, where it is shown that the correlation between cores strongly depends on the core position. Finally, we describe the influence of GAWBS phase noise on digital coherent transmission. We formulate the GAWBS phase noise based on the Gaussian distribution and evaluate its influence on the BER characteristics in a coherent QAM transmission. We found that it is difficult to realize a transoceanic-class QAM transmission with a QAM multiplicity of higher than 64 even without other impairments. Furthermore, we evaluate the SNR penalty induced by the GAWBS noise in a long-haul transmission by taking account of the amplified spontaneous emission (ASE) and nonlinear interference noise, which are unavoidable in actual systems. The calculated results show that the influence of the GAWBS noise is smaller than the other impairments, but it cannot be neglected in system evaluations.

Performance improvements by dynamic amplifier reconfigurations for C + L-band optical networks in the presence of stimulated Raman scattering

C+L-band optical networks suffer from transmission impairments including amplified spontaneous emission noise and Kerr-induced and stimulated-Raman-scattering-induced nonlinear interference. The generalized signal-to-noise ratio (GSNR) profiles across different links of the network play a crucial role in determining the overall network traffic load and operating margins, but the GSNR is highly dependent on the signal power profiles along the link and time-varying channel-loading conditions, particularly for future dynamic mesh networks. As the network is dynamically loaded, we monitor the GSNR across the active channels of each link and investigate the benefits of regularly reconfiguring the erbium-doped fiber amplifier (EDFA) gain and tilts to optimize either (1) the mean GSNR minus the GSNR standard deviation (i.e., to achieve a high and flat GSNR across channels) or (2) the minimum GSNR to improve the traffic load and/or GSNR margins. Different lightpath provisioning strategies are studied, and simulation results for COST 239, a German network, and a sample Alibaba production network show that, compared with static EDFA configurations assuming fully loaded conditions, the GSNR margin and hence network robustness with dynamic EDFA reconfigurations can be improved by at least 0.45, 0.57, and 0.72 dB, respectively, with similar or better network blocking probability. Alternatively, the improved GSNR profiles can enable an average network capacity improvement of at least 9%, 8%, and 16%, respectively, in principle when operating at the same GSNR margin at 30% spectral occupancy.

Impairment-aware routing, modulation, spectrum, and core allocation with bit loading in spectrally–spatially flexible optical networks

This work proposes a physical layer impairment-aware routing, modulation, spectrum, and core allocation optimization framework in elastic optical networks with multi-core fibers. The inter- and intra-core impairments considered are crosstalk between adjacent cores, in-band crosstalk, non-linear interference, and amplified spontaneous emission noise. Further, bit loading is used in the proposed framework, independently modulating each demand’s frequency slots, depending on each frequency slot’s interference level. An optimization framework is initially developed for benchmarking purposes, followed by a heuristic algorithm and demand ordering technique for larger-sized networks. For both optimization and heuristic approaches, an end-to-end acceptable bit error rate is ensured for each provisioned demand. The benefits of the proposed approach are illustrated through simulations, demonstrating that they achieve lower fragmentation and less spectrum usage as compared to other state-of-the-art techniques.

On multi-hump solutions of reverse space-time nonlocal nonlinear Schrödinger equation

In this article multi-soliton solutions of reverse space-time nonlocal nonlinear Schr ödinger (NLS) equation have been constructed. Darboux transformation is applied to the associated linear eigenvalue problem for the generalized NLS equation and we obtain a determinant formula for multi-soliton solutions. Under suitable reduction conditions and appropriate choice of spectral parameters, the generalized expression of first-order nontrivial solution gives some novel solutions such as double-hump and flat-top soliton solutions for reverse space-time nonlocal NLS equation. The dynamics and interaction of double-hump soliton solutions are studied in detail and it is indicated that these solutions undergo collisions without any energy redistribution. For higher-order double-hump solutions, the relative velocities of solitons play a crucial role to have humps and also induce nonlinear interference in the collision zone. The dynamics of individual decaying and growing unstable and stable double-humps as well as their interactions are explained and illustrated.

Dependence of nonlinear interference on mode dispersion and modulation format in strongly-coupled SDM transmissions.

We study the role of the modulation format in the interaction between mode dispersion and the fiber nonlinear interference (NLI) in space-division multiplexed (SDM) systems with strongly-coupled spatial modes. We show that the interplay between mode dispersion and the modulation format has a significant impact on the magnitude of cross-phase modulation (XPM). We propose a simple formula that accounts for the modulation-format dependence of the XPM variance in the presence of arbitrary levels of mode dispersion, thus extending the ergodic Gaussian noise model.

Orthant-symmetric four-dimensional geometric shaping for fiber-optic channels via a nonlinear interference model.

Maximizing the data throughput for optical fiber communication via signal shaping has usually been regarded as challenging due to the nonlinear interference and implementation/optimization complexity. To overcome these challenges, in this paper, we propose an efficient four-dimensional (4D) geometric shaping (GS) approach to design 4D 512-ary and 1024-ary modulation formats by maximizing the generalized mutual information (GMI) using a 4D nonlinear interference (NLI) model, which makes these modulation formats more nonlinear-tolerant. In addition, we propose and evaluate a fast and low-complexity orthant-symmetry based modulation optimization algorithm via neural networks, which allows to improve the optimization speed and GMI performance for both linear and nonlinear fiber transmission systems. The optimized modulation formats with spectral efficiencies of 9 and 10 bit/4D-sym demonstrate a GMI improvement of up to 1.35 dB compared with their quadrature amplitude modulation (QAM) counterparts in additive white Gaussian noise (AWGN) channel. Numerical simulations of optical transmission over two types of fibers show that the 4D NLI model-learned modulation formats could extend the transmission reach by up to 34% and 12% with respect to the QAM formats and the AWGN-learned 4D modulation formats, respectively. Results of effective signal-to-noise ratio are also presented, which confirm that the extra gains in optical fiber channel come from the enhanced SNR by reducing the modulation-dependent NLI.

Performance Analysis and Power Tilt Mitigation of Ultra-Wideband WDM Transmission Systems

Ultra-wideband (UWB) wavelength division multiplexing (WDM) transmission, which utilizes low-loss spectral windows of single-mode fiber for data transmission, is a highly promising method for increasing the capacity of optical communication. In this paper, we investigate the performance of a UWB WDM transmission system that covers the widely used C+L band as well as the additional O-, E-, and S-bands. We establish the transmission system for UWB and discuss the effects of the channel, including Kerr nonlinearity and inter-channel interference from inter-channel stimulated Raman scattering (ISRS) between O-, E-, S-, C-, and L-bands. Moreover, we demonstrate an optimization scheme for compensating the spectral power tilt caused by SRS in the S+C+L band system, which utilizes the Raman amplifier and the partition particle swarm optimization (PPSO) algorithm. The results show that the power tilt value of the algorithm is reduced from 18 to 2.93 dB, and the iteration speed is improved by 10% compared with the normal particle swarm algorithm. The scheme provides an efficient way to improve the generalized mutual information (GMI) performance of UWB WDM systems.

Super-twisting Sliding Mode Control Based on Electrostatic MEMS Micromirror Scanning

In this paper, a Super-twisting sliding-mode control method based on a nonlinear interference observer is proposed for the external perturbation of MEMS micromirrors during beam scanning. Developing a physical model of electrostatic MEMS micromirror, the Super-twisting sliding-mode control algorithm based on nonlinear interference observer is applied to the electrostatically driven MEMS scanning micromirror with side electrodes, with the demonstration on stability of the control system by Lyapunov theory. The method effectively improves the anti-disturbance performance of the system. The simulation results show that the Super-twisting sliding mode control method based on nonlinear disturbance observer can effectively enhance the disturbance inhibition of the system.

Research and Application for Corrosion Rate Prediction of Natural Gas Pipelines Based on a Novel Hybrid Machine Learning Approach

An accurate and stable prediction of the corrosion rate of natural gas pipelines has a major impact on pipeline material selection, inhibitor filling process, and maintenance schedules. At present, corrosion data are impacted by non-linearity and noise interference. The traditional corrosion rate prediction methods often ignore noise data, and only a small number of researchers have carried out in-depth research on non-linear data processing. Therefore, an innovative hybrid prediction model has been proposed with four processes: data preprocessing, optimization, prediction, and evaluation. In the proposed model, a decomposing algorithm is applied to eliminate redundant noise and to extract the primary characteristics of the corrosion data. Stratified sampling is applied to separate the training set and the test set to avoid deviation due to the sampling randomness of small samples. An improved particle swarm optimization algorithm is applied to optimize the parameters of support vector regression. A comprehensive evaluation of this framework is also conducted. For natural gas pipelines in southwest China, the coefficient of determination and mean absolute percentage error of the proposed hybrid model are 0.925 and 5.73%, respectively, with better prediction performance compared to state-of-the-art models. The results demonstrate the best approach for improving the prediction accuracy of the proposed hybrid model. This can be applied to improve the corrosion control effect and to support the digital transformation of the corrosion industry.

Some power allocation algorithms for cognitive uplink satellite systems

Cognitive satellite communication (SatCom) is rapidly emerging as a promising technology to overcome the scarcity of the exclusive licensed band model in order to fulfill the increasing demand for high data rate services. The paper addresses power allocation methods for multi-operator multi-beam uplink satellite communication systems co-existing with a Ka-band terrestrial network, using cognitive radio paradigm. Such a scenario is especially challenging because of (i) the coexisting multiple SatCom operators over the cognitive band need to coordinate the use of their resources under limited inter-operator information exchange, and (ii) nonlinear onboard high power amplifier (HPA) which leads to nonlinear interference between users and beams. In order to tackle the first challenge, we propose distributed power allocation algorithms including the standard Alternate Direction Multiplier Method (ADMM); Regarding the HPA nonlinear impairment, we propose nonlinear-aware power allocation based on Signomial Programming. The proposed solutions outperform state-of-the-art in both cases.

Longitudinal Control Technology for Automatic Carrier Landing Based on Model-compensated Active Disturbance Rejection Control

Carrier aircraft landing is a system engineering with strong nonlinear, strong coupling, and complex environmental interference. Landing control is one of the key technologies for carrier aircraft landing, which directly affects the success of the landing. A longitudinal decoupling control method based on Model Compensated Linear Active Disturbance Rejection Control (MCC-LADRC) is proposed for tracking the deck motion and maintaining the attack angle in the final stage of the carrier landing. The simulation results show that compared with the PID control and traditional LADRC strategy, the MCC-LADRC method can not only control the carrier aircraft to track the deck motion synchronously and accurately, improve the landing accuracy and anti-disturbance capability but also has a good attack angle retention effect and eliminate the coupling between the pitch angle and the attack angle.

Coupled aero-hydro-mooring dynamic analysis of floating offshore wind turbine under blade pitch motion

Accurate prediction of the dynamic responses of the floating offshore wind turbine (FOWT) under the blade pitch motion is quite challenging because of the strong nonlinear effects. In this study, a fully coupled and highly elaborated model was established based on the computational fluid dynamics, with the dynamic fluid body interaction method. The multi-stage movements consisting of the six degrees of freedom motions of the platform, the rotation of the rotor, and the blade pitch motion were defined by the superposition motion technologies. The blade pitch control module was created through the user-defined function to regulate the blade pitch motion. Then, several coupled dynamic simulations of the full-configuration DeepCwind floating wind turbine system were performed in power production, shutdown, and startup cases. The simulation results in the power production case indicate that the blade pitch motion decreases the generated aerodynamic loads and amplifies the response amplitude of the platform as negative damping is introduced in the FOWT system. The simulation results in the shutdown and startup cases indicate that the extreme motion responses are enlarged, and the mooring line tension oscillates dramatically when it is in high-tension states. In addition, the nonlinear interference effects in the unsteady flow fields, such as the shedding vortices broken by the blade pitch motion, are visualized and investigated in detail.

Имитационная программа для оценки влияния нелинейных фазовых искажений на показатели качества сигналов в оптическом тракте

The influence of nonlinear phase interference of self-phase modulation and phase cross-modulation arising in an optical fiber on multichannel, spectrally separated signals is considered. A simulation program has been created in the environment of the object-oriented programming language C#, which makes it possible to calculate the BER in the receiving part depending on the parameters of the optical path. The program has several degrees of freedom in the following parameters: transmission rate, used linear signal code, optical power level in individual channels, length and type of optical fiber. It is shown that in order to achieve the required BER, it is necessary to limit the optical power levels in the channel signals. The results of simulation of signal transmission over a distance of 100 km for the number of channels 40, 80 and 160 with channel rates of 10 Gbit/s and 40 Gbit/s in NRZ and RZ linear codes are presented.

Performance Investigation of DP-16QAM Ultra-wideband- Wavelength-Division Multiplexing Communication System: Optimum Power Consideration

Recently, there is increasing interest in using the 18 THz bandwidth offered by S+C+L band to increase the transmission capacity of fiber communication systems. This leads to the generation of ultra-wideband (UWB) wavelength-division multiplexing (WDM) optical communication systems. In these advanced systems, stimulated Raman scattering (SRS) causes a power transfer from high-frequency channels to low-frequency channels. This effect leads to an increase in the nonlinear interference (NLI) between the UWB-WDM channels. Power optimization techniques are required to balance transfer power between band channels, thus increasing the maximum transmission reach (MTR) along with increasing system capacity. In this paper, the transmission performance of S+C+L band system operating with dual-polarization 16-QAM signaling is investigated using enhanced Gaussian noise model. The transmitter and receiver for each DP channel use a -polarized laser and incorporate two identical configurations, one for x- and the other for y-state of polarization (SOP). The results are presented for two values of symbol rate, 40 and 80 GBaud, where the system carries 360 (=160+80+120) and 180 (=80+40+60) channels, respectively. The results revel that the MTR of both cases is equal to 12 100 km-spans when the channel lunch power equals to -4 and -2 dBm, respectively. This work also shows the effect of NLI components as a function of the number of spans, channel spacing, and channel launch power. The results show that the cross-phase modulation component of the NLI has high accumulated value with transmission distance, while the self-phase modulation component is almost constant.

Design and calibration of spoke piezoelectric six-dimensional force/torque sensor for space manipulator

The large manipulator outside the space cabin is a multi-degree of freedom actuator for space operations. In order to realize the automatic control and flexible operation of the space manipulator, a novel spoke structure piezoelectric six-dimensional force/torque sensor with redundancy ability, high stiffness and good decoupling performance is innovatively proposed. Based on the deformation coordination relationship, the redundancy measurement mechanism is revealed. The mathematical models of the sensor with and without branch fault are established respectively. The finite element model is established to verify the feasibility of structure and redundancy measuring principle of the sensor. Depending on the theoretical analysis and simulation analysis, the prototype of the sensor is developed. Static and dynamic calibration experiments are carried out. The actual output voltage signal of the six-dimensional force/torque sensor is collected to establish the equation between the standard input applied load and the actual output voltage signal. Based on ant colony optimized BP algorithm, performance indexes of the sensor with and without branch fault are analyzed respectively. The experimental results show that the spoke piezoelectric six-dimensional force/torque sensor with the eight-point support structure has good accuracy and reliability. Meanwhile, it has strong decoupling characteristic that can effectively shield the coupling between dimensions. The nonlinear errors and maximum interference errors of decoupled data with and without branch faults are less than 1% and 2%, respectively. The natural frequency of the six-dimensional force sensor can reach 2856.45 Hz and has good dynamic characteristics. The research content lays a theoretical and experimental foundation for the design, development and application of the new six-dimensional force/torque sensors with redundancy. Meanwhile, it will significantly improve the research level in this field, and provide a strong guarantee for the smooth implementation of force feedback control of the space station manipulator project.