Shenghang Luo, Sunish Kumar Orappanpara Soman, Lutz Lampe, Jeebak Mitra, Chuandong Li
Several machine learning inspired methods for perturbation-based fiber nonlinearity (PBNLC) compensation have been presented in recent literature. We critically revisit acclaimed benefits of those over non-learned methods. Numerical results suggest that learned linear processing of perturbation triplets of PB-NLC is preferable over feedforward neural-network solutions.
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We propose a fiber nonlinearity post-compensation technique using the DNN and the second-order perturbation theory. We achieve 1 dB Q-factor improvement for a 32 Gbaud PDM-64-QAM at 1200 km compared to the linear dispersion compensation.
We propose a technique combining the singlechannel digital-back-propagation (SC-DBP) with phaseconjugated-twin-wave (PCTW) to compensate nonlinearities in CO-OFDM superchannel systems. This exhibits a similar performance as multi-channel DBP while providing increased transmission reach compared to SC-DBP, PCTW, and linear dispersion compensation (LDC).
Meeting the ever-growing information rate demands has become of utmost importance for optical communication systems. However, it has proven to be a challenging task due to the presence of Kerr effects, which have largely been regarded as a major bottleneck for enhancing the achievable information rates in modern optical communications. In this work, the optimisation and performance of digital nonlinearity compensation are discussed for maximising the achievable information rates in spectrally-efficient optical fibre communication systems. It is found that, for any given target information rate…
Joint PMD Tracking and Nonlinearity Compensation with Deep Neural Networks
针对光纤通信中PMD时变漂移下的联合补偿问题，提出基于迁移学习的选择性训练方案，仅微调少量权重即可使带PMD分布式补偿的DCRNN模型适配PMD变化，降低重训开销并保持性能增益。
Simultaneous Pre-compensation for Bandwidth Limitation and Fiber Dispersion in Cost-Sensitive IM/DD Transmission Systems
提出基于改进GS算法的pre-BL-EDC方案，在20/28/32 Gbit/s带宽受限IM/DD系统中实现带宽限制与光纤色散的同时预补偿，相比改进GS预EDC获得1.0/1.0/2.0 dB增益。
There is a tremendous need to maximize signal capacity without sacrificing energy consumption and complexity in optical fiber communications due to the rise of network traffic demand and critical latency-aware services such as telemedicine and the Internet-of-Things. In this work, the first system-agnostic and training-data-free fiber nonlinearity compensator (NLC) using affinity propagation (AP) clustering is experimentally demonstrated. It is shown that compared to linear equalization, AP can increase the signal quality-factor up to about 5 dB in 16-quadrature-amplitude-modulated coherent op…
The first-order (FO) perturbation theory-based nonlinearity compensation (PB-NLC) technique has been widely investigated to combat the detrimental effects of the intra-channel Kerr nonlinearity in polarization-multiplexed (Pol-Mux) optical fiber communication systems. However, the NLC performance of the FO-PB-NLC technique is significantly limited in highly nonlinear regimes of the Pol-Mux long-haul optical transmission systems. In this paper, we extend the FO theory to second-order (SO) to improve the NLC performance. This technique is referred to as the SO-PB-NLC. A detailed theoretical anal…
A perturbation-based nonlinear compensation scheme assisted by a feedback from the forward error correction (FEC) decoder is numerically and experimentally investigated. It is shown by numerical simulations and transmission experiments that a feedback from the FEC decoder enables improved compensation performance, allowing the receiver to operate very close to the full data-aided performance bounds. The experimental analysis considers the dispersion uncompensated transmission of a 5 x 32 GBd WDM system with DP-16QAM and DP-64QAM after 4200 km and 1120 km, respectively. The experimental results…
Mitigation of optical fiber nonlinearity is an active research field in the area of optical communications, due to the resulting marked improvement in transmission performance. Following the resurgence of optical coherent detection, digital nonlinearity compensation (NLC) schemes such as digital backpropagation (DBP) and Volterra equalization have received much attention. Alternatively, optical NLC, and specifically optical phase conjugation (OPC), has been proposed to relax the digital signal processing complexity. In this work, a novel hybrid optical-digital NLC scheme combining OPC and a Vo…
Deep Learning-Aided Perturbation Model-Based Fiber Nonlinearity Compensation
该研究针对长距离光纤通信的非线性补偿问题，重新分析了学习型PB-NLC方法的性能复杂度权衡，提出基于双向循环神经网络的全学习结构，实现了更优的性能-复杂度平衡。
Experimental Investigation into Split Nonlinearity Compensation in Single and Multi-channel WDM Systems
本研究针对单通道与多通道WDM系统，实验探究分段非线性补偿方案的性能，发现在信号-ASE拍频限制传输的场景下，5540 km传输距离中该方案相较单端DBP可实现超0.4 dB的SNR增益。
Fuzzy Clustering for Low-Complexity Time Domain Chromatic Dispersion Compensation Scheme in Coherent Optical Fiber Communication Systems
针对相干光纤通信中CDC硬件复杂度高的问题，提出两阶段模糊聚类的软判决TD-CDC方案，在1800 km系统中显著降低复杂度并保持最优Q因子。
Nonlinear effects have been considered as the major limitations in coherent optical (CO) fiber transmission system. DSP based CO receiver with digital backpropagation (DBP) method has recently facilitated the compensation of fiber nonlinear impairments as well as compensating dispersion of optical fiber. In this paper, a comprehensive design is presented for circular-polarization division multiplexed (CPDM) 8-quadrature amplitude modulation (8-QAM) with DSP based CO receiver for the fiber optic communication (FOC) system to investigate the impact of nonlinearities. We have examined the perform…
Efficient nonlinearity compensation in fiber-optic communication systems is considered a key element to go beyond the "capacity crunch''. One guiding principle for previous work on the design of practical nonlinearity compensation schemes is that fewer steps lead to better systems. In this paper, we challenge this assumption and show how to carefully design multi-step approaches that provide better performance--complexity trade-offs than their few-step counterparts. We consider the recently proposed learned digital backpropagation (LDBP) approach, where the linear steps in the split-step metho…
By tailoring probabilistic constellation shaping (PCS) for nonlinearity tolerance, we experimentally demonstrate up to 1.1 dB increase in signal-to-noise ratio (SNR) and 6.4% increase in total net data rate (NDR) compared to linear-channel-optimized PCS on a 2824-km dispersion-managed wavelength-division multiplexed (WDM) optical fiber link.
In this paper, we present an accurate and numerically efficient method to implement the GN and EGN nonlinearity prediction methods when the power evolution along the fiber is in an arbitrary form. This approach will provide us with a reliable tool to efficiently use GN and Enhanced GN (EGN) methods for analysis of the nonlinearity for ultrawideband coherent fiber optic WDM systems (C+L band or even wider bandwidth systems) in the presence of the Inter-channel Stimulated Raman Scattering (ISRS) and systems using forward-pumped or/and backward-pumped Raman amplification.
Derived from the regular perturbation treatment of the nonlinear Schrodinger equation, a machine learning-based scheme to mitigate the intra-channel optical fiber nonlinearity is proposed. Referred to as the perturbation theory-aided (PA) learned digital back-propagation (LDBP), the proposed scheme constructs a deep neural network (DNN) in a way similar to the split-step Fourier method: linear and nonlinear operations alternate. Inspired by the perturbation analysis, the intra-channel cross-phase modulation term is conveniently represented by matrix operations in the DNN. The introduction of t…
A neural network is quantized for the mitigation of nonlinear and components distortions in a 16-QAM 9x50km dual-polarization fiber transmission experiment. Post-training additive power-of-two quantization at 6 bits incurs a negligible Q-factor penalty. At 5 bits, the model size is reduced by 85%, with 0.8 dB penalty.
Nonlinearity mitigation using digital signal processing has been shown to increase the achievable data rates of optical fiber transmission links. One especially effective technique is digital back propagation (DBP), an algorithm capable of simultaneously compensating for linear and nonlinear channel distortions. The most significant barrier to implementing this technique, however, is its high computational complexity. In recent years, there have been several proposed alternatives to DBP with reduced computational complexity, although such techniques have not demonstrated performance benefits c…
For the efficient compensation of fiber nonlinearity, one of the guiding principles appears to be: fewer steps are better and more efficient. We challenge this assumption and show that carefully designed multi-step approaches can lead to better performance-complexity trade-offs than their few-step counterparts.
In this paper, we present a novel closed-form model (CFM) for accurate and fast evaluation of nonlinear interference in modern ultrawideband coherent optical fiber communication systems. Starting from the Gaussian noise model (GN model), using reasonable approximations and machine-learning optimized improvements, we achieve an accurate CFM capable of handling ultrawide band (C+L or wider) optical fiber systems in the presence of Inter-channel Stimulated Raman Scattering (ISRS) and forward-pumped Raman amplification.
Meta-DSP: A Meta-Learning Approach for Data-Driven Nonlinear Compensation in High-Speed Optical Fiber Systems
本文提出Meta-DSP信号处理流程，通过元学习DBP与XPM-ADF实现免重训练的跨速率、跨信道数非线性补偿，并以更低复杂度取得显著性能提升。
The efficiency of digital nonlinearity compensation (NLC) is analyzed in the presence of noise arising from amplified spontaneous emission noise (ASE) as well as from a non-ideal transceiver subsystem. Its impact on signal-to-noise ratio (SNR) and reach increase is studied with particular emphasis on split NLC, where the digital back-propagation algorithm is divided between transmitter and receiver. An analytical model is presented to compute the SNR's for non-ideal transmission systems with arbitrary split NLC configurations. When signal-signal nonlinearities are compensated, the performance …
Second-Order Nonlinearity Estimated and Compensated Diffusion LMS Algorithm: Theoretical Upper Bound, Cramer-Rao Lower bound, and Convergence Analysis
本文提出一种估计与补偿二阶非线性的扩散LMS算法，推导了误差上界、Cramer-Rao下界及收敛性分析，仿真验证了其在无线传感器网络中提升分布式估计性能的有效性。
In this paper, we propose a linear polarization coding scheme (LPC) combined with the phase conjugated twin signals (PCTS) technique, referred to as LPC-PCTS, for fiber nonlinearity mitigation in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The LPC linearly combines the data symbols on the adjacent subcarriers of the OFDM symbol, one at full amplitude and the other at half amplitude. The linearly coded data is then transmitted as phase conjugate pairs on the same subcarriers of the two OFDM symbols on the two orthogonal polarizations. The nonlinear distortions…
The first-order (FO) perturbation theory has been widely investigated to design the digital nonlinearity compensation (NLC) technique to deal with the intra-channel fiber nonlinearity effect in coherent optical communication systems. The main advantages of the perturbation theory-based approach are the possibility of the implementation on a single stage for the entire fiber link and one sample per symbol operation. In this paper, we propose to extend the FO perturbation theory-based NLC (FO-PB-NLC) technique to the second-order (SO), referred to as the SO-PB-NLC, to enhance the NLC performance…
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 uni…
Probabilistic constellation shaping (PCS) offers a significant performance improvement over uniform signaling. It was recently discovered that long blocks are not required to achieve maximum shaping gain when transmitting over the nonlinear fiber channel because short-length PCS effectively mitigates fiber nonlinear interference (NLI). The reason for this behavior is that short-length PCS implicitly induces some temporal properties in the shaped transmit sequence that are beneficial for the fiber-optic channel. To achieve robust data-aided digital signal processing of high-order QAM, periodic …
In this paper, the performance of adaptive turbo equalization for nonlinearity compensation (NLC) is investigated. A turbo equalization scheme is proposed where a recursive least-squares (RLS) algorithm is used as an adaptive channel estimator to track the time-varying intersymbol interference (ISI) coefficients associated with inter-channel nonlinear interference (NLI) model. The estimated channel coefficients are used by a MIMO 2x2 soft-input soft-output (SISO) linear minimum mean square error (LMMSE) equalizer to compensate for the time-varying ISI. The SISO LMMSE equalizer and the SISO for…
In optical communication systems, fibre nonlinearity is the major obstacle in increasing the transmission capacity. Typically, digital signal processing techniques and hardware are used to deal with optical communication signals, but increasing speed and computational complexity create challenges for such approaches. Highly parallel, ultrafast neural networks using photonic devices have the potential to ease the requirements placed on the digital signal processing circuits by processing the optical signals in the analogue domain. Here we report a silicon photonice-lectronic neural network for …
Ultra-wideband fiber optical transmission suffers from both Kerr nonlinearity and stimulated Raman scattering (SRS). Mathematical models that address the interplay between Kerr nonlinearity and SRS exist. These models are based on the Gaussian-noise (GN) and enhanced Gaussian noise (EGN) models. In this paper, we propose a modulation-format-dependent model, accounting for an enhanced link function, which is valid for non-identical spans where the fiber span loss and SRS gain/loss are not necessarily compensated for by the amplifier at the end of each span. A new signal power profile is also in…
The compliant nature of soft wearable robots makes them ideal for complex multiple degrees of freedom (DoF) joints, but also introduce additional structural nonlinearities. Intuitive control of these wearable robots requires robust sensing to overcome the inherent nonlinearities. This paper presents a joint kinematics estimator for a bio-inspired multi-DoF shoulder exosuit capable of compensating the encountered nonlinearities. To overcome the nonlinearities and hysteresis inherent to the soft and compliant nature of the suit, we developed a deep learning-based method to map the sensor data to…
Recently, data-driven approaches motivated by modern deep learning have been applied to optical communications in place of traditional model-based counterparts. The application of deep neural networks (DNN) allows flexible statistical analysis of complicated fiber-optic systems without relying on any specific physical models. Due to the inherent nonlinearity in DNN, various equalizers based on DNN have shown significant potentials to mitigate fiber nonlinearity. In this paper, we propose a turbo equalization (TEQ) based on DNN as a new alternative framework to deal with nonlinear fiber impairm…
We introduce for the first time the utilization of Long short-term memory (LSTM) neural network architectures for the compensation of fiber nonlinearities in digital coherent systems. We conduct numerical simulations considering either C-band or O-band transmission systems for single channel and multi-channel 16-QAM modulation format with polarization multiplexing. A detailed analysis regarding the effect of the number of hidden units and the length of the word of symbols that trains the LSTM algorithm and corresponds to the considered channel memory is conducted in order to reveal the limits …
We investigate the performance of a machine learning classification technique, called the Parzen window, to mitigate the fiber nonlinearity in the context of dispersion managed and dispersion unmanaged systems. The technique is applied for detection at the receiver side, and deals with the non-Gaussian nonlinear effects by designing improved decision boundaries. We also propose a two-stage mitigation technique using digital back propagation and Parzen window for dispersion unmanaged systems. In this case, digital back propagation compensates for the deterministic nonlinearity and the Parzen wi…
Fiber Kerr nonlinearity is a fundamental limitation to the achievable capacity of long-distance optical fiber communication. Digital back-propagation (DBP) is a primary methodology to mitigate both linear and nonlinear impairments by solving the inverse-propagating nonlinear Schrödinger equation (NLSE), which requires detailed link information. Recently, the paradigms based on neural network (NN) were proposed to mitigate nonlinear transmission impairments in optical communication systems. However, almost all neural network-based equalization schemes yield high computation complexity, which pr…
Fiber Nonlinearity Mitigation in Coherent Optical Systems
该研究综述了相干光系统中光纤非线性抑制的两类主流方法及最新进展，提出星座整形、低复杂度DBP等未来方向，指出其兼具理论与实用价值。
We numerically demonstrate an all-optical nonlinearity pre-compensation module for state-of-the-art long-reach Raman-amplified unrepeatered links. The compensator design is optimized in terms of propagation symmetry to maximize the performance gains under WDM transmission, achieving 4.0dB and 2.6dB of SNR improvement for 250-km and 350-km links.
Neural Network Architectures for Optical Channel Nonlinear Compensation in Digital Subcarrier Multiplexing Systems
本文研究数字子载波复用光传输系统中的光纤非线性补偿问题，提出基于CNN和LSTM等人工神经网络结构的非线性均衡器，并通过模块化设计逐步优化性能与复杂度，为未来相干光收发器提供实用方案。
The massive deployment of light-emitting diode (LED) lightning infrastructure has opened the opportunity to reuse it as visible light communication (VLC) to leverage the current RF spectrum crisis in indoor scenarios. One of the main problems in VLC is the limited dynamic range of LEDs and their nonlinear response, which may lead to a severe degradation in the communication, and more specifically in the bit error rate (BER). This is aggravated by the extensive usage of multicarrier multiplexing, based on optical orthogonal frequency division multiplexing (O-OFDM), characterized by a high peak-…
Fiber nonlinearity compensation of probabilistically shaped constellations with adaptive turbo equalization is investigated for the first time. Potential for more than 100% transmission reach extension is demonstrated by combining probabilistic shaping, single-channel digital backpropagation, and adaptive turbo equalization.
Machine learning techniques have recently received significant attention as promising approaches to deal with the optical channel impairments, and in particular, the nonlinear effects. In this work, a machine learning-based classification technique, known as the Parzen window (PW) classifier, is applied to mitigate the nonlinear effects in the optical channel. The PW classifier is used as a detector with improved nonlinear decision boundaries more adapted to the nonlinear fiber channel. Performance improvement is observed when applying the PW in the context of dispersion managed and dispersion…
Probabilistic Amplitude Shaping and Nonlinearity Tolerance: Analysis and Sequence Selection Method
本文提出线性低通滤波器模型分析概率幅度整形的非线性效应，并基于该模型设计新的序列选择度量，以提升光纤通信系统的非线性容限。
170-260 GHz Sub-THz Optical Heterodyne Analog Radio-over-Fiber Link for 6G Wireless System
针对自由运行激光器频率与相位波动影响光外差亚太赫兹传输的问题，该研究通过数字损伤补偿，在10 km模拟RoF链路上实现170–260 GHz OFDM信号生成。
Geometric Clustering for Hardware-Efficient Implementation of Chromatic Dispersion Compensation
针对光纤通信色散补偿算法硬件能效验证不足的问题，本文提出时域聚类均衡器TDCE技术，通过抽头重叠效应分析与创新并行化方法在FPGA上实现，相比最优频域均衡器FDE最高节省70.7%能耗与71.4%乘法器资源，证明实现策略对硬件效率的关键作用。
Probabilistic Shaping for Nonlinearity Tolerance
本文以教程形式探讨光纤通信中面向非线性容忍度的概率整形，基于非线性光纤信道一阶时域微扰近似分析线性与非线性整形增益，重点研究主流方法下的概率幅度整形及序列选择整形的多元分布优化特性。
Investigation of analog signal distortion introduced by a fiber phase sensitive amplifier
本研究通过数值模拟与实验验证，分析光纤相位敏感放大器（PSA）在微波光子链路调幅信号中引入的失真，对比不同调制器情况并探究增益饱和的影响，确定了PSA自身非线性极低的条件。
Fiber nonlinear interference (NLI) modeling and monitoring are the key building blocks to support elastic optical networks (EONs). In the past, they were normally developed and investigated separately. Moreover, the accuracy of the previously proposed methods still needs to be improved for heterogenous dynamic optical networks. In this paper, we present the application of machine learning (ML) in NLI modeling and monitoring. In particular, we first propose to use ML approaches to calibrate the errors of current fiber nonlinearity models. The Gaussian-noise (GN) model is used as an illustrative…
A Dual-Dip Heterogeneous LPFG Sensing System via Annealing under Bending with Temperature and Humidity Compensation
本文提出一种双 dips 异质长周期光纤光栅传感平台，通过弯曲辅助退火实现各向异性折射率再分布和模式依赖耦合增强，克服温度交叉灵敏度，实现温度、弯曲和湿度的多参数传感。
We demonstrate a high capacity IF-over-fiber mobile fronthaul solution for multi-user massive MIMO 5G RAN. Using this scheme, a record aggregated radio bandwidth of 25.6 GHz was transmitted on a single optical wavelength over 40 km without fiber chromatic dispersion compensation
Constellation shaping is a practical and effective technique to improve the performance and the rate adaptivity of optical communication systems. In principle, it could also be used to mitigate the impact of nonlinear effects, possibly increasing the information rate beyond the current limit dictated by fiber nonlinearity. However, this appealing idea is frustrated by the difficulty of designing an effective shaping strategy that takes into account the nonlinearity and long memory of the fiber channel, as well as the possible interplay with other nonlinearity mitigation strategies. As a result…
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, yieldin…
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