Compensation Of Nonlinear Impairments Research Articles

Nonlinear impairment compensation in multi-channel communication systems based on correlated digital backpropagation with separation of walk-off effect

Digital backpropagation (DBP) is a commonly used method to compensate for the nonlinear impairments of optical fiber channels in the electrical domain, offering a new approach to enhancing the data capacity without affecting the system performance. However, due to the repeated Fourier transform and inverse transform of the split-step Fourier method (SSFM), the complexity of DBP algorithm has increased significantly. In this paper, a correlated backpropagation algorithm with the separation of the walk-off effect is developed, which improves the computational step and significantly reduces the complexity of the algorithm. Simulation results demonstrate that in a 6-channel PDM-16QAM system, the proposed hybrid algorithm reduces the computational complexity by 73.96 % compared to the traditional DBP algorithm for an 800 km transmission.

Nonlinear Impairment Compensation Using Transfer Learning-Assisted Convolutional Bidirectional Long Short-Term Memory Neural Network for Coherent Optical Communication Systems

By combining the nonlinear impairment features derived from the first-order perturbation theory, we propose a nonlinear impairment compensation (NLC) scheme based on the transfer learning-assisted convolutional bidirectional long short-term Memory (CNN-BiLSTM) neural network structure. When considering the correlation of nonlinear impairment between preceding and succeeding consecutive adjacent symbols on the current moment symbol and integrating the multidimensional feature extraction and time memory characteristics of CNN-BiLSTM, the nonlinear impairment information contained in the input feature can be fully utilized to accurately predict the nonlinear impairment showing significant compensation effect. Meanwhile, transfer learning (TL) is introduced to greatly reduce the complexity of the scheme on the basis of high compensation performance. To verify the effectiveness of the proposed scheme, we construct single-channel (SC) and 5-channel 28 GBaud polarization division multiplexing 16 quadrature amplitude modulation (PDM-16QAM)/85 GBaud PDM-64QAM simulation systems, and SC and 3-channel 28 GBaud PDM-16QAM experimental systems. The experimental results show that when compared with simple recurrent neural network (SRNN) NLC and DBP 20 steps per span (DBP20StPs), the Q-factor gain of our scheme is about 1 dB and 1.7 dB in the SC system, and about 1.1 dB and 1.5 dB in the 3-channel system at the optimal launch power, respectively. It is interesting to highlight that, by applying TL to the simulation and experimental systems, our scheme based on only 5% of the training samples can achieve compensation performance comparable to or higher quality than retraining at various launch powers.

Beyond 200 Gbit/s/λ VSB PS-PAM8 Employing Joint Neural Network Equalization at C-band

We experimentally demonstrate a high-speed vestigial sideband (VSB) probability shaping 8-ary pulse amplitude modulation (PS-PAM8) system at C-Band. The strong-coupled linear and nonlinear impairments in high-speed VSB transmission systems lead to performance degradation. Neural network-based equalization has been widely adopted in the optical transmission system. However, the effective combination of linear and nonlinear impairment compensation in NN equalization has not been discussed intensively. In this experiment, we have proposed an equalizer based on the joint neural network (JNN) to compensate for the linear and nonlinear impairments. With the proposed JNN equalizer and PS technique, 92 GBaud PS-PAM8 signals can be delivered over 10 km standard single mode fiber (SSMF). Given the forward error correction (FEC) overhead and the entropy of PS-PAM8 signals, the net bit rate can reach 207 Gbit/s/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> , satisfying the demand for a 200 Gbit/s/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula> data connection.

Performance and Complexity Analysis of Conventional and Deep Learning Equalizers for the High-Speed IMDD PON

To accommodate the exponential growth of network services in the five-generation (5G) and beyond wireless system, 50 Gb/s/λ passive optical network (PON) is developed for mobile xhaul applications. Intensity modulation and direct detection (IMDD) technology together with digital signal procession (DSP) is being considered as the promising solution for 50 Gb/s/λ PON due to its low cost, low power consumption, and compact footprint. Different DSP algorithms with varied structures are proposed for linear and nonlinear impairments compensation in the high-speed PON, while the performance and complexity analysis of these algorithms is still missing. To find the most efficient equalizers, in this paper, four conventional equalizers, including feed-forward equalizer, decision feedback equalizer (DFE), Volterra equalizer (Vol) and Volterra DFE equalizer (Vol-DFE), together with two deep learning equalizers namely fully-connected neural network, and long short-term memory equalizer are experimentally compared in a 10G optics based 50G-PON system in terms of the equalization performance, computation complexity, optimization difficulty, and generalization ability. After the evaluation of our proposed fair comparison algorithm, we consider Vol-DFE is the most efficient one considering both performance and complexity. Attributes to the strong and efficient equalization capability of Vol-DFE, C-band 50 Gb/s PAM-4 signal transmission can be supported in a 10G optics based IMDD system with a 3 dB bandwidth of 6.11 GHz, and a power budget up to 38 dB can be achieved.

SOA Assisted Wavelength Reusing for 25G Colorless PON With Low-Cost 10G EAM

This paper demonstrates a C-band 25G colorless passive optical network (PON) based on semiconductor optical amplifier (SOA) and 10G electro-absorption modulator (EAM). The experimental results show that the SOA in the optical network unit (ONU) can erase the downlink signal by taking advantage of the gain saturation feature, realizing the reuse of downstream wavelength. Meanwhile, the SOA gain can compensate for the EAM loss by optimizing the current and injection power. Apart from this, equalization algorithms at the optical line terminal are investigated for linear and nonlinear impairments compensation. Besides, the system robustness to the ASE and the maximum transmission speed are also evaluated. Finally, the system capacity can reach up to 25 Gbps with NRZ format at a bit-error ratio threshold of 2 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> , proving that this system is a promising technology for future high-speed colorless 2 × 25G or 4 × 25G Wavelength division Multiplexing (WDM) PON system.

Fiber nonlinear impairments compensation based on nonlinear step size and modified adaptive digital back propagation

Abstract In this paper, we propose a low-complexity fiber nonlinearity impairments compensation scheme based on nonlinear step size and modified adaptive digital back propagation. To verify the feasibility of the proposed algorithm, we construct a simulation system of single channel 12.5 GBaud polarization division multiplexing 16-ary quadrature amplitude modulation (PDM-16QAM) optical transmission system. Comprehensive numerical simulation results demonstrate that the proposed scheme can not only search for the fiber nonlinear coefficient adaptively, but also has the characteristics of high performance and low complexity.

Weight Pruning Techniques Towards Photonic Implementation of Nonlinear Impairment Compensation Using Neural Networks

Neural networks (NNs) are attractive for nonlinear impairment compensation applications in communication systems, such as optical fiber nonlinearity, nonlinearity of driving amplifiers, and nonlinearity of semiconductor optical amplifiers. Without prior knowledge of the transmission link or the hardware characteristics, optimal parameters are completely constructed from a data-driven approach by exploring training datasets, once the NN structure is given. On the other hand, due to computational power and energy consumption, especially in high-speed communication systems, the computational complexity of the optimized NN needs to be confined to the hardware, such as FPGA or ASIC without sacrificing its performance improvement. In this paper, two approaches are presented to accommodate the NN-based algorithms for high-speed communication systems. The first approach is to reduce computational complexity of the NN-based nonlinearity compensation algorithms on the basis of weight pruning (WP). WP can significantly reduce the computational complexity, especially because the nonlinear compensation task studied here results in a sparse NN. The authors have studied an enhanced approach of WP by imposing an additional restriction on the selection of non-zero weights on each hidden layer. The second approach is to implement NNs onto a silicon-photonic integrated platform, enabling power efficiency to be further improved without sacrificing the high-speed operation.

Optical nonlinear impairment compensation based on Deep Neural Network (DNN) for coherent modulation systems

One and most important of the intrinsic challenges facing the optical fibers communication systems and main restriction to limited the system capacity is the fiber nonlinearity impairments. Classical Nonlinear Impairments Compensation (NLC) techniques are widely used and exist on the basis of the approximate Nonlinear Schrodinger Equation (NLSE) solution, their use and requires excessive signal resources, and high-level knowledge accuracy. In addition, their parameterizations can be numerically unstable. Algorithms of Artificial Intelligence (AI) are utilized to determine and resolve the deficiencies by learning from the receiving information itself. To the best of our knowledge, this novel approach is implemented. Therefore, this article proposes a system nonlinearity and single-step compensation algorithm according to a Deep Neural Network (DNN) as a new alternative framework for future optical communications. So, we proposed to use the DNN to compensation the nonlinearity impairments in optical communication systems. The suggested DNN is accessible to higher-order QAM modulations with achieving greater gain in nonlinear impairments compensation compare to classical NLC techniques based on Digital Back Propagation (DBP). Its performance is evaluated experimentally on coherent 65536-bit sequence length with 25 Gbaud single polarization 4-16-64 QAM with 50 and 120 Gb/s back-to-back measurements through using pre-distort symbols at the transmitter for showing Q factor development after 5000 km standard single-mode fiber transmission link. The DNN's weights are to train data with the intrachannel cross-phase modulation (XPM) and self-phase modulation (SPM) that used as input features.

A low complexity nonlinearity impairment compensation scheme assisted by label propagation algorithm

In this paper, we firstly applied label propagation algorithm (LPA) to coherent optical communication system for nonlinear impairment compensation (NLC), which could exploit the relationship among constellation points to segment the community with only very small amount of label data to predict the label situation on most test data. The effectiveness of the proposed scheme was verified through 28 GBaud polarization division multiplexing (PDM)-16 quadrature amplitude modulation (QAM), PDM-32QAM and PDM-64QAM simulation system. By analyzing the simulation results, we obtained the best propagation coefficient α, which demonstrated that the proposed scheme could effectively make nonlinear decision on received symbols and compensate signal impairment caused by Kerr nonlinear effect and amplified spontaneous emission (ASE) noise, showing a strong robustness and generalization to variations of the transmission environment under different modulation formats, transmission distances, launch power and channel numbers. Then, the proposed scheme was further studied by 20 GBaud PDM-16QAM long-haul transmission experiments. The results demonstrated that the proposed scheme required no training process and exhibited optimistic compensation performance to the coherent optical communication system with nonlinear impairments. Finally, we analyzed computational complexity of the LPA-assisted NLC scheme in detail, which was O(m*N).

Mitigation of Nonlinear Distortions for a 100 Gb/s Radio-Over-Fiber-Based WDM Network

Next-generation cloud radio access networks (C-RANs) are anticipated to provide multi-Gbps data rate transmission and ultra-high bandwidth capacity, which is one of the key performance indicators for future mobile networks. The integral layout of fiber optics and radio network manages the capabilities of the C-RAN, but needs to be optimized in terms of cost, reliability and further scalibility. For C-RAN architectures, Radio over Fiber (RoF) transport-based fronthaul is a promising candidate but the associated issues of distortions due to nonlinear impairments (NLIs) from power amplifier, linear distortions (LDs) due to modulating lasers and high peak to average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals need to be addressed. This work investigates these performance limiting factors and presents a DSP receiver-based solution to mitigate the effects of NLIs, LDs and high PAPR. Simulations are performed by applying a various range of transmission input powers, different quadrature amplitude modulation (QAM) formats for the OFDM signal, optimized filtering at the receiver end and varying channel spacing among the optical WDM channels to analyze the performance of the proposed receiver under different conditions. The simulations and theoretical model of the proposed case studies verify that the presented solution for the RoF transport utilize less power, performs better for longer transmission distances, supports higher modulation formats and transports large number of WDM channels in the presence of NLIs and DLs as compared to the conventional RoF approach. With compensation of NLIs and LDs, transmission distance up to 10 km is investigated using 16 WDM channels with aggregate data rate of 100 Gb/s which shows that the proposed receiver can be used for future C-RAN fronthaul networks.

Compensation of Nonlinear Impairments Using Inverse Perturbation Theory With Reduced Complexity

We propose a modification of the conventional perturbation-based approach of fiber nonlinearity compensation that enables straight-forward implementation at the receiver and meets feasible complexity requirements. We have developed a model based on perturbation analysis of an inverse Manakov problem, where we use the received signal as the initial condition and solve Manakov equations in the reversed direction, effectively implementing a perturbative digital backward propagation enhanced by machine learning techniques. To determine model coefficients we employ machine learning methods using a training set of transmitted symbols. The proposed approach allowed us to achieve 0.5 dB and 0.2 dB $Q^2$ -factor improvement for 2000 km transmission of 11 × 256 Gbit/s DP-16QAM signal compared to chromatic dispersion equalization and one step per span two samples per symbol digital back-propagation technique, respectively. We quantify the trade-off between performance and complexity.

Field and lab experimental demonstration of nonlinear impairment compensation using neural networks

Fiber nonlinearity is one of the major limitations to the achievable capacity in long distance fiber optic transmission systems. Nonlinear impairments are determined by the signal pattern and the transmission system parameters. Deterministic algorithms based on approximating the nonlinear Schrodinger equation through digital back propagation, or a single step approach based on perturbation methods have been demonstrated, however, their implementation demands excessive signal processing resources, and accurate knowledge of the transmission system. A completely different approach uses machine learning algorithms to learn from the received data itself to figure out the nonlinear impairment. In this work, a single-step, system agnostic nonlinearity compensation algorithm based on a neural network is proposed to pre-distort symbols at transmitter side to demonstrate ~0.6 dB Q improvement after 2800 km standard single-mode fiber transmission using 32 Gbaud signal. Without prior knowledge of the transmission system, the neural network tensor weights are constructed from training data thanks to the intra-channel cross-phase modulation and intra-channel four-wave mixing triplets used as input features.

Impact of InterChannel Interference in gridless nyquist-wdm systems with and without nonlinear impairments compensation

&#x0D; &#x0D; &#x0D; &#x0D; This paper presents a characterization of interchannel interference (ICI) effects in gridless Nyquist-wdm systems due to two contributions, namely, overlapping among optical carriers and stimulation of nonlinear optical fiber impairments. ICI is assessed regarding bit error rate (BER) at 16 and 32 Gbaud, as a function of several system parameters. Nonlinear impairment compensation based on the digital back-propagation algorithm is implemented in the DSP-based coherent receiver. Results demonstrated that ICI due to channels overlapped has a higher impact concerning BER than nonlinear optical fiber impairments. Besides, the use of the back-propagation algorithm improves system performance, reducing up to 3 and 0.7 orders of magnitude of BER in QPSK and 16QAM cases, respectively. It means that this algorithm can minimize nonlinear effects under varying system parameters, but its performance is limited in sub-Nyquist cases.&#x0D; &#x0D; &#x0D; &#x0D;

Метод компенсации нелинейных искажений сигнала в волоконных системах связи на основе теории возмущений и машинного обучения

Метод компенсации нелинейных искажений сигнала в волоконных системах связи на основе теории возмущений и машинного обучения

Nonlinear impairment compensation for DFT-S OFDM signal transmission with directly modulated laser and direct detection

We experimentally demonstrate a 16-ary quadrature amplitude modulation (16QAM) DFT-spread optical orthogonal frequency division multiplexing (OFDM) transmission system utilizing a cost-effective directly modulated laser (DML) and direct detection. For 20-Gbaud 16QAM-OFDM signal, with the aid of nonlinear equalization (NLE) algorithm, we respectively provide 6.2-dB and 5.2-dB receiver sensitivity improvement under the hard-decision forward-error-correction (HD-FEC) threshold of 3.8×10−3 for the back-to-back (BTB) case and after transmission over 10-km standard single mode fiber (SSMF) case, related to only adopt post-equalization scheme. To our knowledge, this is the first time to use dynamic nonlinear equalizer (NLE) based on the summation of the square of the difference between samples in one IM/DD OFDM system with DML to mitigate nonlinear distortion.

Digital compensation of cross-phase modulation distortions using perturbation technique for dispersion-managed fiber-optic systems

A digital compensation scheme based on a perturbation theory for mitigation of cross-phase modulation (XPM) distortions is developed for dispersion-managed fiber-optic communication systems. It is a receiver-side scheme that uses a hard-decision unit to estimate data for the calculation of XPM fields using the perturbation technique. The intra-channel nonlinear distortions are removed by intra-channel digital backward propagation (DBP) based on split-step Fourier scheme before the hard-decision unit. The perturbation technique is shown to be effective in mitigating XPM distortions. However, wrong estimations in the hard-decision unit result in performance degradation. A hard-decision correction method is proposed to correct the wrong estimations. Numerical simulations show that the hybrid compensation scheme with DBP for dispersion and intra-channel nonlinear impairments compensation and the perturbation technique for XPM compensation brings up to 3.7 dBQ and 1.7 dBQ improvements as compared with the schemes of linear compensation only and intra-channel DBP, respectively. The perturbation technique for XPM compensation requires only one-stage (or two-stage when hard-decision correction is applied) compensation and symbol-rate signal processing.

Nonlinear compensation and crosstalk suppression for 4 × 1608Gb/s WDM PDM-QPSK signal with heterodyne detection

We experimentally investigate digital intra-channel nonlinear impairment compensation and inter-channel crosstalk suppression for 4 × 160.8-Gb/s wavelength division multiplexing (WDM) polarization division multiplexing quadrature phase shift keying (PDM-QPSK) transmission over 1300-km single-mode fiber-28 (SMF-28) on a 50-GHz grid with the spectral efficiency of 3.21b/s/Hz, adopting simplified heterodyne coherent detection. By using nonlinear compensation based on DBP with crosstalk suppression based on post filter and maximum likelihood sequence estimation (PF&MLSE), the BER has been improved from 1.0 × 10(-3) to 3.5 × 10(-4) for 4 × 160.8Gb/s WDM PDM-QPSK with heterodyne detection after 1300km SMF-28 transmission.

Nonlinear impairment compensation using expectation maximization for dispersion managed and unmanaged PDM 16-QAM transmission

In this paper, we show numerically and experimentally that expectation maximization (EM) algorithm is a powerful tool in combating system impairments such as fibre nonlinearities, inphase and quadrature (I/Q) modulator imperfections and laser linewidth. The EM algorithm is an iterative algorithm that can be used to compensate for the impairments which have an imprint on a signal constellation, i.e. rotation and distortion of the constellation points. The EM is especially effective for combating non-linear phase noise (NLPN). It is because NLPN severely distorts the signal constellation and this can be tracked by the EM. The gain in the nonlinear system tolerance for the system under consideration is shown to be dependent on the transmission scenario. We show experimentally that for a dispersion managed polarization multiplexed 16-QAM system at 14 Gbaud a gain in the nonlinear system tolerance of up to 3 dB can be obtained. For, a dispersion unmanaged system this gain reduces to 0.5 dB.

Long-haul DWDM transmission systems employing optical phase conjugation

In this paper, we review the recent progress in transmission experiments by employing optical phase conjugation (OPC) for the compensation of chromatic dispersion and nonlinear impairments. OPC is realized with difference frequency generation (DFG) in a periodically poled lithium-niobate (PPLN) waveguide, for transparent wavelength-division multiplexed (WDM) operation with high conversion efficiency. We discuss extensively the principle behind optical phase conjugation and the realization of a polarization independent OPC subsystem. Using OPC for chromatic dispersion compensation WDM 40-Gb/s long-haul transmission is described. As well, transmission employing both mixed data rates and mixed modulation formats is discussed. No significant nonlinear impairments are observed from the nonperiodic dispersion map used in these experiments. The compensation of intrachannel nonlinear impairments by OPC is described for WDM carrier-suppressed return-to-zero (CSRZ) transmission. In this experiment, a 50% increase in transmission reach is obtained by adding an OPC unit to a transmission line using dispersion compensating fiber (DCF) for dispersion compensation. Furthermore, the compensation of impairments due to nonlinear phase noise is reviewed. An in-depth analysis is conducted on what performance improvement is to be expected for various OPC configurations and a proof-of-principle experiment is described showing over 4-dB improvement in Q-factor due to compensation of nonlinear impairments resulting from nonlinear phase noise. Finally, an ultralong-haul WDM transmission of 22times20-Gb/s return-to-zero differential quadrature phase-shift keying (RZ-DQPSK) is discussed showing that OPC can compensate for chromatic dispersion, as well as self-phase modulation (SPM) induced nonlinear impairments, such as nonlinear phase noise. Compared to a "conventional" transmission link using DCF for dispersion compensation, a 44% increase in transmission reach is obtained when OPC is employed. In this experiment, we show the feasibility of using only one polarization-independent PPLN subsystem to compensate for an accumulated chromatic dispersion of over 160 000 ps/nm