Fiber Nonlinearity Compensation Research Articles

Hybrid optical-electronic compensation of fiber nonlinearity for long-haul coherent optical transmission

Abstract From the concepts of the dispersion-folded digital backward propagation (DBP) and optical phase conjugation (OPC), a hybrid optical-electronic nonlinearity-compensation scheme is proposed to enhance the system performance of the dispersion-managed transmission. The computational complexity of the proposed scheme, compared with that of the conventional DBP method, is reduced significantly while the performance penalty is negligible. The compensation efficiency of the proposed scheme has been validated in a 5 (and 9)-channel PM-16QAM system at 256 Gbit/s.

Fast fiber nonlinearity compensation method for PDM coherent optical transmission systems based on the Fourier neural operator.

Fiber nonlinearity compensation (NLC) is likely to become an indispensable component of coherent optical transmission systems for extending the transmission reach and increasing capacity per fiber. In this work, we introduce what we believe to be a novel fast black-box neural network model based on the Fourier neural operator (FNO) to compensate for the chromatic dispersion (CD) and nonlinearity simultaneously. The feasibility of the proposed approach is demonstrated in uniformly distributed as well as probabilistically-shaped 32GBaud 16/32/64-ary quadrature amplitude modulation (16/32/64QAM) polarization-division-multiplexed (PDM) coherent optical communication systems. The experimental results demonstrate that about 0.31 dB Q-factor improvement is achieved compared to traditional digital back-propagation (DBP) with 5 steps per span for PDM-16QAM signals after 1600 km standard single-mode fiber (SSMF) transmission at the optimal launched power of 4 dBm. While, the time consumption is reduced from 6.04 seconds to 1.69 seconds using a central processing unit (CPU), and from 1.54 seconds to only 0.03 seconds using a graphic processing unit (GPU), respectively. This scheme also reveals noticeable generalization ability in terms of launched power and modulation format.

Joint Fiber Nonlinearity Mitigation and Compensation for Digital Sub-carrier Multiplexing System

Joint Fiber Nonlinearity Mitigation and Compensation for Digital Sub-carrier Multiplexing System

Intelligent and adaptive intra-channel and inter-channel fiber nonlinearity compensation in coherent optical transmission systems.

Fiber nonlinearity mitigation is a crucial technology for extending transmission reach and increasing channel capacity in high-baud rate wavelength division multiplexing (WDM) systems. In this work, we propose a novel, to the best of our knowledge, architecture that combines learned modified digital back-propagation (L-MDBP) to compensate for intra-channel nonlinearity and a two-stage decision-directed least mean square (DDLMS) adaptive equalizer to mitigate inter-channel nonlinearity. By leveraging globally optimized model parameters and adaptive channel estimation, the proposed scheme achieves superior performance and lower computation complexity compared with conventional DBP. Specifically, in an 8 × 64 Gbaud 16-ary quadrature amplitude modulation (16QAM) experimental system over 1600 km of standard single-mode fiber (SSMF), our approach shows a 0.30-dB Q2-factor improvement and a complexity reduction of 82.3% compared with DBP with 8 steps per span (SPS). Furthermore, we enhance the adaptability of the architecture by introducing an online transfer learning (TL) technique, which requires only 2% of initial training epochs.

Neural network architectures for optical channel nonlinear compensation in digital subcarrier multiplexing systems.

In this work, we propose to use various artificial neural network (ANN) structures for modeling and compensation of intra- and inter-subcarrier fiber nonlinear interference in digital subcarrier multiplexing (DSCM) optical transmission systems. We perform nonlinear channel equalization by employing different ANN cores including convolutional neural networks (CNN) and long short-term memory (LSTM) layers. First, we develop a fiber nonlinearity compensation for DSCM systems based on a fully-connected network across all subcarriers. In subsequent steps, and borrowing from the perturbation analysis of fiber nonlinearity, we gradually upgrade proposed designs towards modular structures with better performance-complexity advantages. Our study shows that putting proper macro structures in design of ANN nonlinear equalizers in DSCM systems can be crucial in development of practical solutions for future generations of coherent optical transceivers.

Joint PMD Tracking and Nonlinearity Compensation With Deep Neural Networks

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

Design of fully interpretable neural networks for digital coherent demodulation.

In this paper, we propose a digital coherent demodulation architecture using fully interpretable deep neural networks (NNs). We show that all the conventional coherent digital signal processing (DSP) is deeply unfolded into a well-structured NN so that the established training algorithms in machine learning can be applied. In contrast to adding or replacing certain algorithms of existing DSP in coherent receivers, we replace all the coherent demodulation algorithms with a fully interpretable NN (FINN), making the whole NN interpretable. The FINN is modular and flexible to add or drop modules, including chromatic dispersion compensation (CDC), the digital back-propagation (DBP) algorithm for fiber nonlinearity compensation, carrier recovery and residual impairments. The resulted FINN can be quickly initialized by straightforwardly referring to the conventional DSP, and can also enjoy further performance enhancement in the nonlinear fiber transmissions by NN. We conduct a 132-Gb/s polarization multiplexed (PM)-16QAM transmission experiment over 600-km standard single mode fiber. The experimental results show that without fiber nonlinearity compensation, FINN-CDC obtains less than 0.06-dB SNR gain than chromatic dispersion compensation (CDC). However, with fiber nonlinearity compensation, 2-steps per span FINN-DBP (FINN-2sps-DBP) and FINN-1sps-DBP bring about 0.59-dB and 0.53-dB SNR improvement compared with the conventional 2sps-DBP and 1sps-DBP, respectively.

Low-Complexity Triplet-Correlative Perturbative Fiber Nonlinearity Compensation for Long-Haul Optical Transmission

In this paper, we propose a triplet-correlative perturbative nonlinearity compensation (TC-PNC) scheme to compensate for intra-channel fiber nonlinear impairments. The complexity of TC-PNC is much lower than both of the conventional perturbative nonlinearity compensation (PNC) and degenerate PNC (DPNC), while the compensation performance of TC-PNC is much better than DPNC and is slightly worse than PNC. Compared to PNC and DPNC, the implementation complexity of TC-PNC is reduced by 94.73% and 22.53%, respectively. The compensation performance is evaluated by both simulations and experiments. In simulations with a transmission distance of 2000 km for 70 Gbaud dual-polarization 16-ary quadrature amplitude modulation (16QAM) signals, the signal-to-noise ratio (SNR) gains of TC-PNC are 0.3 dB and 0.77 dB compared to DPNC and the uncompensated case, respectively. In experiments for 30 Gbaud dual-polarization probabilistically shaped 16QAM (PS-16QAM) signals with a transmission distance of 432 km, the effectiveness of TC-PNC is validated by comparing the performance relative to PNC and DPNC.

Advanced Digital Signal Processing and Variable-Rate Coding for Unrepeatered Optical Transmission

In this paper, we evaluate the selective combination of algorithms for fiber nonlinearity compensation, transceiver impairments mitigation and variable-rate coding in unrepeatered optical transmission. A post-emphasis filter and a two-stage 4×4 multiple-input and multiple-output equalizer compensate the impact of bandwidth limitations and in-phase and quadrature skew. Nonlinear compensation is accomplished by a fast-converging adaptive digital back-propagation algorithm and maximum likelihood sequence estimation. Forward error correction is provided by a variable-rate spatially-coupled low-density parity-check code. The performance and complexity of the proposed digital subsystems are experimentally evaluated by the unrepeatered wavelength division multiplexing transmission of 17×200-Gb/s (DP-16QAM 32-GBd) channels over 350-km of large effective area and low-loss single-mode fibers. The experimental results for different combinations of algorithms elucidate the trade-off of complexity and performance in unrepeatered optical transmission.

Inverse regular perturbation with ML-assisted phasor correction for fiber nonlinearity compensation.

We improve an inverse regular perturbation (RP) model using a machine learning (ML) technique. The proposed learned RP (LRP) model jointly optimizes step-size, gain and phase rotation for individual RP branches. We demonstrate that the proposed LRP can outperform the corresponding learned digital back-propagation (DBP) method based on a split-step Fourier method (SSFM), with up to 0.75 dB gain in a 800 km standard single mode fiber link. Our LRP also allows a fractional step-per-span (SPS) modeling to reduce complexity while maintaining superior performance over a 1-SPS SSFM-DBP.

A Photonics-Inspired Compact Network: Toward Real-Time AI Processing in Communication Systems

Machine learning methods are ubiquitous in communication systems and have proven powerful for applications including radio-frequency (RF) fingerprinting, automatic modulation classification, and signal recovery in communication systems. However, the high throughput requirement of a communication link makes AI models difficult to implement in real-time on edge devices. In this work, we address this issue by improving both the algorithm and hardware to target real-time AI processing in communication systems. For algorithm development, we propose the first compact deep network consisting of a silicon photonic recurrent neural network model in combination with a simplified convolutional neural network classifier to identify RF emitters by their random transmissions. Our model achieves 96.32% classification accuracy over a set of 30 identical ZigBee devices when using 50 times fewer training parameters than an existing state-of-the-art CNN classifier (Merchant et al., 2018). Thanks to the large reduction in network size, we emulate the system using a small-scale FPGA board, the PYNQ-Z1, and demonstrate real-time RF fingerprinting with 0.219 ms latency. In addition, for hardware implementation, we further demonstrate a fully-integrated silicon photonic neural network for fiber nonlinearity compensation (Huang et al., 2021), which improves the received signal by 0.60 dB.

Hybrid-word-length quantization scheme for implement-efficient perturbation-based fiber nonlinearity compensation

A hybrid-word-length quantization scheme for the perturbation-based fiber nonlinearity compensation is proposed in this paper. The key feature of the proposed scheme is quantizing small-absolute-value coefficients with aggressive single-bit word length and large-absolute-value coefficients with multiple-bit word length. A significant complexity reduction can be obtained because of the simplified architecture of the single-bit multiplier. The proposed scheme was investigated in both simulation and experiment. Results show that the hardware complexity was reduced by approximately an order of magnitude compared with the uniform quantization scheme when the performance degradation was 0.2 dB, which validated the efficiency of the proposed scheme.

Fiber Nonlinearity Compensation: DBP Versus Link-Optimized OPC in Coherent Transmission

In this letter, we numerically compare the system performance of nonlinearity-compensated transmission based on digital back-propagation (DBP) and optical phase conjugation (OPC) technique in coherent transmission with lumped erbium doped fiber amplifiers (EDFAs). The tested transmission for DBP is a conventional dispersion-managed link, while it is an optimized design, the so-called dispersion inversion link for OPC-based system. Both of them have the same amount and type of fibers, and thus the same transmission reach. The numerical results show that DBP-aided systems have better performance for a shorter transmission reach while OPC technique presents its performance advantage when the transmission reach is increased. For a given transmission distance, the performance of OPC systems can further be improved by introducing additional OPCs. Results of 3840-km (<inline-formula> <tex-math notation="LaTeX">$48\times 80$ </tex-math></inline-formula>km) dispersion-managed transmission show that only mid-link OPC is enough to get similar performance with full-field DBP. By employing 6-OPCs in the links, the SNR of OPC-based system outperforms DBP by up to 1.9dB, while this SNR advantage will increase to 3dB after 5760-km (<inline-formula> <tex-math notation="LaTeX">$72\times 80$ </tex-math></inline-formula>km) transmission.

Distributed Raman Amplification for Fiber Nonlinearity Compensation in a Mid-Link Optical Phase Conjugation System.

In this paper, we review different designs of distributed Raman amplifiers which have been proposed to minimize the signal power profile asymmetry in mid-link optical phase conjugation systems. We demonstrate how the symmetrical signal power profiles along the fiber can be achieved using various distributed Raman amplification techniques in the single-span and more realistic multi-span circumstances. In addition, we show the theoretically predicted results of the Kerr nonlinear product reduction with different Raman techniques in mid-link optical phase conjugator systems, and then in-line/long-haul transmission performance using numerical simulations.

A Fiber Nonlinearity Compensation Scheme With Complex-Valued Dimension-Reduced Neural Network

A fiber nonlinearity compensation scheme based on a complex-valued dimension-reduced neural network is proposed. The proposed scheme performs all calculations in complex values and employs a dimension-reduced triplet feature vector to reduce the size of the input layer. Simulation and experiment results show that the proposed neural network needed only 20% of computational complexity to reach the saturated performance gain of the real-valued triplet-input neural network, and had a similar saturated gain to the one-step-per-span digital backpropagation. In addition, the proposed scheme was 1.7 dB more robust to the noise from training data and required less bit precision for quantizing trained weights, compared with the real-valued triplet-input neural network.

Combined Neural Network and Adaptive DSP Training for Long-Haul Optical Communications

Machine Learning (ML) algorithms have shown to complement standard digital signal processing (DSP) tools in mitigating fiber nonlinearity and improving long-haul transmission performance. However, dynamic transmission impairments such as polarization effects and carrier phase noise corrupt the training data and conventional cost functions for neural network (NN) training become unsuitable. Simple cascade of ML and standard adaptive DSP blocks will also result in suboptimal transmission performance or require impractical training methodologies in presence of such dynamic transmission impairments. We show how the adaptive DSP blocks can be treated as extra stateful NN layers and be combined with the main NN so that standard backpropagation-like training algorithms in ML can be applied. In this case, the adaptive filters are viewed as NN states which are updated in the forward pass of the backpropagation. We study the combined training of linear and nonlinear parameters in the digital backpropagation (DBP) algorithm for fiber nonlinearity compensation (named generalized DBP (GDBP) hereafter), residual impairments, polarization effects, frequency offsets and carrier phase noise compensation filters as a single NN in a 7 × 288 Gb/s polarization multiplexed (PM)-16QAM transmission experiment over 1125 km. We derived the complete set of backpropagation-like gradients and state update equations for the static and dynamic parameters of the combined NN. We further proposed and open-sourced a JAX-based coding framework for their easy and practical implementation. GDBP is more generalized than other DBP variants proposed in literature and for a given total number of steps, GDBP is the first experimental demonstration of optimal single-channel DBP based-fiber nonlinearity compensation algorithm. In addition, for complexity constrained situations with shortened filter taps, GDBP enables a 1 dB performance improvement over other DBP variants.

A silicon photonic–electronic neural network for fibre nonlinearity compensation

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 solving fibre nonlinearity compensation of submarine optical fibre transmission systems. Our approach uses a photonic neural network based on wavelength-division multiplexing built on a CMOS-compatible silicon photonic platform. We show that the platform can be used to compensate optical fibre nonlinearities and improve the signal quality (Q)-factor in a 10,080 km submarine fibre communication system. The Q-factor improvement is comparable to that of a software-based neural network implemented on a 32-bit graphic processing unit-assisted workstation. Our reconfigurable photonic-electronic integrated neural network promises to address pressing challenges in high-speed intelligent signal processing.

Fiber nonlinearity compensation using optical phase conjugation in dispersion-managed coherent transmission systems

Abstract In the discretely amplified transmission systems with erbium-doped fiber amplifiers, the system performance of nonlinearity-compensated optical transmission based on pre-dispersed spectral inversion (PSI) is investigated numerically. We find that PSI offers more significant performance improvement in dispersion-managed (DM) links than that in non-dispersion-managed (noDM) links. On the other hand, the DM link is more sensitive to the span offset from the center of the transmission link than noDM link. The performance difference between DM and noDM links is 1 dB if the span offset equals four spans in 20 × 90 km nonlinear transmission. Furthermore, we show that for the dispersion-managed transmission, in order to obtain the best system performance, the amount of pre-dispersion of the PSI, should be optimized over different dispersion maps.

Review on nonlinearity effect in radio over fiber system and its mitigation

Abstract Modern communication generation for high data rate requirement is fifth generation. The fifth generation has many advantages like low delay, high spectrum availability, high reliability, low jitter, and more capacity. To combat with the high capacity and high data rate requirement, optical fiber helps in the backhaul of 5G network. When fiber is used as a mode of propagation, many nonlinearities arises. This nonlinearity effect in the optical fiber communication is one of the most undesirable phenomena for the modern communication system which results in harmonic distortion, intermodulation distortion, phase distortion, and adjacent channel interference, etc. In most fiber optic communication systems, the major fiber nonlinear effect is the Kerr nonlinearity and Scattering effect that produced due to the variation of refractive index due to signal intensity. To minimize the effect of nonlinear distortion, some techniques are used which considerably improve the transmission capacity by reducing or compensating the effect of nonlinear distortion along with minimal infrastructure modifications and minimum cost for implementation. To overcome the effect of nonlinearity, fiber nonlinearity mitigation techniques are preferred to achieve the significant performance gains. Mitigation techniques can be implemented to improve and optimize the performance of optical communication network. In this paper, a brief description of the fiber nonlinearity effect and a review of various fiber nonlinearity compensation techniques are described.

Interchannel nonlinearity compensation using a perturbative machine learning technique

We propose an extension of the perturbation-based approach for fiber nonlinearity compensation that is capable of mitigating both intra- and interchannel nonlinearity with a moderate increase in implementation complexity. Being guided by inverse perturbation theory we develop a straight-forward modification of the conventional model that takes into account nonlinear interactions between symbols from neighboring spectral channels. We employ machine learning techniques such as the normal equation model with regularization for joint identification of perturbation coefficients that are responsible for intra- and interchannel interactions. We investigate the application of the proposed approach for compensating nonlinear signal distortions in a 1200 km fiber-optic 3 x 400 Gbit/s WDM DP-64QAM transmission link. It was shown up to 0.83 dB and 0.51 dB Q2-factor improvement compared to chromatic dispersion equalization and one step per span two samples per symbol digital back-propagation technique, respectively. We estimate the implementation complexity of the approach.