The modeling of optical wave propagation in optical fiber is a task of fast and accurate solving the nonlinear Schrödinger equation (NLSE), and can enable the optical system design, digital signal processing verification and fast waveform calculation. Traditional waveform modeling of full-time and full-frequency information is the split-step Fourier method (SSFM), which has long been regarded as challenging in long-haul wavelength division multiplexing (WDM) optical fiber communication systems because it is extremely time-consuming. Here we propose a linear-nonlinear feature decoupling distributed (FDD) waveform modeling scheme to model long-haul WDM fiber channel, where the channel linear effects are modelled by the NLSE-derived model-driven methods and the nonlinear effects are modelled by the data-driven deep learning methods. Meanwhile, the proposed scheme only focuses on one-span fiber distance fitting, and then recursively transmits the model to achieve the required transmission distance. The proposed modeling scheme is demonstrated to have high accuracy, high computing speeds, and robust generalization abilities for different optical launch powers, modulation formats, channel numbers and transmission distances. The total running time of FDD waveform modeling scheme for 41-channel 1040-km fiber transmission is only 3 minutes versus more than 2 hours using SSFM for each input condition, which achieves a 98% reduction in computing time. Considering the multi-round optimization by adjusting system parameters, the complexity reduction is significant. The results represent a remarkable improvement in nonlinear fiber modeling and open up novel perspectives for solution of NLSE-like partial differential equations and optical fiber physics problems.
Nokia（诺基亚）；Aston University（阿斯顿大学）；Delft University of Technology（代尔夫特理工大学）
We present a novel end-to-end autoencoder-based learning for coherent optical communications using a "parallelizable" perturbative channel model. We jointly optimized constellation shaping and nonlinear pre-emphasis achieving mutual information gain of 0.18 bits/sym./pol. simulating 64 GBd dual-polarization single-channel transmission over 30x80 km G.652 SMF link with EDFAs.
Employing massively distributed antennas brings radio access points (RAPs) closer to users, thus enables aggressive spectrum reuse that can bridge gaps between the scarce spectrum resource and extremely high connection densities in future wireless systems. Examples include cloud radio access network (C-RAN), ultra-dense network (UDN), and cell-free massive multiple-input multiple-output (MIMO) systems. These systems are usually designed in the form of fiber-wireless communications (FWC), where distributed antennas or RAPs are connected to a central unit (CU) through optical front-hauls. A larg…
We report on the realization of a long-haul radio frequency (RF) transfer scheme by using multiple-access relay stations (MARSs). The proposed scheme with independent link noise compensation for each fiber sub-link effectively solves the limitation of compensation bandwidth for long-haul transfer. The MARS can have the capability to share the same modulated optical signal for the front and rear fiber sub-links, simplifying the configuration at the repeater station and enabling the transfer system to have the multiple-access capability. At the same time, we for the first time theoretically mode…
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
The integrable nonlinear Schrödinger equation (NLSE) is a fundamental model of nonlinear science which also has important consequences in engineering. The powerful framework of the periodic inverse scattering transform (IST) provides a description of the nonlinear phenomena modulational instability and Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence in terms of exact solutions. It associates the complex nonlinear dynamics with invariant nonlinear spectral degrees of freedom that may be used to encode information. While optical fiber is an ideal testing ground of its predictions, maintaining integra…
Long-range Rayleigh-based Distributed Acoustic Sensing (DAS) systems are often limited in their sensitivity and bandwidth. The former limitation is a result of the low backscattered power and poor \textit{dynamic-strain to optical-phase} transduction efficiency. The latter constraint results from the trade-off between range and scan-rate which limits the sampling interval to the longest delay in the sensing fiber. Quasi-DAS (Q-DAS) can yield enhanced sensitivity but may still suffer from low backscattered power and low scan-rate for long-haul, many-sensor, systems. In this work we study the us…
A novel ultra-long distributed vibration sensing (DVS) system using forward transmission and coherent detection is proposed and experimentally demonstrated. In the proposed scheme, a pair of multi-span optical fibers are deployed for sensing, and a loop-back configuration is used by connecting the two fibers at the far end. The homodyne coherent detection is used to retrieve the phase and state-of-polarization (SOP) fluctuations caused by a vibration while the localization of the vibration is realized by tracking the phase changes along the two fibers. The proposed scheme has the advantage of …
Wavelength division multiplex (WDM) system with on / off keying (OOK) modulation and direct detection (DD) is generally simple to implement, less expensive and energy efficient. The determination of the possible design capacity limit, in terms of the bit rate-distance product in WDM-OOK-DD systems is therefore crucial, considering transmitter / receiver simplicity, as well as energy and cost efficiency. A 32-channel wavelength division multiplex system is designed and simulated over 1000 km fiber length using Optsim commercial simulation software. The standard channel spacing of 0.4 nm was use…
We report the experimental observation of a novel transmission phenomenon in optical long-haul communication systems. Un-polarized ASE depolarizes via nonlinear fiber interactions a cw laser light during their co-propagation which leads to small but measurable ultra-fast polarization state fluctuations at the fiber output. We provide a phenomenological approach and a theory that qualitatively corroborates our experimental results. One of our major findings suggests that the applicability of the often used Manakov equation needs to be scrutinized for highly accurate studies of nonlinear polariz…
Simple fiber optic communication systems can be implemented using energy modulation of isolated time-limited pulses. Fundamental solitons are one possible solution for such pulses which offer a fundamental advantage: their shape is not affected by fiber disperison and nonlinearity. Furthermore, a simple energy detector can be used at the receiver to detect the transmitted information. However, systems based on energy modulation of solitons are not competitive in terms of data rates. This is partly due to the fact that the effective time duration of a soliton depends on its chosen amplitude. In…
Analytical Model of Nonlinear Fiber Propagation for General Dual-Polarization Four-Dimensional Modulation Format
Hefei University of Technology（合肥工业大学）；Intelligent Interconnected Systems Laboratory of Anhui Province（安徽省智能互联系统实验室）；Eindhoven University of Technology（埃因霍温理工大学）
We rederive from first principles and generalize the theoretical framework of the nonlinear Gaussian noise model to the case of coherent optical systems with multiple fiber types per span and ideal Nyquist spectra. We focus on the accurate numerical evaluation of the integral for the nonlinear noise variance for hybrid fiber spans. This task consists in addressing four computational aspects: (i) Adopting a novel transformation of variables (other than using hyperbolic coordinates) that changes the integrand to a more appropriate form for numerical quadrature; (ii) Evaluating analytically the i…
In this paper we carry out a joint optimization of probabilistic (PS) and geometric shaping (GS) for four-dimensional (4D) modulation formats in long-haul coherent wavelength division multiplexed (WDM) optical fiber communications using an auto-encoder framework. We propose a 4D 10 bits/symbol constellation which we obtained via end-to-end deep learning over the split-step Fourier model of the fiber channel. The constellation achieved 13.6% reach increase at a data rate of approximately 400 Gbits/second in comparison to the ubiquitously employed polarization multiplexed 32-QAM format at a forw…
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…
In this work, a new data-driven fiber channel modeling method, generative adversarial network (GAN) is investigated to learn the distribution of fiber channel transfer function. Our investigation focuses on joint channel effects of attenuation, chromic dispersion, self-phase modulation (SPM), and amplified spontaneous emission (ASE) noise. To achieve the success of GAN for channel modeling, we modify the loss function, design the condition vector of input and address the mode collapse for the long-haul transmission. The effective architecture, parameters, and training skills of GAN are also di…
In optical fiber communication, system identification (SI) for the nonlinear Schrödinger equation (NLSE) has long been studied mainly for fiber nonlinearity compensation (NLC). One recent line of inquiry to combine a behavioral-model approach like digital backpropagation (DBP) and a data-driven approach like neural network (NN). These works are aimed for more NLC gain; however, by directing our attention to the learned parameters in such a SI process, system status information, i.e., optical fiber parameters, will possibly be extracted. Here, we show that the model-based optimization and inter…
Distributed Feedback Laser plays a key role as a light source component in optical fiber communication systems ranging from metro, long-haul to submarine one thanks to its competitive features of superior narrow spectral width and wavelength cohesion. Characterizing such lasers via obtaining their electrical and spectral data and extracting their internal parameters therefore remains a critical task in designing and troubleshooting optical fiber systems. This paper presents first an agile framework for a rapid collection of laser data via automatic measurement and second an efficient approach …
In this work, we address the question of the adaptability of artificial neural networks (NNs) used for impairments mitigation in optical transmission systems. We demonstrate that by using well-developed techniques based on the concept of transfer learning, we can efficaciously retrain NN-based equalizers to adapt to the changes in the transmission system, using just a fraction (down to 1%) of the initial training data or epochs. We evaluate the capability of transfer learning to adapt the NN to changes in the launch power, modulation format, symbol rate, or even fiber plants (different fiber t…
Brillouin optical time domain analyzer (BOTDA) fiber sensors have shown strong capability in static long haul distributed temperature/strain sensing. However, in applications such as structural health monitoring and leakage detection, real-time measurement is quite necessary. The measurement time of temperature/strain in a BOTDA system includes data acquisition time and post-processing time. In this work, we propose to use hardware accelerated support vector regression (SVR) for the post-processing of the collected BOTDA data. Ideal Lorentzian curves under different temperatures with different…
The nonlinear Shannon capacity limit has been identified as the fundamental barrier to the maximum rate of transmitted information in optical communications. In long-haul high-bandwidth optical networks, this limit is mainly attributed to deterministic Kerr-induced fiber nonlinearities and from the interaction of amplified spontaneous emission noise from cascaded optical amplifiers with fiber nonlinearity: the stochastic parametric noise amplification. Unlike earlier impractical approaches that compensate solely deterministic nonlinearities, here we demonstrate a novel electronic-based deep ne…
Increased traffic demands globally and in particular in short-reach links in data centers will require optical communication systems to continue scaling at an accelerated pace. Nevertheless, energy constraints start to limit the bit rate that can be practically transmitted over optical systems both at the shortest distances in data centers and at the longest distances in ultra-long submarine links. Short-reach links in data centers face strict constraints on power consumption, size, and cost, which will demand low-power solutions that scale to bit rates beyond 100 Gbit/s per wavelength, while …
Optimizing modulation and detection strategies for a given channel is critical to maximize the throughput of a communication system. Such an optimization can be easily carried out analytically for channels that admit closed-form analytical models. However, this task becomes extremely challenging for nonlinear dispersive channels such as the optical fiber. End-to-end optimization through autoencoders (AEs) can be applied to define symbol-to-waveform (modulation) and waveform-to-symbol (detection) mappings, but so far it has been mainly shown for systems relying on approximate channel models. He…
First Single-Carrier Transmission at Net Data Rates of 1.6 Tb/s over 9075 km and 2.4 Tb/s over 1210 km Using 300 GBd Dual-Polarization Signals and Probabilistic Constellation Shaping
Conventional optical coherent receivers capture the full electrical field, including amplitude and phase, of a signal waveform by measuring its interference against a stable continuous-wave local oscillator (LO). In optical coherent communications, powerful digital signal processing (DSP) techniques operating on the full electrical field can effectively undo transmission impairments such as chromatic dispersion (CD), and polarization mode dispersion (PMD). Simpler direct detection techniques do not have access to the full electrical field and therefore lack the ability to compensate for these …
The nonlinear Fourier transform has the potential to overcome limits on performance and achievable data rates which arise in modern optical fiber communication systems when nonlinear interference is treated as noise. The periodic nonlinear Fourier transform (PNFT) has been much less investigated compared to its counterpart based on vanishing boundary conditions. In this paper, we design a first experiment based on the PNFT in which information is encoded in the invariant nonlinear main spectrum. To this end, we propose a method to construct a set of periodic waveforms each having the same fixe…
Coherent optical multi-carrier communications have recently dominated metro-regional and long-haul optical communications. However, the major obstacle of networks involving coherent multi-carrier signals such as coherent optical orthogonal frequency-division multiplexing (CO-OFDM) is the fiber-induced nonlinearity and the parametric noise amplification from cascaded optical amplifiers which results in significant nonlinear distortion among subcarriers. Here, we present the first nonlinear equalizer in optical communications using the traditional Density-Based Spatial Clustering of Applications…
The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission scheme inherently compatible with the nonlinear fiber is obtained. Despite potential advantages, the periodic NFT (PNFT) has been studied less compared to its counterpart based on vanishing boundary conditions, due to the mathematical complexity of the inverse transform. In this paper we extract the theory of the algebrogeometric integration method underlying the…
