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 of LSTM based receiver with respect to performance and complexity. The numerical results show that LSTM Neural Networks can be very efficient as post processors of optical receivers which classify data that have undergone non-linear impairments in fiber and provide superior performance compared to digital back propagation, especially in the multi-channel transmission scenario. The complexity analysis shows that LSTM becomes more complex as the number of hidden units and the channel memory increase can be less complex than DBP in long distances (> 1000 km).
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.
In this work we expand the possibilities of a known class of chaos-based coded modulation (CCM) systems to address the problem of high-power amplifier (HPA) nonlinearity. The hypothesis is that the CCM nonlinear nature can be exploited to counteract its effects on the system performance, avoiding the need of a predistorter. We propose an optimization method for the design of the CCM to prove this hypothesis. The results show that, for a given back-off level, a nonlinear mapping function for the chaos-based encoder and decoder can be designed to compensate the HPA effect on the error rate.
We show that short-length probabilistic shaping reduces nonlinear interference in optical fiber transmission. SNR improvements of up to 0.8 dB are obtained. The shaping gain vanishes when interleaving is employed and not undone before transmission.
We study the performance of gradient-descent optimization to estimate the coefficients of the discrete-time first-order regular perturbation (FRP). With respect to numerically computed coefficients, the optimized coefficients yield a model that (i) extends the FRP range of validity, and (ii) reduces the model's complexity.
Imperial College London（帝国理工学院）；Shanghai Jiao Tong University（上海交通大学）
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…
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).
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…
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…
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…
Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
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…
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…
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…
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.
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…
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 interplay of shaped signaling and fiber nonlinearities is reviewed in the asymptotic and finite-length regime. We present explanations and discuss implications of an optimum shaping length of just a few hundred symbols.
In this letter, we study the impact of nonlinear high power amplifier (HPA) on simultaneous wireless information and power transfer (SWIPT), for a point-to-point multiple-input multiple-output communication system. We derive the rate-energy (RE) region by taking into account the HPA nonlinearities and its associated memory effects. We show that HPA significantly degrades the achievable RE region, and a predistortion technique is investigated for compensation. The performance of the proposed predistortion scheme is evaluated in terms of RE region enhancement. Numerical results demonstrate that …
Nonlinearities can be introduced into communication systems by the physical components such as the power amplifier, or during signal propagation through a nonlinear channel. These nonlinearities can be compensated by a nonlinear equalizer at the receiver side. The nonlinear equalizer also operates on the additive noise, which can lead to noise enhancement. In this work we evaluate this trade-off between distortion reduction and noise-enhancement via nonlinear equalization techniques. We first, evaluate the trade-off between nonlinearity compensation and noise enhancement for the Volterra equal…
Chalmers University（查尔莫斯大学）；Duke University（杜克大学）；Eindhoven University of Technology（埃因霍温理工大学）
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.
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…
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…
University of West Attica（西阿提卡大学）；University of the Aegean（爱琴大学）
We investigate the complexity and performance of recurrent neural network (RNN) models as post-processing units for the compensation of fibre nonlinearities in digital coherent systems carrying polarization multiplexed 16-QAM and 32-QAM signals. We evaluate three bi-directional RNN models, namely the bi-LSTM, bi-GRU and bi-Vanilla-RNN and show that all of them are promising nonlinearity compensators especially in dispersion unmanaged systems. Our simulations show that during inference the three models provide similar compensation performance, therefore in real-life systems the simplest scheme …
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…
A Dual-Dip Heterogeneous LPFG Sensing System via Annealing under Bending with Temperature and Humidity Compensation
Fujian Medical University（福建医科大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Hainan Vocational University of Science and Technology（海南科技职业大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；Beijing University of Technology（北京工业大学）
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 …
Fiber-optical networks are a crucial telecommunication infrastructure in society. Wavelength division multiplexing allows for transmitting parallel data streams over the fiber bandwidth, and coherent detection enables the use of sophisticated modulation formats and electronic compensation of signal impairments. In the future, optical frequency combs may replace multiple lasers used for the different wavelength channels. We demonstrate two novel signal processing schemes that take advantage of the broadband phase coherence of optical frequency combs. This approach allows for a more efficient es…
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.
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 …
The effect of Kerr-induced optical fiber nonlinearities in C-band (5 THz) EDFA and C+L-band (12.5 THz) Raman-amplified optical communication systems has been studied considering the impact of third-order fiber dispersion. The performance of digital nonlinearity compensation with single channel and 250-GHz bandwidth in both EDFA and Raman amplified systems has been investigated, respectively. The achievable information rates (AIRs) and optimum code rates in each individual transmission channel have been evaluated for the DP-64QAM, the DP-256QAM and the DP-1024QAM modulation formats, both with a…
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…
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…
