Deep Learning-Aided Perturbation Model-Based Fiber Nonlinearity Compensation

Fiber nonlinearity effects cap achievable rates and ranges in long-haul optical fiber communication links. Conventional nonlinearity compensation methods, such as perturbation theory-based nonlinearity compensation (PB-NLC), attempt to compensate for the nonlinearity by approximating analytical solutions to the signal propagation over optical fibers. However, their practical usability is limited by model mismatch and the immense computational complexity associated with the analytical computation of perturbation triplets and the nonlinearity distortion field. Recently, machine learning techniques have been used to optimise parameters of PB-based approaches, which traditionally have been determined analytically from physical models. It has been claimed in the literature that the learned PB-NLC approaches have improved performance and/or reduced computational complexity over their non-learned counterparts. In this paper, we first revisit the acclaimed benefits of the learned PB-NLC approaches by carefully carrying out a comprehensive performance-complexity analysis utilizing state-of-the-art complexity reduction methods. Interestingly, our results show that least squares-based PB-NLC with clustering quantization has the best performance-complexity trade-off among the learned PB-NLC approaches. Second, we advance the state-of-the-art of learned PB-NLC by proposing and designing a fully learned structure. We apply a bi-directional recurrent neural network for learning perturbation triplets that are alike those obtained from the analytical computation and are used as input features for the neural network to estimate the nonlinearity distortion field. Finally, we demonstrate through numerical simulations that our proposed fully learned approach achieves an improved performance-complexity trade-off compared to the existing learned and non-learned PB-NLC techniques

Second-order perturbation theory-based digital predistortion for fiber nonlinearity compensation

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 analysis is performed to derive the SO perturbative field for a Pol-Mux optical transmission system. Following that, we investigate a few simplifying assumptions to reduce the implementation complexity of the SO-PB-NLC technique. The numerical simulations for a single-channel system show that the SO-PB-NLC technique provides an improved bit-error-rate performance and increases the transmission reach, in comparison with the FO-PB-NLC technique. The complexity analysis demonstrates that the proposed SO-PB-NLC technique has a reduced computational complexity when compared to the digital back-propagation with one step per span

Learning for Perturbation-Based Fiber Nonlinearity Compensation

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

Parallel Neural Network Structures for Signal-to-Noise Ratio Estimation in Optical Fiber Communication Systems

This paper proposes two novel neural network (NN) structures to estimate long-term steady linear and nonlinear signal-to-noise ratio (SNR) components in optical fiber communication systems. The first proposed structure is a parallel NNbased (ParNN) estimator, which estimates each SNR component using a different NN structure and input feature set. A combination of gated recurrent unit and dense layers is used to estimate the linear SNR component. On the other hand, the nonlinear SNR component is estimated using a combination of convolutional layer with dense layer. The proposed input features of the ParNN estimator are generated solely from the received signal without knowledge of the transmitted signal. These features are formed of the lower quartile, upper quartile, and entropy, which can accurately characterize the behavior of the SNR components by measuring the received signal spread and uncertainty. For further improvement of the ParNN estimator, an additional stage is added to form the proposed enhanced ParNN (EParNN) estimator. This additional stage consists of two feedforward NNs (FFNNs), each with a single dense layer, where the first FFNN is used to estimate the linear SNR component and the second one estimates the nonlinear SNR component. The input of this additional stage is a combination of the input features and output of the ParNN estimator. The computational complexity is derived for the proposed estimators. The training and testing dataset is built from 16-ary quadrature amplitude modulation of a dual polarization on a wide range of standard single-mode fiber system configurations, e.g., number of wavelength division multiplexing channels, optical launch power, and number of spans. Numerical results demonstrate that the proposed ParNN estimator achieves better SNR estimation accuracy with comparable computational complexity compared to the most efficient work in the literature. The proposed ParNN estimator can independently estimate each SNR component, in which the complexity per SNR component is reduced.</p

Experimental Evaluation of Hybrid Fibre−Wireless System for 5G Networks

This article describes a novel experimental study considering a multiband fibre–wireless system for constructing the transport network for fifth-generation (5G) networks. This study describes the development and testing of a 5G new radio (NR) multi-input multi-output (MIMO) hybrid fibre–wireless (FiWi) system for enhanced mobile broadband (eMBB) using digital pre-distortion (DPD). Analog radio over fibre (A-RoF) technology was used to create the optical fronthaul (OFH) that includes a 3 GHz supercell in a long-range scenario as well as a femtocell scenario using the 20 GHz band. As a proof of concept, a Mach Zehnder modulator with two independent radio frequency waveforms modifies a 1310 nm optical carrier using a distributed feedback laser across 10 km of conventional standard single-mode fibre. It may be inferred that a hybrid FiWi-based MIMO-enabled 5G NR system based on OFH could be a strong competitor for future mobile haul applications. Moreover, a convolutional neural network (CNN)-based DPD is used to improve the performance of the link. The error vector magnitude (EVM) performance for 5G NR bands is predicted to fulfil the Third Generation Partnership Project’s (3GPP) Release 17 standards

Comparison of Short Blocklength Sphere Shaping and Nonlinearity Compensation in WDM Systems

In optical communication systems, short blocklength probabilistic enumerative sphere shaping (ESS) provides both linear shaping gain and nonlinear tolerance. In this work, we investigate the performance and complexity of ESS in comparison with fiber nonlinearity compensation via digital back propagation (DBP) with different steps per span. We evaluate the impact of the shaping blocklength in terms of nonlinear tolerance and also consider the case of ESS with a Volterra-based nonlinear equalizer (VNLE), which provides lower complexity than DBP. In single-channel transmission, ESS with VNLE achieves similar performance in terms of finite length bit-metric decoding rate to uniform signaling with one step per span DBP. In the context of a dense wavelength-division multiplexing (WDM) transmission system, we show that ESS outperforms uniform signaling with DBP for different step sizes