Complex-Valued Neural Network Design for Mitigation of Signal Distortions in Optical Links

Freire, Pedro J.; Neskornuik, Vladislav; Napoli, Antonio; Spinnler, Bernhard; Costa, Nelson; Khanna, Ginni; Riccardi, E.; Prilepsky, Jaroslaw E.; Turitsyn, Sergei K.

doi:10.1109/jlt.2020.3042414

Cited by 53 publications

(44 citation statements)

References 34 publications

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“…the nonlinear transformation, but the possibility to denoise signal using NNs. We started with the WafeNet-type architecture 62 , which is effectively a deep CNN, and applied Bayesian optimization 66 to find the optimal set of hyperparameters. Initially, we set the task of optimizing the entire architecture, so the hyperparameters were not only the parameters of the layers but also their number.…”

Section: Discussionmentioning

confidence: 99%

Neural networks for computing the continuous nonlinear Fourier spectrum in focusing nonlinear Schrodinger equation: NFT-Net

Sedov

Freire

Seredin

et al. 2021

Preprint

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We combine the nonlinear Fourier transform (NFT) signal processing with machine learning methods for solving the direct spectral problem associated with the nonlinear Schrödinger equation. The latter is one of the core nonlinear science models emerging in a range of applications. Our focus is on the unexplored problem of computing the continuous nonlinear Fourier spectrum associated with decaying profiles, using a specially-structured deep neural network which we coined NFT-Net. The Bayesian optimisation is utilised to find the optimal neural network architecture. The benefits of using the NFT-Net as compared to the conventional numerical NFT methods becomes evident when we deal with noise-corrupted signals, where the neural networks-based processing results in effective noise suppression. This advantage becomes more pronounced when the noise level is sufficiently high, and we train the neural network on the noise-corrupted field profiles. The maximum restoration quality corresponds to the case where the signal-to-noise ratio of the training data coincides with that of the validation signals. Finally, we also demonstrate that the NFT b-coefficient important for optical communication applications can be recovered with high accuracy and denoised by the neural network with the same architecture.

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Section: Discussionmentioning

confidence: 99%

Neural networks for computing the continuous nonlinear Fourier spectrum in focusing nonlinear Schrodinger equation: NFT-Net

Sedov

Freire

Seredin

et al. 2021

Preprint

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“…In our current study, we use a similar structure as in [17] , where the NN model is made up of a bidirectional LSTM layer followed by a dense layer. Finally, we note that, in contrast to the previous studies where the grid search was executed to guess the optimal number of hidden unities and memory size, this paper uses the BO to identify the best-performing biLSTM structure [9].…”

Section: B Long Short-term Memory Nnsmentioning

confidence: 99%

“…In this section, we show the maximum achievable Qfactor for all equalizers without constraining the computational complexity. The Bayesian optimization (BO) tool, introduced in [9] for optical NN-based equalizers, was implemented to identify the optimum values of hyper-parameters for each NN topology, which provides the best Q-factor in the experimental test dataset. As it was recently shown, the BO renders superior performance compared to other types of search algorithms for machine learning hyperparameter tuning [57].…”

Section: B Optimized Nn-based Architecturesmentioning

confidence: 99%

“…We point out that the term "topology" in our research identifies the particular NN structure (architecture) with a specific fixed distribution of hyper-parameters. We emphasize that, in contrast to other similar investigations, we employ the Bayesian optimization procedure [9] for each NN type studied. This provides the optimal distribution of hyper-parameters pertaining to each NN type, such that we identify the best functioning regime (in terms of the performance delivered) for each architecture without complexity constraints.…”

Section: Introductionmentioning

confidence: 99%

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Performance Versus Complexity Study of Neural Network Equalizers in Coherent Optical Systems

Freire

Osadchuk

Spinnler

et al. 2021

J. Lightwave Technol.

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We present the results of the comparative performance-versus-complexity analysis for the several types of artificial neural networks (NNs) used for nonlinear channel equalization in coherent optical communication systems. The comparison is carried out using an experimental set-up with the transmission dominated by the Kerr nonlinearity and component imperfections. For the first time, we investigate the application to the channel equalization of the convolution layer (CNN) in combination with a bidirectional long short-term memory (biLSTM) layer and the design combining CNN with a multilayer perceptron. Their performance is compared with the one delivered by the previously proposed NN-based equalizers: one biLSTM layer, three-dense-layer perceptron, and the echo state network. Importantly, all architectures have been initially optimized by a Bayesian optimizer. First, we present the general expressions for the computational complexity associated with each NN type; these are given in terms of real multiplications per symbol. We demonstrate that in the experimental system considered, the convolutional layer coupled with the biLSTM (CNN+biLSTM) provides the largest Q-factor improvement compared to the reference linear chromatic dispersion compensation (2.9 dB improvement). Then, we examine the trade-off between the computational complexity and performance of all equalizers and demonstrate that the CNN+biLSTM is the best option when the computational complexity is not constrained, while when we restrict the complexity to some lower levels, the three-layer perceptron provides the best performance.

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“…Initially designed for digital radio communication, these schemes mostly consisted of training ANNs to learn the generalization of component/medium-induced distortions, which permitted the mitigation of impairments that cannot be analytically modeled. In the field of optical communications, the use of ML approaches has gained massive attention over the past decade, predominantly targeting tasks, such as fiber and transceiver nonlinearity mitigation [12], [22]- [24], but also extensively explored in optical performance monitoring techniques [25], [26] and network resource allocation strategies [27].…”

Section: Related Workmentioning

confidence: 99%

Bayesian Optimization for Nonlinear System Identification and Pre-Distortion in Cognitive Transmitters

Sena

Erkılınç

Dippon³

et al. 2021

J. Lightwave Technol.

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We present a digital signal processing (DSP) scheme that performs hyperparameter tuning (HT) via Bayesian optimization (BO) to autonomously optimize memory tap distribution of Volterra series and adapt parameters used in the synthetization of a digital pre-distortion (DPD) filter for optical transmitters. Besides providing a time-efficient technique, this work demonstrates that the self-adaptation of DPD hyperparameters to correct the component-induced nonlinear distortions as different driver amplifier (DA) gains, symbol rates and modulation formats are used, leads to an improvement in transmitter performance. The scheme has been validated in backto-back (b2b) experiments using dual-polarization (DP) 64 and 256 quadrature amplitude modulation (QAM) formats, and symbol rates of 64 and 80 GBd. For DP-64QAM at 64 GBd, it isshown that the DPD scheme reduces the required optical signalto-noise ratio (OSNR) at a bit error ratio of 10 -2 by 0.9 dB and 0.6 dB with respect to linear DPD and a heuristic nonlinear DPD approach, respectively. Moreover, we show that the proposed approach also reduces filter complexity by 75% in conjunction with the use of memory polynomials (MP), while achieving a similar performance to Volterra pre-distortion filters.

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Complex-Valued Neural Network Design for Mitigation of Signal Distortions in Optical Links

Abstract: We propose a convolutional-recurrent channel equalizer and experimentally demonstrate 1dB Q-factor improvement both in single-channel and 96×WDM, DP-16QAM transmission over 450km of TWC fiber. The new equalizer outperforms previous NN-based approaches and a 3-steps-per-span DBP.

Cited by 53 publications

References 34 publications

Neural networks for computing the continuous nonlinear Fourier spectrum in focusing nonlinear Schrodinger equation: NFT-Net

Neural networks for computing the continuous nonlinear Fourier spectrum in focusing nonlinear Schrodinger equation: NFT-Net

Performance Versus Complexity Study of Neural Network Equalizers in Coherent Optical Systems

Bayesian Optimization for Nonlinear System Identification and Pre-Distortion in Cognitive Transmitters

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