We investigate the application of dynamic deep neural networks for nonlinear equalization in long haul transmission systems. Through extensive numerical analysis we identify their optimum dimensions and calculate their computational complexity as a function of system length. Performing comparison with traditional back-propagation based nonlinear compensation of 2 steps-per-span and 2 samples-per-symbol, we demonstrate equivalent mitigation performance at significantly lower computational cost.

A scheme for compensation of nonlinear effects in multichannel data transfer systems based on dynamic neural networks is proposed. An improved quality of optical signal transfer in this scheme in comparison with the signal transfer in a scheme based on a neural network using symbols from only one channel is demonstrated.

Practical implementation of digital signal processing for mitigation of transmission impairments in optical communication systems requires reduction of the complexity of the underlying algorithms. Here, we investigate the application of convolutional neural networks for compensating nonlinear signal distortions in a 3200 km fiber-optic 11x400-Gb/s WDM PDM-16QAM transmission link with a focus on the optimization of the corresponding algorithmic complexity. We propose a design that includes original initialisation of the weights of the layers by a filter predefined through the training a single-layer convolutional neural network. Furthermore, we use an enhanced activation function that takes into account nonlinear interactions between neighbouring symbols. To increase learning efficiency, we apply a layer-wise training scheme followed by joint optimization of all weights applying additional training to all of them together in the large multi-layer network. We examine application of the proposed convolutional neural network for the nonlinearity compensation using only one sample per symbol and evaluate complexity and performance of the proposed technique. Index Terms-Convolutional neural networks. Nonlinearity mitigation in fiber-optic links.

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Nonlinear Schrödinger equation (NLSE) is often used as a master path-average model for fiber-optic transmission lines. In general, NLSE describes the coexistence of dispersive waves and soliton pulses. Propagation of signal in such a nonlinear channel is conceptually different from linear systems. We demonstrate here that the conventional orthogonal frequency-division multiplexing (OFDM) input optical signal at powers typical for modern communication systems might have soliton components statistically created by the random process corresponding to the information content. Applying Zakharov-Shabat spectral problem to a single OFDM symbol with multiple sub-carriers we quantify the effect of statistical soliton occurrence in such an information-bearing optical signal. Moreover, we observe that at signal powers optimal for transmission OFDM symbol incorporates multiple solitons with high probability. The considered optical communication example is relevant to a more general physical problem of generation of coherent structures from noise.

Abstract:We perform an extensive numerical analysis of Raman-Assisted Fibre Optical Parametric Amplifiers (RA-FOPA) in the context of WDM QPSK signal amplification. A detailed comparison of the conventional FOPA and RA-FOPA is reported and the important advantages offered by the Raman pumping are clarified. We assess the impact of pump power ratios, channel count, and highly nonlinear fibre (HNLF) length on crosstalk levels at different amplifier gains. We show that for a fixed 200 m HNLF length, maximum crosstalk can be reduced by up to 7 dB when amplifying 10x58Gb/s QPSK signals at 20 dB net-gain using a Raman pump of 37 dBm and parametric pump of 28.5 dBm in comparison to a standard single-pump FOPA using 33.4 dBm pump power. It is shown that a significant reduction in four-wave mixing crosstalk is also obtained by reducing the highly nonlinear fibre interaction length. The trend is shown to be generally valid for different net-gain conditions and channel grid size. Crosstalk levels are additionally shown to strongly depend on the Raman/parametric pump power ratio, with a reduction in crosstalk seen for increased Raman pump power contribution.

We propose a modification of the conventional perturbation-based approach of fiber nonlinearity compensation that enables straightforward implementation at the receiver and meets feasible complexity requirements. We have developed a model based on perturbation analysis of an inverse Manakov problem, where we use the received signal as the initial condition and solve Manakov equations in the reversed direction, effectively implementing a perturbative digital backward propagation enhanced by machine learning techniques. To determine model coefficients we employ machine learning methods using a training set of transmitted symbols. The proposed approach allowed us to achieve 0.5 dB and 0.2 dB Q 2-factor improvement for 2000 km transmission of 11x256 Gbit/s DP-16QAM signal compared to chromatic dispersion equalization and one step per span two samples per symbol digital back-propagation technique, respectively. We quantify the trade-off between performance and complexity.

In this paper we investigate the application of dynamic multi-layer perceptron networks for long haul transmission systems showing performance improvement and significant superiority of neural network complexity over digital back-propagation method.