Nonlinearity mitigation with a perturbation based neural network receiver
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Nonlinearity mitigation with a perturbation based neural network receiver Marina M. Melek1 · David Yevick1 Received: 19 May 2020 / Accepted: 21 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We propose a less complex neural network that estimates and equalizes the nonlinear distortion of single frequency dual polarization data transmitted through a single mode optical fiber. We then analyze the influence of the size of the input data symbol window on the neural network design and the enhancement of the quality factor (Q-factor) that can be achieved by integrating the neural network with a perturbative nonlinearity compensation model. We significantly reduce the complexity of the neural network by determining the most significant inputs for the neural network from the self-phase modulation terms (intracross phase modulation and intra-four wave mixing) in the model. The weight matrices of the neural network are determined without prior knowledge of the system parameters while the complexity of the network is reduced in two stages through weight trimming technique and principle component analysis (PCA). Applying our procedure to a 3200 km double polarization 16-QAM optical system yields a ≈ 0.85 dB Q-factor enhancement with a 35% smaller number of inputs compared to previous designs. Keywords Optical communications · Fiber nonlinearity · Artificial intelligence · Neural networks
1 Introduction The large signal distortions that result from fiber nonlinearities present a major challenge for high-capacity long transmission optical communication systems. Accordingly, compensation techniques have been advanced at both the receiver and transmitter to mitigate these effects (Cartledge et al. 2017). The most widely cited and analyzed algorithm is digital backpropagation (DBP) (Ip and Kahn 2008; Liga et al. 2014). This universal technique employs the split step Fourier transform (SSFT) to solve the nonlinear Schrodinger equation (NLSE) (Agrawal 2006),
* Marina M. Melek [email protected] 1
Department of Physics, University of Waterloo, Waterloo, ON N2L 3G1, Canada
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j 𝜕 2 A(t, z) 𝜕A(t, z) 𝛼 = − A(t, z) + 𝛽2 − j𝛾|A(t, z)|2 A(t, z) (1) 𝜕z 2 2 𝜕t2 [ ]† for the field A(t, z) = Ax (t, z)Ay (t, z) . In (1), 𝛼 , 𝛽2 and 𝛾 are the group absorption coefficient, velocity dispersion and the nonlinearity coefficient, respectively. By evolving the received field through a simulated fiber with the negative of the actual fiber dispersion and nonlinearity, the pulse distortion can in principle be fully compensated. However, the associated computational overhead is relatively large. An alternative procedure separates the nonlinear term in (1) according to Aout (z, t) = Ain 0 (z, t) + ΔA(z, t)
(2)
t) denotes the field obtained through linear propagation while ΔA(z, t) reprewhere Ain o (z, sents the nonlinear distortion. The nonlinear perturbation of the symbol at t = 0 can then be approximated as (Tao et al. 2011;
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