Multichannel Nonlinear Equalization in Coherent WDM Systems Based on Bi-Directional Recurrent Neural Networks

Kerr nonlinearity in the form of self- and cross-phase modulation imposes a fundamental limitation to the capacity of wavelength division multiplexed (WDM) optical communication systems. Digital back-propagation (DBP) is a widely adopted technique for the mitigation of impairments induced by Kerr nonlinearity. However, multi-channel DBP is too complex to be implemented commercially in WDM systems. Recurrent neural networks (RNNs) have been recently exploited for nonlinear signal processing in the context of optical communications. In this work, we propose multi-channel equalization through a bidirectional vanilla recurrent neural network (bi-VRNN) in order to improve the performance of the single-channel bi-VRNN algorithm in the transmission of WDM polarization multiplexed signals. We compare the proposed digital algorithm to full-field DBP and to the single channel bi-RNN in order to reveal its merits with respect to both performance and complexity. We finally provide experimental verification in QPSK transmission, showcasing over 2.5 dB optical signal-to-noise ratio (OSNR) gain and a significant reduction in bit-error-rate (BER) by an order of magnitude compared to single channel equalization. Moreover, a complexity reduction of up to 43% was achieved compared to the single-channel RNN, and up to 550% compared to the single channel DBP in the case of 24-span long haul transmission.