Functional-Link Neural Network for Nonlinear Equalizer in Coherent Optical Fiber Communications

We propose and experimentally demonstrate a simple nonlinear equalizer based on functional-link neural network (FLNN). The nonlinear stochastic mapping enables FLNN to serve as a nonlinear network, so we construct an FLNN with the signals from the two polarizations and the mapped features as input to combat the fiber nonlinearity in coherent optical transmission systems. The FLNN can use the Moore-Penrose generalized inverse or the ridge regression to solve the weights, which can speed up the training process, and avoid the iterative and time-consuming training process that exist universally in most of the deep neural networks. We also extend the FLNN to the multi-channel transmissions. All of the received signals from different channels are stretched as the input and then we use a joint FLNN to extract features and equalize the nonlinear distortions. We conduct simulations and experiments to verify the proposed scheme. In the simulation and experiment, we transmit a 128 Gb/s polarization division multiplexed 16-QAM (PDM-16-QAM) signal over 1000-km and 600-km standard single mode fiber (SSMF), respectively. Both the simulation and experimental results show that the FLNN has similar performance as deep neural network (DNN), which can improve the transmission performance in the nonlinear region. Moreover, the FLNN can avoid the gradient dissipation and local minimum problems in DNN, which simplify the training process. We also extend the proposed scheme in a five-channel ($5\times160$ Gb/s) multiplexed transmission system. In simulation, we use joint FLNN and joint DNN to compensate the nonlinear distortions, respectively. We find that the BERs of the five channels can be below 7 HD-FEC with nonlinear equalizer.