Computational complexity comparison of feedforward/radial basis function/recurrent neural network-based equalizer for a 50-Gb/s PAM4 direct-detection optical link

The computational complexity and system bit-error-rate (BER) performance of four types of neural-network-based nonlinear equalizers are analyzed for a 50-Gb/s pulse amplitude modulation (PAM)-4 direct-detection (DD) optical link. The four types are feedforward neural networks (F-NN), radial basis function neural networks (RBF-NN), auto-regressive recurrent neural networks (AR-RNN) and layer-recurrent neural networks (L-RNN). Numerical results show that, for a fixed BER threshold, the AR-RNN-based equalizers have the lowest computational complexity. Amongst all the nonlinear NN-based equalizers with the same number of inputs and hidden neurons, F-NN-based equalizers have the lowest computational complexity while the AR-RNN-based equalizers exhibit the best BER performance. Compared with F-NN or RNN, RBF-NN tends to require more hidden neurons with the increase of the number of inputs, making it not suitable for long fiber transmission distance. We also demonstrate that only a few tens of multiplications per symbol are needed for NN-based equalizers to guarantee a good BER performance. This relatively low computational complexity signifies that various NN-based equalizers can be potentially implemented in real time. More broadly, this paper provides guidelines for selecting a suitable NN-based equalizer based on BER and computational complexity requirements