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.
Transfer learning-aided NNs are proposed for nonlinear equalization in a 50-Gb/s 20-km PAM4 link. About 90% reduction in epochs and 56% in training symbols are achieved with NNs transferred from the most similar source system.
We propose a novel, to the best of our knowledge, cascade recurrent neural network (RNN)-based nonlinear equalizer for a pulse amplitude modulation (PAM)4 short-reach direct detection system. A 100 Gb/s PAM4 link is experimentally demonstrated over 15 km standard single-mode fiber (SSMF), using a 16 GHz directly modulated laser (DML) in C-band. The link suffers from strong nonlinear impairments which is mainly induced by the mixture of linear channel effects with square-law detection, the DML frequency chirp, and the device nonlinearity. Experimental results show that the proposed cascade RNN-based equalizer outperforms other feedforward or non-cascade neural network (NN)-based equalizers owing to both its cascade and recurrent structure, showing the great potential to effectively tackle the nonlinear signal distortion. With the aid of a cascade RNN-based equalizer, a bit-error rate (BER) lower than the 7% hard-decision forward error correction (FEC) threshold can be achieved when the receiver power is larger than 5 dBm. Compared with traditional non-cascade NN-based equalizers, the training time could also be reduced by half with the help of the cascade structure.
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