Overfitting Problem of ANN- and VSTF-Based Nonlinear Equalizers Trained on Repeated Random Bit Sequences

In this paper, we investigated the overfitting characteristics of nonlinear equalizers based on an artificial neural network (ANN) and the Volterra series transfer function (VSTF), which were designed to compensate for optical nonlinear waveform distortion in optical fiber communication systems. Linear waveform distortion caused by, e.g., chromatic dispersion (CD) is commonly compensated by linear equalizers using digital signal processing (DSP) in digital coherent receivers. However, mitigation of nonlinear waveform distortion is considered to be one of the next important issues. An ANN-based nonlinear equalizer is one possible candidate for solving this problem. However, the risk of overfitting of ANNs is one obstacle in using the technology in practical applications. We evaluated and compared the overfitting of ANN- and conventional VSTF-based nonlinear equalizers used to compensate for optical nonlinear distortion. The equalizers were trained on repeated random bit sequences (RRBSs), while varying the length of the bit sequences. When the number of hidden-layer units of the ANN was as large as 100 or 1000, the overfitting characteristics were comparable to those of the VSTF. However, when the number of hidden-layer units was 10, which is usually enough to compensate for optical nonlinear distortion, the overfitting was weaker than that of the VSTF. Furthermore, we confirmed that even commonly used finite impulse response (FIR) filters showed overfitting to the RRBS when the length of the RRBS was equal to or shorter than the length of the tapped delay line of the filters. Conversely, when the RRBS used for the training was sufficiently longer than the tapped delay line, the overfitting could be suppressed, even when using an ANN-based nonlinear equalizer with 10 hidden-layer units.