Learned Volterra models for nonlinearity equalization in wavelength-division multiplexed systems

Multichannel digital equalization has proved capable of mitigating fiber-induced inter-channel impairments which constitute a main limitation in wavelength-division multiplexed systems. In this paper, we present three multiple-input-multiple-output learned equalization architectures based on the inverse Volterra series transfer function (IVSTF): a fully parallel frequency-domain approach (L-IVSTF), a field-enhanced version with improved adaptability (FE L-IVSTF), and a time-domain implementation (L-simIVSTF). We demonstrate that machine-learning optimization enables efficient multichannel equalization for all the structures, with the 9 × 9 L-simIVSTF and FE L-IVSTF equalizers achieving an average signal-to-noise ratio improvement of ∼2.2 dB over chromatic dispersion compensation. The three models are thoroughly characterized and compared in terms of performance and computational cost, pinpointing the FE L-IVSTF as the model with the best trade-off.