Blind Nonlinearity Equalization by Machine Learning based Clustering for Single- and Multi-Channel Coherent Optical OFDM

Fiber-induced intra- and inter-channel nonlinearities are experimentally tackled using blind nonlinear equalization (NLE) by unsupervised machine learning based clustering (MLC) in <formula><tex>$\sim$</tex></formula>46-Gb/s single-channel and <formula><tex>$\sim$</tex></formula>20-Gb/s (middle-channel) multi-channel coherent multi-carrier signals (OFDM-based). To that end we introduce, for the first time, Hierarchical and Fuzzy-Logic C-means (FLC) based clustering in optical communications. It is shown that among the two proposed MLC algorithms, FLC reveals the highest performance at optimum launched optical powers (LOPs), while at very high LOPs Hierarchical can compensate more effectively nonlinearities only for low-level modulation formats. FLC also outperforms K-means, Fast-Newton support vector machines, supervised artificial neural networks and a NLE with deterministic Volterra analysis, when employing BPSK and QPSK. In particular, for the middle channel of a QPSK WDM coherent optical OFDM system at optimum -5 dBm of LOP and 3200 km of transmission, FLC outperforms Volterra-NLE by 2.5 dB in Q-factor. However, for a 16-quadrature amplitude modulated single-channel system at 2000 km, the performance benefit of FLC over IVSTF reduces to <formula><tex>$\sim$</tex></formula>0.4 dB at a LOP of 2 dBm (optimum). Even when using novel sophisticated clustering designs in 16 clusters, no more than additional <formula><tex>$\sim$</tex></formula>0.3 dB Q-factor enhancement is observed. Finally, in contrast to the deterministic Volterra-NLE, MLC algorithms can partially tackle the stochastic parametric noise amplification.