## 5 Experimental Setup and Performance of Machine Learning Algorithm in CO-OFDM  
The experimental setup and parameters are shown in Figure 9 and Table 1 for both single-channel and WDM CO-OFDM at 2000 km and 3200 km of transmission, respectively, using EDFA-based recirculating loops and a standard single-mode fiber (SSMF). The set-up, procedures and parameters are identical to [21; 22; 28; 31; 33; 35; 36]. In summary, 400 OFDM symbols (20.48 ns length) were generated using a 512-point IFFT on 210 QPSK/16-QAM subcarriers. To eliminate inter-symbol-interference from linear effects, a cyclic prefix (CP) of 2% was included. For the clustering algorithms, FS-DBP, V-NLE and without (w/o) NLE, the raw bit-rates were ~20 Gb/s (QPSK) and 40 Gb/s (16-QAM). However, for supervised machine learning such as SVR and ANN (as indicated in Table 1), 10% of data are sacrificed for training for both single- and multi-channel cases, above which the quality(Q)-factor is saturated as depicted in Figure 10 for WDM CO-OFDM. Such training is performed separately for each LOP, requiring relatively the same amount of training-data. At the receiver side, a coherent optical homodyne receiver was used, while the offline OFDM demodulator included timing synchronization, frequency offset compensation (due to the receiver local oscillator, LO), channel estimation and equalization with the help of an initial training sequence, as well as IQ imbalance and CD compensation using an overlapped frequency domain equalizer. For the WDM CO-OFDM system a laser grid of 100 kHz-linewidth distributed feedback lasers (DFBs) on 100 GHz grid was used and the noise loading channels were inserted using ASE source and a wavelength selective switch (WSS). In the inset spectrum of Figure 10 (as well as in the inset of Figure 9) the received WDM lines are shown. The NLEs performances were assessed by the total subcarriers' bit-error-rate (BER) and Q-factor (=20 log\({}_{10}\left[\sqrt{2}erfc^{-1}(2 BER)\right]\)) measurements averaging over 10 recorded traces (\(\sim\)10\({}^{6}\) bits) by error counting (hard-decision-decoding, HDD). Figure 8: Affinity propagation (AP) clustering procedure (e.g., quaternary phase-shift keying (QPSK)) [36]. In Figure 11, the Q-factor against the LOP per channel is plotted for various machine learning and deterministic NLEs for the QPSK middle-channel in WDM CO-OFDM. It shown that AP tackles non-linearities more effective than any other algorithm under test since it compensates both the PNA and the accumulated inter-subcarrier FWM which appears random (due to the impact of a high PAPR). This is corroborated in Figure 11b, where the Q-factor for the middle subcarriers is plotted which suffers the most mainly from inter-subcarrier FWM [48] (secondary from inter-subcarrier cross-phase modulation, XPM) at the optimum LOP. However, some of the inter-channel nonlinearities are also compensated better by AP, which are not as strong as the intra-channel (i.e., inter-subcarrier nonlinear distortions). In Figure 11f, the clear nonlinear decisions (soft/overlapping clustering) compared \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Net bit-rate & 18.2 Gb/s(WDM), 40 Gb/s(1-ch.) \\ Net bit-rate for ANN & 16.8 Gb/s (WDM), 38 Gb/s(1-c.) \\ Raw bit-rate & 20 Gb/s (WDM), 46 Gb/s (1-ch.) \\ Format of modulation & QPSK (WDM), 16-QAM (1-ch.) \\ Number of symbols & 400 \\ Symbol time duration & 20.48 ns \\ Generated subcarriers & 210 \\ CP & 2\% \\ Size of FFT \& inverse()FFT & 512 \\ ANN Training overhead & 10\% \\ ANN Train. symbol length & 40 symbols \\ Local oscillator linewidth & 100 kHz \\ OH-LITE fiber attenuation & 18.9–19.5 dB/100 km \\ Number of spans & 30 (WDM), 20 (1-chan.) \\ Length-per-span & 100 km \\ Center wavelength & 1550.2 nm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Transmission and transceiver OFDM parameters.