## 5 Experimental Setup and Performance of Machine Learning Algorithm in CO-OFDM
Figure 9: Experimental setup for multi- (upper) and single-channel (lower) CO-OFDM incorporating Volterra-non-linear equalization (V-NLE) and FS-DBP in time domain and the machine learning algorithms in frequency domain (after the FFT in CO-OFDM) [21; 22; 28; 31; 33; 35; 36]. ECL: external cavity laser, AWG: arbitrary waveform generator, AOM: acousto-optic modulator, EDFA: Erbium-doped fiber amplifier, GFF: gain-flattening filter, LO: local oscillator, DFB: distributed feedback laser, ASE: amplified spontaneous emission, PMM: polarization maintaining multiplexer, WSS: wavelength selective switch, BPF: bandpass filter, OSA: optical spectrum analyzer. Inset: received optical spectrum for all channels, highlighting the 5 middle channels. to \(K\)-means hard decisions (exclusive clustering) is also depicted for a received QPSK constellation diagram at \(-7\) dBm of LOP. In Figure 11c-e we show the performance of unsupervised, supervised and fast machine learning algorithms, i.e., Sato/Godard-CMA BNLEs, ANN/SVR, and Fast-Newton-SVM (F-SVM), respectively. Results in Figure 11c-e conclude that AP clustering algorithm has the best performance in QPSK WDM CO-OFDM, and then SVR and FL follow. Finally, in Figure 11 it is shown that at low power a Q-factor improvement of the adopted machine learning algorithms is observed over the deterministic algorithms and linear equalization. This is due to the ability of machine learning NLEs to partially tackle the accumulated ASE noise from concatenated optical amplifiers. Such statement is strong considering the negligible noise induced from electrical components and digital-to-analogue and analogue-and-digital converters (error vector magnitude below 7% for optical back-to-back). In Figure 12, results are depicted for single-channel 16-QAM CO-OFDM using the same algorithms. Similarly, AP shows the greatest performance reaching almost 15 dB in Q-factor and outperforming the FS-DBP. This means that the strong nonlinear phase noise of 16-QAM can be successfully tackled by AP, which seems to effectively compensating intra-channel deterministic and stochastic nonlinearities. However, it should be noted that all algorithms at low powers present poor performance due to the stronger PNA and ASE noise. It should be noted that an ANN was also implemented in [20; 21], however, the bit-rate and training testing was different than SVR and so is not included here to be compared. Nevertheless, as shown in [20; 21] the performance is anticipated to be worse than SVR and consequently and from AP. Figure 10: Training overhead evolution example at \(-5\) dBm of launched optical power (LOP) per channel for supervised support vector machine-regression (SVR) and artificial neural network (ANN). Inset: received optical spectrum of wavelength-division multiplexing (WDM) CO-OFDM system [22; 28]. Figure 11: WDM QPSK CO-OFDM results [22; 28; 29; 33; 35; 36] (**a**) Q-factor vs. launched optical (LOP) per channel among clustering and deterministic algorithms. (**b**) Middle subcarriers Q-factor distribution at \(-\)5 dBm of LOP (optimum). (**c**) Q-factor vs. LOP for unsupervised SVMs. (**d**) Performance comparison between supervised support vector machine-regression (SVR) and artificial neural network (ANN). (**e**) Performance comparison between Fast-Newton-SVM (F-SVM) and benchmark clustering/deterministic algorithms. (**f**) Received constellation diagrams for affinity propagation (AP) and \(K\)-means at \(-\)7 dBm of LOP. LE: linear equalization; NLE: nonlinear equalization; V-NLE/IVSTF: inverse Volterra-series transfer function NLE; BNLE: blind NLE; FS-DBP: full-step digital back-propagation; FC/FLC: Fuzzy-logic clustering.