## 2 Experimental Section
The in-phase and quadrature components of the coherent OFDM signal are electrically amplified using two linear RF driver amplifiers (SHF807), which feed a quadrature modulator (CMZM). The first CMZM generates the odd channels while the second generates the even channels, in order to totally decorrelate the data carried by adjacent channels. The odd and even combs are combined together using a 3-dB polarization maintaining (PM) coupler. The polarization multiplexing is realized by dividing the signal into two paths, putting a delay of one-OFDM-symbol-duration on one of the paths, switching it to the perpendicular polarization, and combining them together, as shown in Figure 2. The one-OFDM-symbol-duration delay corresponds to 1152 samples (1024 FFT size samples and 128 CP samples). Then, the OFDM super-channel is combined with 58 wavelengths modulated at 100 Gb/s using DP-QPSK and spaced 50-GHz apart from each other. The transmission line is composed of 10 spans of 100 km of SSMF. A single-stage erbium doped fiber amplifiers (EDFAs), with 20 dB gain and \(\sim\)4.5 dB noise figure, is applied at the end of each span and for all the 10 spans. At this point, we note that the linear and non-linear equalization schemes that are presented in this paper are not adaptive but feed forward schemes. Although they may require exact knowledge of the system's parameters to operate, their operation is not affected by the amount of accumulated noise at the receiving end. On the other hand, their effectiveness in improving the system performance is affected by the noise added by the EDFA elements along the link and the nonlinear mixing between signal and noise. This additional non-linear noise effect cannot be treated by any equalization scheme at the receiver, but only with the use of distributed compensation methods, such as all optical regenerators or cascaded optical phase conjugation (OPC) elements [24]. A dynamic gain equalizer (DGE) is introduced in the middle of the link to flatten the multiplex power after 10 \(\times\) 100 km. At the end of the link, an optical bandpass filter (BPF) selects the OFDM band under measurement. This one is detected by a polarization- and phase-diversity coherent receiver using an external cavity laser (ECL) with 100 kHz linewidth as local oscillator (LO). The effective number of bits (ENoB) in the digital-to-analog converters (DACs) and in the analog-to-digital converters (ADCs) is approximately 5. We use \(10^{6}\) bits to evaluate the bit error rate (BER) by error counting. We consider three scenarios to explore the physical limits of the NLEs performance: (a) a single-channel transmission of a single-band DP, 16 QAM OFDM signal (Figure 3a); (b) WDM transmission with a 2-band DP, 16 QAM OFDM signal (Figure 3b), and, finally (c) WDM transmission with a 4-band, DP, 16 QAM OFDM super-channel at the center of the WDM comb (Figure 3c). The power spectra are recorded by a high-spectral-resolution (20 MHz) optical spectrum analyzer (OSA). The first scenario corresponds to a to a pseudo-single-channel transmission scenario in which the cross-phase modulation (XPM) and the four wave mixing (FWM) are considered practically negligible (Figure 3a). In the second scenario, the inter-channel nonlinearities are increased (Figure 3b). Finally, the third study case exacerbates the intra- and inter-channel nonlinearities (Figure 3c). The guard-band spacing between the third OFDM band and its immediate left/right neighbors are 250/230 GHz, 22/31 GHz and 2/2 GHz for the study cases (a), (b) and (c), respectively. For the detection of the OFDM band under study, we used a 50 GSa/s sampling rate real-time oscilloscope, followed by resampling at 32 GSa/s. The latter is the sampling frequency used by the NLEs. The off-line OFDM signal processing is thoroughly described in [25]. In the coherent receiver, IVSTF-NLE and DBP-SSF equalizers are placed at the initial stages of the digital signal processing (DSP), where CD compensation is usually performed [26]. The detected OFDM band has an aggregate symbol rate of 18 Gbaud.