## 4 Results and Discussion
### Experimental Results  
Figure 5a shows the maximum \(Q^{2}\)-factor as a function of the launch power after 10 \(\times\) 100 km of SSMF for single-channel transmission with linear compensation only, as well as with IVSTF or DBP-SSF\({}_{1,2,8}\) NLEs (scenario described in Figure 3a). The \(Q^{2}\)-factor improvement is \(\sim\)1 dB (i.e., BER = 3.2 \(\times\) 10\({}^{-3}\) with linear equalization only (wo. NLE) and BER = 9.9 \(\times\) 10\({}^{-4}\) with linear and nonlinear equalization (w. NLE)) for all NLEs, which agrees with the published results for the single-channel, single-carrier system in [16].  
Figure 5b corresponds to a WDM coherent optical system with two OFDM bands at its center (scenario described in Figure 3b). In this case, the \(Q^{2}\)-factor improvements are \(\sim\)0.44 dB (i.e., BER = 5.3 \(\times\) 10\({}^{-3}\) wo. NLE and BER = 3.6 \(\times\) 10\({}^{-3}\) w. NLE) for the 3 rd-order IVSTF-NLE, \(\sim\)0.5 dB for the DBP-SSF\({}_{1}\) NLE, and \(\sim\)0.6 dB (i.e., BER = 5.3 \(\times\) 10\({}^{-3}\) wo. NLE and BER = 3.2 \(\times\) 10\({}^{-3}\) w. NLE) for the DBP-SSF\({}_{2,8}\) NLEs. We observe that, in this scenario, the performance of the DBP-SSF method saturates at two steps per span.  
Figure 5c shows representative plots of the \(Q^{2}\)-factor vs. input power per band for a central 4-band OFDM super-channel surrounded by WDM DP QPSK channels (scenario described in Figure 3c). The measured \(Q^{2}\)-factor improvements are \(\sim\)0.33 dB (i.e., BER = 7.5 \(\times\) 10\({}^{-3}\) wo. NLE and BER = 5.8 \(\times\) 10\({}^{-3}\) w. NLE) for the 3 rd-order IVSTF-NLE, \(\sim\)0.28 dB for the DBP-SSF\({}_{1}\) NLE, \(\sim\)0.35 dB (i.e., BER = 7.5 \(\times\) 10\({}^{-3}\) wo. NLE) and BER = 5.7 \(\times\) 10\({}^{-3}\) w. NLE) by the DBP-SSF\({}_{2}\) NLE and \(\sim\)0.4 dB (i.e., BER = 7.5 \(\times\) 10\({}^{-3}\) wo. NLE and BER = 5.5 \(\times\) 10\({}^{-3}\) w. NLE) by DBP-SSF\({}_{8}\) NLE.  
Figure 5: Experimental results on \(Q^{2}\)-factor vs. input power per band without/with IVSTF-NLE and DBP-SSF\({}_{1,2,8}\) in **(a)** single-channel with a single OFDM band; **(b)** a single-OFDM-band super-channel surrounded by WDM DP-QPSK channels; and **(c)** a WDM, 4-band OFDM super-channel surrounded by WDM DP-QPSK channels after transmission through 10 \(\times\) 100 km SSMF.  
Summing up our observations from the experimental results, we note that all NLEs mitigate equally well the intra-channel nonlinear effects (Figure 5a) but their performances degrade when the inter-channel nonlinear crosstalk is also considered (Figure 5c). This modest performance improvement is mainly due to the detection and compensation of each OFDM band separately, leaving inter-channel nonlinearities uncompensated. We observe that the IVSTF-NLE is worse compared to DBP-SSF method for input powers per band higher than the optimum because as the input power per band increases, the nonlinear effects become stronger requiring more computational steps to achieve their compensation. In addition, we observe that the DBP-SSF method reaches its optimum performance at 8 steps per span. Nevertheless, the latter is only marginally more powerful compared to the DBP-SSF\({}_{2}\) NLE. Therefore, as the nonlinear phenomena become stronger, larger number of steps per span are required for the DBP-SSF method to reach its performance limit. On the contrary, the 3 rd-order IVSTF-NLE, which operates with a single step per span, performs almost as good as the DBP-SSF\({}_{2}\) NLE, with the latter being twice more complex than the former. Finally, we emphasize that the primary focus of the experimental results is to compare and gain a better insight about the potential of each NLE in the presence of very strong nonlinear effects. Although the performance results of all NLEs is modest, especially in the worst-case scenario (see Figure 5c), they are indicative of the fact that the 3 rd-order IVSTF-NLE can compete with significantly lower computational effort the heavily iterative DBP-SSF with multi-steps per span.