## 5 Conclusions  
We compare, experimentally, the performance of a 3 rd-order IVSTF-NLE and the DBP-SSF method, with various numbers of steps per span, in a coherent optical WDM system, with a central 400 Gb/s 4-band, DP-16 QAM OFDM super-channel exacerbating the intra- and inter-channel nonlinearities. Then, we extend the study numerically by estimating the maximum transmission reach, provided by the NLEs under study, with respect to the FEC limit after transmission in a LEAF. Both, the experimental and the simulation, results reveal that the performance of the single-step-per-span 3 rd-order IVSTF-NLE can compete the well-known DBP-SSF method. The latter requires eight-steps-per-span in order to reach its optimum performance which, however, is comparable with the performance with the almost eight times less complex 3 rd-order IVSTF-NLE. Although the differences in the performance of the DBP-SSF\({}_{1,2}\) NLEs, compared to the DBP-SSF\({}_{8}\) NLE and the 3 rd-order IVSTF-NLE, are only marginal,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**NLE** & **Optimum \(N_{\text{FFT}}\)** & **Maximum \(Q^{2}\) (dB)** & **Maximum BER** &
\begin{tabular}{c} **Number of Real** \\ **Multiplications** \\ \end{tabular} \\ \hline
3 rd-order IVSTF & 256 & 6.5 & \(1.7\times 10^{-2}\) & 631 \\ DBP-SSF\({}_{1}\) & 256 & 6.4 & \(1.8\times 10^{-2}\) & 595 \\ DBP-SSF\({}_{2}\) & 512 & 6.43 & \(1.8\times 10^{-2}\) & 1302 \\ DBP-SSF\({}_{8}\) & 512 & 6.5 & \(1.7\times 10^{-2}\) & 5208 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Maximum \(Q^{2}\)-factor and the corresponding number of real multiplications per sample per polarization required at the optimum \(N_{\text{FFT}}\), after 14 \(\times\) 100 km of SSMF at optimum input power equal to \(-\)3 dBm.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**NLE** & **Optimum \(N_{\text{FFT}}\)** & **Maximum \(Q^{2}\) (dB)** & **Maximum BER** &
\begin{tabular}{c} **Number of Real** \\ **Multiplications** \\ \end{tabular} \\ \hline
3 rd-order IVSTF & 512 & 6.65 & \(1.6\times 10^{-2}\) & 552 \\ DBP-SSF\({}_{1}\) & 512 & 6.6 & \(1.6\times 10^{-2}\) & 512 \\ DBP-SSF\({}_{2}\) & 512 & 6.65 & \(1.6\times 10^{-2}\) & 1023 \\ DBP-SSF\({}_{8}\) & 512 & 6.7 & \(1.5\times 10^{-2}\) & 4092 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Maximum \(Q^{2}\)-factor and the corresponding number of real multiplications per sample per polarization required at the optimum \(N_{\text{FFT}}\), after 11 \(\times\) 100 km of LEAF at optimum input power equal to \(-\)6 dBm.  
Figure 8: \(Q^{2}\)-factor as a function of the \(N_{\text{FFT}}\), at the optimum input power per band, after (**a**) 14 \(\times\) 100 km of SSMF and (**b**) 11 \(\times\) 100 km of LEAF.  
they are still indicative of the robustness of each and every NLE in the presence of exacerbated nonlinear effects. Thus, the 3 rd-order IVSTF-NLE could be a reasonable choice for compensating nonlinear impairments with lower computational complexity and, by extension, lower cost.  
More generally, our study confirms that digital nonlinear equalization is especially efficient to mitigate intra-channel nonlinear effects and less convenient when also inter-channel nonlinearities are involved. However, with the increase of data rate carried by the sub-channels constituting the super-channel (supported by the improvement of bandwidth/resolution of DACs/ADCs), digital nonlinear equalization could know a renewed interest because, at high bit/symbol rate per sub-channel, intra-channel nonlinearities are predominant.  
[PERSON] and [PERSON] conceived the experiment. [PERSON] and [PERSON] designed and performed the experiment; [PERSON] analyzed the experimental data, conducted the theoretical study and wrote the paper. [PERSON] contributed to the authorship of the experimental setup. [PERSON] provided valuable advice considering the writing of the paper. [PERSON] and [PERSON] supervised the whole work.  
The authors declare no conflict of interest.