## 4 Results and Discussion
To distort the 64-QAM constellation we set the modulation  
Figure 4: Simulations results in case of transmitter I/Q imbalances. BER vs. phase mismatch for an amplitude mismatch of 0.125 and 28 dB OSNR. depth of the modulator to \(m~{}=~{}V_{\rm PP}/V_{\pi}~{}=~{}2.2\) and generated an I/Q imbalance with 5% phase deviation from 90\({}^{\circ}\). The number of training symbols for SVM is set to 1024. The BER as a function of the launch power after 100 km dispersion uncompensated transmission is shown in Figure 5. The launch power of the 64-QAM signal ranges from \(-6\) to +12 dBm. We investigate different combinations of equalizers and detection techniques. Figure 5a first presents the results for FFE[1] and NLVE[4; 2; 5] in conjunction with LD. In addition, the red curve shows a detection based on SVM only without any previously inserted equalizer. It can be seen that a nonlinear detection with SVM only is already quite powerful. Here, the lowest BER is achieved by SVM at 3 dBm launch power, which is about six times lower than the BER using the FFE. Up to 4 dBm the best results can be achieved with SVM detection. Above 4 dBm nonlinear effects dominate and the optimally configured NLVE shows the best performance while the SVM is not as good as the NLVE but still better than the FFE. The launch power to stay below HD-FEC can be increased by 2 dB, if NLVE[4; 2; 5] is used and by 1 dB if the SVM is used compared to FFE[1]. If an FFE[1] or NLVE[4; 2; 5] is now added before the SVM, the overall system performance can be improved significantly, as shown in Figure 5b,c. Especially the combination of NLVE[4; 2; 5] and SVM further minimizes the BER significantly as can be seen in Figure 5c at 3 dBm launch power, where the BER is reduced from \(7.7\times 10^{-5}\) to \(3.1\times 10^{-6}\) by SVM. The optimum setting for the NLVE is given by NLVE[4; 2; 5]. So, the total number of NLVE coefficients sums up to \(N_{t}~{}=~{}82\), according to Equation (8). The majority of coefficients belongs to the third order of the NLVE. Therefore, in our further investigations we have reduced the number of delay elements in the third order to \(N_{3}~{}=~{}3\). Consequently, the number of coefficients is decreased from 75 to 18 (74%). Figure 6 shows the obtained BER as a function of the launch power for the optimal and reduced NLVE. The SVM is trained with 1024 and the NLVE with 2048 symbols. It can be seen that further reducing the coefficients of the NLVE leads to a decline of the overall system performance. To stay below the HD-FEC, the launch power is reduced by 1 dB in case of NLVE[3; 2; 3] and LD compared to the NLVE[4; 2; 5] and LD. Furthermore, NLVE[4; 2; 3] is continuously worse than a detection by SVM only. By combining the reduced NLVE[4; 2; 3] and the SVM, it can be observed that better results are achieved compared to the optimally adjusted NLVE[4; 2; 5] and LD. At 3 dBm launch power, the BER of NLVE[4; 2; 3] and LD (green dashed line) is \(1.2\times 10^{-4}\) and can be reduced to \(1\times 10^{-5}\) by SVM (orange dashed line). Figure 5: BER as a function of the launch power at 100 km dispersion unmanaged transmission: (**a**) shows equalization by FFE[1] and NLVE[4; 2; 5] combined with LD and only SVM detection. (**b**) shows the combined structure FFE[1] and SVM and (**c**) shows the combination NLVE[4; 2; 5] with SVM. Finally, we examined the impact of the number of training symbols on the performance of the NLVE and the SVM. The obtained results are presented in Figure 7 including the investigations for the NLVE with optimal and reduced coefficients in combination with LD and SVM based nonlinear detection plus a single detection only by SVM. We increased the number of training symbols from 512 to 3584 at 5 dBm launch power. The main improvement is observed after an increase from 512 to 1024 symbols for all investigated structures. The training of the SVM is based on the classes that are included in the classification task.