## 4 Results and Discussion  
Initially the behavior of SVM against I/Q imbalances was examined. In an I/Q modulator, the ideal phase shift between the I- and Q-branch is 90\({}^{\circ}\). Due to physical imperfections of the system components and the non-perfect tuning of the \(\pi/2\) phase shift, amplitudes and phase mismatches may occur. These I/Q imbalances may considerably disturb the signal constellation [21]. We investigate the I/Q imbalances in a B2B scenario according to Figure 3a at an optical signal-to-noise ratio (OSNR) of 28 dB, where the signal is disturbed at the transmitter side. The amplitude mismatch is set to 0.125  
Figure 3: Simulation setup of the 64 Gbd 64-QAM single-polarization coherent optical simulation system including two different setups for the link. By using the setup (**a**) a B2B transmission with noise loading is examined. The setup (**b**) consists of a 100 km SSMF transmission with subsequent electronic dispersion compensation (EDC) to investigate a dispersion uncompensated link. and the phase mismatch is varied between 0\({}^{\circ}\) and 30\({}^{\circ}\). To cope with these imperfections, we examine the performance of the BCSVM and the OVA-SVM and compare them to LD. In order to compare the SVM with other enhanced detection techniques, the KMA is added to this comparison. The training length of the respective SVMs and KMA is set to 1024 symbols. Moreover, the number of iterations for KMA is set to 5. Figure 4 shows the performance of the various detection methods depending on the transmitter I/Q imbalances. As expected, detection by machine learning algorithms is more robust against I/Q imbalances compared to LD. For low phase mismatch, the performance of the two enhanced detection techniques seems similar. However, above 12\({}^{\circ}\) phase mismatch the KMA's performance rapidly deteriorates. For SVM a decline in performance can be observed above 20\({}^{\circ}\) phase mismatch. Compared with OVA-SVM, the BCSM achieves slightly better performance, which is in the range of \(1\times 10^{-4}\). It should be mentioned that SVM and KMA are two completely different procedures. The SVM has already been introduced as classification algorithm in Section 2.1. The KMA, in contrast, belongs to a cluster-based detection. The training of KMA is iterative and unsupervised, while the training of the SVM is supervised. The KMA is initialized with the centers of the cluster. Therefore, it is necessary to know how many clusters are present and where the centers are approximately expected. If the actual cluster is too far away from the expected cluster, the KMA is no longer able to separate the clusters correctly. This can be seen for example in the constellation of the KMA at 17.5\({}^{\circ}\) phase mismatch, where the field at the top right has been assigned to about two full constellation points. Although the centers of the clusters are updated in each iteration. This effect may also occur in case of a phase rotation induced by SPM. Furthermore, the KMA is only a linear algorithm in essence, while the SVM is a nonlinear classifier due to the usage of kernels. Accordingly, the KMA is unsuitable for highly complex and nonlinear data distributions and is therefore no longer used as comparison in the following investigations. Regarding the visualization of the decision thresholds, the different working principles of the algorithms can be observed. Based on the RBF kernel, the SVM calculates significantly rounder and softer decision thresholds than the KMA. Additionally, a difference between the multi-class methods of the SVM can be seen. Therefore, we would like to point out at this point that besides the selection of the kernel also the choice of the SVM multi-class method may have a more or less significant influence on the results. Next, we include the fiber in our simulations. To evaluate the ability of the SVM to compensate nonlinear impairments in the 100 km setup for different launch powers, we compare the nonlinear detection by SVM with an FFE and an NLVE.