## 3 Simulation Setup  
The proposed techniques are subsequently thoroughly evaluated in numerical simulations for a 64 GBd 64-QAM system. For simulation purposes we will initially restrict ourselves to a single-polarization system but it can be extended straight forward to a dual-polarization system. A schematic of the general setup is given in Figure 3. A \(2^{16}\) randomly generated bit sequence, using the MATLAB R2018a (9.4.0.813654) rand function, is mapped to the 64-QAM symbols. The digital  
Figure 2: Illustration of one iteration during training for (**a**) OVO, (**b**) OVA and (**c**) BCSVM methods in case of 16-QAM transmission. The opposite classes are marked in red and blue and the corresponding hyperplane is indicated by the dashed line.  
to analog conversion is modelled as a root-raised cosine pulse shaping filter with roll-off factor \(\beta~{}=~{}0.3\). The symbols are modulated on the carrier (wavelength \(\lambda_{c}~{}=~{}1550\) nm) via an I/Q MZ-modulator. The linewidth of the laser is set to zero. The modulated optical signal is coupled into the fiber after it is amplified by the erbium doped fiber amplifier (EDFA) with a noise figure (NF) of 5 dB.  
In order to investigate the performance of the enhanced detection algorithms, two types of communication systems are modeled. The link setup (**a**) is used to test a back-to-back (B2B) scenario, that is, no transmission link was simulated. The setup (**b**) is used to examine a dispersion uncompensated link, where the dispersion is compensated by DSP at the end of the transmission. The parameters for the SSMF are given by the attenuation coefficient \(\alpha\) = 0.2 dB/km, the dispersion coefficient \(D~{}=~{}17\) ps/(nm\(\cdot\)km), dispersion slope \(S~{}=~{}0.06\) ps/(nm\({}^{2}\cdot\)km) and the nonlinear coefficient \(\gamma~{}=~{}1.3\) (W\(\cdot\)km)\({}^{-1}\). For a complete compensation of span loss an EDFA (NF \(=5\) dB) is applied. After transmission a Gaussian optical filter with 90 GHz bandwidth is used to reduce ASE noise. The received signal is detected by a coherent receiver and downsampled to 128 GS/s. After matched filtering an ideal EDC is used to compensate for dispersion. After the equalization stage, which consists of either an FFE, an NLVE or no equalizer at all (w/o), the signal is downsampled to symbol frequency and detected. Detection and demodulation is performed either linear by using conventional linear decision thresholds and demapping, here called linear detection (LD), or by machine learning algorithms such as SVM or KMA [8,9]. System performance is evaluated by BER. The hard-decision forward error correction (HD-FEC) limit is assumed to be 3.7 \(\times~{}10^{-3}\). We examine the suitability of the SVM as a classifier and combine the mentioned equalizer schemes with the SVM to achieve the maximum gain of the machine learning algorithm.  
Since more coefficients require more training symbols, increasing the number of coefficients without adjusting the number of training symbols might decrease the performance. Thus, for a correct adjustment of the Volterra equalizer it is necessary to determine the optimal number of coefficients and training symbols. For the further investigations the training length of 2048 symbols and memory lengths of NLVE[4,2,5] was determined after optimization.