## 2 System Modelling
### Simulation Conditions and Parameters  
This subsection presents the simulation conditions used to evaluate the effectiveness of the ML techniques to mitigate the impact of the random ICXT on the system performance. This work is focused on short-reach connections, and thus, the length of the MCF does not exceed 50 km.  
For the simulation, a thermal noise with a noise equivalent power (NEP) of \(10\,\mathrm{pW}/\mathrm{Hz}^{1/2}\) is considered. To estimate the BER, Monte Carlo simulation using a bit stream with \(2^{14}\) bits is performed. To evaluate each BER value, 100 errors are considered. All parameters used are indicated in Tables 1-3.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Symbol rate (Gbaud) & 64 \\ Modulation & 16-QAM \\ Roll-off factor & 0.05 \\ Input MCF power (dBm) & 0 \\ CSPR (dB) & 13 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Signal parameters.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Attenuation (dB/km) & 0.22 \\ Interfered core effective refractive index & 1.4453 \\ Interfering core effective refractive index & 1.4455 \\ Wavelength (nm) & 1552 \\ Skew \(\times\) bitrate & 0.001 \\ ICXT level (dB) & \(-13\) \\ Length (km) & 35 \\ \hline \hline \end{tabular}
\end{table}
Table 2: MCF parameters.  
Figure 5: Schematic diagram of the FNN used to mitigate the impact of the ICXT in DD-MCF short-reach networks.  
The FNN is trained using 20,000 symbols, as indicated in Table 3. These 20,000 symbols correspond to a transmission time of 0.3 \(\upmu\)s. The complexity and online requirements of the algorithm depend on the time required by the training phase of the FNN and the update rate. The rate at which the network must be trained depends on the variation of the ICXT along time. In particular, the neural network should be trained in time intervals over which the variation of the ICXT is almost negligible. Previous works have been shown that the decorrelation time of the ICXT is of the order of a few minutes or higher [20]. This means that, if we choose to train the network once per second, to guarantee that the ICXT is constant during the active phase of the network, the training overhead is negligible. The training phase will also require some processing time to optimize the weights and biases of the FNN. Although this processing time is dependent on the real time implementation employed, we expect that it will not affect the symbol rate of the system.  
To use a KK receiver, we need to ensure the minimum phase condition. Thus, the carrier-to-signal power ratio (CSPR) must be optimized according to a noise equivalent power (NEP) of 10 \(\mathrm{pW}/\sqrt{\mathrm{Hz}}\).  
Figure 6 shows the BER as a function of the CSPR for four different fiber lengths. Results are obtained considering the absence of ICXT and perfect dispersion compensation. Figure 6 shows that the optimum CSPR is approximately 13 dB. This optimum operation point results from a trade-off between signal-to-noise ratio and verification of the minimum phase condition. For low CSPR levels, the condition is not satisfied. For high CSPR levels, the SNR degrades.  
The FNN has one single hidden layer with 10 neurons. Further investigation showed that the FNN has a similar performance with number of neurons higher than 2, although the lower the number of neurons, the longer the training time. The algorithm used for training is the scaled conjugate gradient and the activation function used is the tangent sigmoid.