## 3 Models and Algorithms
### Lightpath Provisioning
Propagation in optical fiber was modeled by solving the nonlinear Schrodinger equation using the Runge-Kutta method (see [22]). EDFAs and TDFAs were modeled as ideal OAs characterized by a single gain and noise figures. Note that such simplification is intended to clearly show the differentiated behavior of the channels in the different transmission bands. An adaptive step-size algorithm was also included to further reduce the computation time required by the Runge-Kutta method. Finally, at the Rx, a DSP block performed ideal chromatic dispersion compensation and phase recovery. The dataset was populated with a total of 1000 samples, which were used for training, validating, and testing the DNN link models [30]. The DNN link models were characterized by: (_i_) 20 inputs for the features of the four selected CPs; (_ii_) two hidden layers with 12 neurons and _tanh_ (\(\cdot\)) activation function; and (_iii_) 20 outputs for the propagated features. A specific DNN link model was trained for each different RCh and configuration of the link, i.e., the number of spans and span length (in steps of 10 km). ### Reference Channels Selection

Let us first select the RChs that will be afterwards used during the lightpath provisioning process. Figure 6 shows the value for every channel of some \(\sigma\) features belonging to two exterior CPs. We observe that a piecewise linear approach with six segments results in relatively accurate models. Note that six segments result in seven different RChs. However, the location of the cut-points is different for each individual feature, as well as for the different link configurations. For example, the fourth cut-point ranges from 153 to 174 in the plots in Figure 6. Therefore, Algorithm 1 finds the centroid among the values for the same cut-point index from the different \(\sigma\) features and link configurations. Figure 7 shows the results of an extensive study using the generated datasets, where pre-FEC BER is shown for links with three, six, and nine spans where the pre-FEC BER \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **S-Band** & **C-Band** & **L-Band** \\ \hline Wavelength range [nm] & 1481.7–1530.1 & 1530.1–1564.8 & 1564.8–1616.7 \\ \hline Bandwidth [THz] & 6.19 & 4.35 & 5.76 \\ \hline \multirow{2}{*}{Num of Channels (Ids)} & 128 & 87 & 122 \\  & (1–128) & (129-215) & (216–337) \\ \hline Type of Amplifier & TDFA & EDFA & EDFA \\ \hline Amplifier Noise Figure & & 5 \\ \hline Nonlinear coefficient & & & \\ Dispersion, Attenuation & & & \\ \hline Launch Power & & 0 dBm \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Considered MB optical systems. ### Feature Composition

Let us focus now on the composition of the features. Recall that the features of the RChs after propagation through the set of DNN link models for the given route are already available, and Algorithm 2 is used to estimate those for a target channel. Figure 8 shows the contour plots for RCh 225 (Figure 8a) and the non-propagated channel 75 (Figure 8b) after signal propagation along nine spans. Figure 8c focuses on the two propagated CPs (one interior and one exterior) for RCh 225 and the composed ones for channel 75. In both cases, we observe high accuracy in the channels estimated features (in red) w.r.t. the ones obtained from the simulator (in black). Figure 8: Reconstructed constellations for an RCh (**a**) and a non-RCh (**b**). Details of two CPs, one exterior and one interior (**c**). Figure 7: Pre-FEC BER vs. number of piecewise linear segments. To evaluate the accuracy of the QoT estimation, Figure 9 compares the pre-FEC BER calculated by numerical simulation with the one estimated using Algorithm 6 without NLI noise mitigation, i.e., assuming square boundaries for the detection areas. The results obtained for RCh 97 and two non-propagated ones, i.e., ch. 180 and ch. 310, are depicted for different transmission distances. We observe that the pre-FEC BER estimation for the three channels is very accurate, in line with the results in [20] for the C-band.