## 3 Models and Algorithms
### Lightpath Provisioning
With the features of the entire expected optical signal for the candidate path, the pre-FEC BER is estimated (line 14), and the candidate channel is returned in case the estimated value is found to be under the threshold (line 15). Otherwise, the channel is discarded, and the process continues with the rest of the available channels (line 16). In the case that none of the available channels can provide the requested BER, the application of NLI noise mitigation is considered (lines 17-21). To that end, the available channel with the minimum BER is selected using the pre-computed pre-FEC BER vs. channel curve (line 17), and the features for that channel are computed from those of the reference channels, as well as the features of the non-propagated CPs (lines 18-19). The optimal detection areas for the expected signal are then computed using an algorithm that also returns the estimated BER after NLI noise mitigation (line 20). In the case that the resulting BER is under the threshold, the channel, together with the computed detection areas, is returned (line 21); otherwise, none of the available channels has been found to guarantee the BER threshold (line 22). Finally, Algorithm 6 presents the pseudocode for NLI noise mitigation that receives as input the expected features of the signal at the Rx and the number \(m\) of CPs in the signal and computes the detection areas, as well as the BER estimated based on probabilities \(\Phi^{i}_{out}\) computed on the corresponding detection area \(A^{i}\) for each CP. The algorithm first creates a grid by dividing the coordinate plane into small non-overlapping squares (\(a\)), with width and height equal to \(\delta\), and the detection areas are obtained using Algorithm 3 (lines 1-2 in Algorithm 6). Next, \(\Phi_{out}\) is estimated by computing \(\Phi^{i}_{out}\) for each CP \(i\) on the defined grid and averaging for the number of CPs to obtain the symbol error rate (lines 3-9). Finally, the BER is estimated and returned together with the computed detection areas (line 10). ```
1:\(Y\), \(m\) OUTPUT: [\(A^{i}\)], \(BER\)
2:\(A\leftarrow\)CreateGrid()
3:\([A^{i}]\leftarrow\) ComputeDetectionAreas(\(Y\), \(A\), \(m\)) (Algorithm 3)
4:\(\Phi_{out}\gets 0\)
5:for\(i=1..m\)do
6:\(\Phi_{A}(i)\gets 0\)
7:for each\(a\) in \(A^{i}\)do
8:\(\Phi_{A}(i)\leftarrow\Phi_{A}(i)+a.\)maxProb
9:\(\Phi^{i}_{out}\gets 1-\Phi_{A}(i)\)
10:\(\Phi_{out}\leftarrow\Phi_{out}+\Phi^{i}_{out}/m\)
11:return[\(A^{i}\)], \(\Phi_{out}/\log_{2}m\)
```

**Algorithm 6** Nonlinear Mitigation

## 4 Simulation Results

In this section, we evaluate the OCATA-MB digital twin to support MB lightpath provisioning, as well as the proposed on-line MB-RSA algorithm. First, the simulation environment used to generate the datasets needed for training DNN models is presented, and the architecture of the DNN link models is defined. Next, the RChs are selected and used for the feature composition. Then, the nonlinear mitigation technique is evaluated as stand-alone and, finally, used as part of the MB-RSA algorithm. ### MB Optical System Simulation and Modeling

A MATLAB-based simulator of a coherent WDM system developed in [22] was used to generate IQ constellations for 16 QAM@32 GBd signals shaped by a root-raised cosine filter with a 0.06 roll-off factor. For the C+L+S system, we considered 337 optical channels with 50 GHz channel spacing for full spectrum usage. We assumed a pre-FEC BER threshold equal to \(10^{-2}\) in all the cases. Table 2 summarizes the configurations used in the MB transmission simulator. Pseudorandom binary sequences of length \(2^{16}\) were used as the input of every channel. The signal was propagated through spans of standard single-mode fiber, ranging from 70 to 100 km, with a launch power of 0 dBm. Gain flattening filters were used at the end of each fiber span to compensate for the power tilt induced by the ISRS effect. The attenuation factor, chromatic dispersion, and nonlinear (gamma) parameters varied with frequency. The fractional contribution of the delayed Raman response was 0.245 [29].