## 3 Models and Algorithms
### Nonlinear Mitigation

Let us now analyze the number of areas k that need to be considered in Algorithm 6 to obtain accurate \(\Phi_{\text{out}}\) computations. Figure 10 illustrates the convergence of \(\Phi_{\text{out}}\) with \(k\) for channel 337; similar results can be obtained for the other channels. We observe that a very small error is obtained when 10,000 or more areas are considered, which greatly limits the time of Algorithm 3 to compute the detection areas. Figure 11 shows the estimated pre-FEC BER with and without nonlinear mitigation with the detection areas optimized using Algorithm 6 for three channels, each one from a different band, as a function of the number of fiber spans, when fixing \(k=10000\). We observe an improvement in the resulting pre-FEC BER in all three channels independently of the transmission distance. In particular, we observe that the maximum transmission distance is highly dependent on the selected channel, which stresses the application of OCATA-MB during the lightpath provisioning phase to select a channel that can ensure that the pre-FEC BER threshold is not exceeded. In addition, by configuring the optimal detection areas in the Rx, the maximum achievable transmission distance is effectively extended. Indeed, Figure 11 shows that the reach of Channel 1 can be extended by one additional span without exceeding the pre-FEC BER threshold when nonlinear mitigation is implemented. Similar conclusions can be drawn for Channels 150 and 337. For illustrative purposes, Figure 12 shows the optimized detection areas for Channels 1, 150, and 337 after

Figure 9: Evolution of pre-FEC BER as a function of the number of spans for several channels. transmission along six spans. We observe different shapes of the detection areas for the different channels needed to mitigate the different impact of NLI noise, mainly due to SRS. ### Lightpath Provisioning

Finally, let us evaluate the performance of the OCATA-assisted on-line MB-RSA algorithm defined in Algorithm 4. To this end, a simulation environment was implemented in Python, and the Spanish 10-node core network topology (Figure 13a) with links with various configurations was assumed. In addition, to evaluate the performance of the NLI noise mitigation strategy, Algorithm 4 was used with and without NLI noise mitigation (i.e., with and without executing lines 17-21). For benchmarking purposes, the traditional first-fit channel assignment with QoT assurance was considered, where QoT was estimated

Figure 11: Real and estimated pre-FEC BER with squared and optimized detection areas vs. # spans for ch. 1 (a), 150 (b), and 337 (c). Figure 12: Optimal detection areas (k = 10,000) for QAM-16 signals for five spans. (a) Ch. 1 in the S band, (b) Ch. 150 in the C band, and (e) Ch. 337 in the L band. Figure 10: Estimated pre-FEC BER for different number of areas. for the selected channel, and the request was rejected in case the required QoT was not met for that channel. The simulation assumed a static traffic model, i.e., the simulation started with no traffic on the network, and connection requests were served sequentially between randomly chosen source and destination nodes. Once a connection was successfully provisioned on the network, it stayed without being changed or removed from the network. For the sake of simplicity, a set of 1000 connection requests was generated beforehand, checking that the shortest route could provide the required QoT for at least one channel assignment. The simulator was then run for every considered approach with the same pre-generated list of connection requests. The number of shortest routes between each pair of nodes was limited to three in all the cases. Figure 13b shows the number of requests blocked, whereas Figure 13c depicts the blocking ratio as a function of the number of connection requests.