Considering the difficulty associated with obtaining real field monitoring data, we used synthetic data to train and test the proposed machine learning-based classifiers. For building a knowledge base (KB) consisting of the synthetic data, it is necessary to calculate the BERs corresponding to the varying different input features. As mentioned above, compared with the approximate formula method using the GN model, the method of obtaining BERs by solving the WDM transmission equations with the SSFM can provide relatively accurate results. Moreover, although the computational complexity is high, the generation of synthetic data can be regarded as the preliminary preparation stage of the classifier training, and the time spent is not considered in the performance index of the classifiers in future predictions. Therefore, we used a relatively time-consuming solution to obtain the BERs by solving the WDM transmission equations using SSFM. Meanwhile, to verify the performance improvement using the synthetic data generated by the transmission equations, we generated synthetic data using the GN model for comparison. Therefore, KB comprises two parts: part I is generated by the transmission equations and part II by the GN model.
For KB part I, generated by the transmission equations, Fig. 2(a) shows the simulation system structure used in the process of generating the synthetic data. It comprises five transmitters, an optical link with N optical fiber spans and amplifiers, a digital coherent receiver integrated with an electric domain compensation function, and a BER calculator. The amplifier accurately compensates for the fiber loss but also adds noise. Without the loss of generality, the center channel is assumed to be a probe channel, and its performance and the XPM effect are studied, whereas the other four channels are interference channels. The fiber parameters include the group velocity dispersion coefficient, fiber loss, and nonlinear parameters. The receiving end performs the demodulation and the electric domain compensation to determine the BERs of the probe channel. Each instance comprises the total lightpath length ranging from 50 to 5000 km; span lengths of 50, 80, and 100 km; the number of spans ranging from 1 to 50; channel launch power varying from –10 to 4 dBm with a 2 dBm interval; and three modulation formats, quadrature phase shift keying(QPSK), 16QAM, and 64QAM. We set the EDFA noise to 5 dB. The channel spacing was set to 50 GHz. The noise bandwidth was 32 GHz, and the symbol rate used was 32 GBaud. According to the principles introduced in Section 2.2.2, the resulting partial KB contains BER observations of 3600 different lightpaths and corresponding labels. Among them, there are 1118 instances of BER<T and 2482 instances of BER>T.
Fig.2 (a) Simulation setup. (b) Workflow of the classification process. MUX: multiplexer, IQ modulator: in-phase quadrature modulator, SSMF: standard single-mode fiber, EDFA: Erbium-doped fiber amplifier, DSP: digital signal processing |
Full size|PPT slide
For KB part II, generated by the GN model, each instance comprises the total lightpath length ranging from 50 to 5000 km; span lengths of 50, 80, and 100 km; the number of spans ranging from 1 to 50; and channel launch power ranging from –10 to 4 dBm. The power interval is 2 dBm, and there are three modulation formats, QPSK, 16QAM, and 64QAM. We set the noise of the EDFAs to 5 dB. The channel spacing is set to 50 GHz. The noise bandwidth is 32 GHz, and the symbol rate is 32 GBaud. First, the GN model is used to roughly estimate the nonlinear noise, and the OSNR is calculated by combining the nonlinear noise with the ASE noise. Thereafter, the corresponding BER is obtained by the mapping relationship between OSNR and BER. According to the principles introduced in Section 2.2.1, the dataset based on the GN model has a total of 3600 instances, where the numbers of BER<T and BER>T instances are 1269 and 2331, respectively.
Figure 3 shows that the KB was divided into three cases. According to the division method described below, these three cases all have 2520 instances for training and 1080 instances for testing. For case I, the training dataset was entirely generated by 2520 instances randomly extracted from KB part I, and the test dataset comprises the remaining 1080 instances. For case II, the training dataset was obtained by 2520 instances randomly extracted from KB part II, and the test dataset remains unchanged from case I. For case III, we randomly extracted 50% of the training dataset of case II and 50% of the training dataset of case I and merged them to form a new training dataset, whereas the test dataset remains the same as case I and case II. Note that the test dataset is the same dataset generated by the transmission equations in the three cases. This is because these data are sufficiently similar to the real field data to accurately measure the performance of the trained classifiers.
Tab.1 Performance of the classifiers |
classifier type | case I | case II | case III |
KNN | LR | SVM | KNN | LR | SVM | KNN | LR | SVM | |
accuracy/% | 97.87 | 89.63 | 99.17 | 83.24 | 84.44 | 88.24 | 97.13 | 85.37 | 99.35 | |
error rate/% | 2.13 | 10.37 | 0.83 | 16.76 | 15.56 | 11.76 | 2.87 | 14.63 | 0.65 | |
false positives rate/% | 1.02 | 4.63 | 0.37 | 9.26 | 8.33 | 5.00 | 1.02 | 6.39 | 0.37 | |
We used the various machine learning classifiers mentioned earlier to classify the lightpaths; thereafter, we compared their performances and selected the best machine learning classifier, as shown in Fig. 2(b). We employed the trained optimal parametric classifiers to predict the BERs of the lightpaths in the test dataset. If the BER of a lightpath is below T, it is a Boolean logic variable equal to 1; otherwise, it is equal to 0, which is the label predicted by the classifier. Here, a label equal to 1 means that it is a “good QoT,” and a label equal to 0 implies that it is a “poor QoT.”
The confusion matrixes in Fig. 4 show the classification results achieved by the classifiers considered in this work for the three different cases. The columns of the matrixes describe the actual classes of the test instances, whereas the rows are the predicted classes by each classifier. Two metrics were generally used to evaluate the classifiers: the classification accuracy and the false positive rate. The false positive (anticipated instances of “good QoT,” when the actual class is “poor QoT”) rate can be used to further refine the prediction performance of each classifier. Figures 4(a), 4(b), and 4(c) show the corresponding confusion matrix for the three cases, respectively. Table 1 depicts that after comparing the results of the three cases, we found that when the dataset is composed of case I, the three classifiers, KNN, LR, and SVM, achieve the highest classification accuracies, i.e., 97.87%, 89.63%, and 99.17%, respectively. However, when the dataset comprises case II, the classification accuracies of the three classifiers are the lowest, i.e., 83.24%, 84.44%, and 88.24%, respectively. When the dataset is composed of case III, the classification accuracies of the three classifiers are between those of the previous two, i.e., 97.13%, 85.37%, and 99.35%, respectively. By observing the relationship between the false positive rate and the classification accuracy in the three cases, it is easy to find that the false positive rate is negatively correlated to the classification accuracy. This indicates that the higher the accuracy of the classifier, the lower the false positive rate of the classifier. It is evident that the classifier with the highest classification accuracy also has the lowest false positive rate, accounting for its best overall performance.
The above comparison results indicate that the classifiers corresponding to case I exhibit the best performance when tested using the test data that are sufficiently similar to real field data. We believed that this is mainly because the training dataset of case I are composed entirely of accurate synthetic data generated by the transmission equations, and the trained classifiers are the most reliable and practical. In case II, the performance is poor when tested using the same data. We believed this is because the training dataset is composed entirely of inaccurate synthetic data generated by the GN model, and the trained classifiers are unreliable. The accuracies of cases I and II also indicate the extent of the GN model deviation from the more realistic transmission equations. This is further verified by case III. In case III, because the training dataset is a mixture of the data generated by both the GN model and the transmission equations, the performance of the trained classifiers was between those of the previous two. Comparing the results obtained in cases I and II, we found that SVM is the best classifier in both cases, although KNN exhibits a different trend. In case I, the classification accuracy of KNN is slightly lower than that of SVM but considerably higher than that of LR. In case II, KNN is not as accurate as LR. The transmission equations approach constitute a better alternative to the GN model (or other similar margin-based models) in the absence of real data (i.e., at the deployment stage of a network) or the case that real data are scarce (i.e., for enriching the dataset/reducing probing lightpaths). We believed the priority of the three classifiers should be SVM>KNN>LR, as shown in case I, rather than SVM>LR>KNN, shown in case II.