## 5 Discussion of the Results
### Authentication  
In this section, we investigate the performance of WSST in comparison to the other techniques for the problem of authentication. The confusion matrix provided in Figure 9 shows that the final three mobile phones were the most difficult to distinguish. Then, in this section, we focus on the authentication of two of these phones (Phone 10 and Phone 12). As for the previous results, we used the optimal values of WSST from the previous section and the SVM machine learning algorithm identified in Table 2.  
Figure 11 shows the results for the EER metric for the authentication of Phone 10 against Phone 12. The scenario is that Phone 12 claimed to be Phone 10 and the EER was used to measure how well the algorithm was able to authenticate Phone 10. Figure 11 shows the comparison of the performance of WSST against the other representations. The results are consistent with the analysis on the identification accuracy: the WSST-based approach provided a higher authentication accuracy (lower EER for medium/high values of SNR) in comparison to the other representations. For lower values of SNR, the other techniques performed better than WSST, which was consistent with the findings of the previous section where STFT performed better than WSST at lower SNR. On the other side, a low accuracy limits the practical use of this technique. Then, for low values of SNR, all the techniques would have a limited use (as also reported in the literature), and filtering techniques should be used to remove the presence of noise [7]. Figure 12 shows the ROCs for the WSST-based approach with SVM for different values of SNR. The results are consistent with the previous Figure 11 because higher values of SNR generated ROC curves that showed a better authentication. iPhone) has been removed from the training set and then tested against the training model built with the other 11 devices, where nine devices belonged to three different models (i.e., three Sony Experia devices, three HTC One devices and three Samsung S5 devices) and two devices belonged to the same iPhone model. The expected result was that the classification algorithm should predict that the unknown phone did not belong to the three models Sony Experia, HTC One and Samsung S5. It should predict that it was an iPhone model. On the other side, the classification algorithm should also predict that the unknown device was not one of the two specific iPhones (called iPhone 1 and iPhone 2 in the rest of this section). In an ideal case, the classification results should indicate a random choice (50% probability) that the unknown device was one of the two iPhones. The results for Case (a) are shown in Table 3 for all the different representations. The SVM algorithm has been used in this case. For completeness, the classification has been repeated for  
Figure 11: Evaluation of the authentication performance in the presence of noise between Device 10 and Device 12 using EER for the different techniques. SNR is expressed in dB. Figure 12: ROCs for the authentication performance between Device 10 and Device 12 for specific values of SNR. SNR is expressed in dB. different values of SNR. The predicted percentage in the first column shows the predictions against the devices of the three models (Sony Experia, HTC One and Samsung S5), and the second and third columns show the predicted percentage against the iPhone 1 and iPhone 2. The results confirm the initial assumptions: for high values of SNR, the algorithm successfully predicted that the unknown device was not one of the three models (i.e., Sony Experia, HTC One and Samsung S5) as the predictions were zeros for all the techniques (first column in Table 3). The predicted percentage was not zero for the iPhone 1 and iPhone 2 as the algorithm predicted that the unknown device was of type iPhone. We note that the WSST-based technique provided the best predictions, because the predicted percentage was almost equally divided between iPhone 1 and iPhone 2.