## 5 Discussion of the Results
### Identification
#### 5.1.1 Optimization of the Hyperparameters  
The WSST has different parameters (e.g., degrees of freedom), which can be optimized for the specific problem to be addressed. In this paper, we choose the two following parameters for our analysis: (a) the number of octaves and (b) the mother wavelet: Morlet or bump. Another parameter is the identification of a specific segment of the digital representation of the signal, which can be more  
Figure 3: Spectrogram of the synchrosqueezing transform of the digitized signal from the wireless devices. Figure 2: Normalized magnitude of 12 bursts (one for each wireless device). appropriate for classification. Signals captured from the wireless devices are usually represented as bursts, which are repeated in time, and they are usually composed by a transient portion and a steady portion. The digital representation of the GSM burst signal used in this work is provided in Figure 2. As described in the related work, some papers focus only on the transient phase of the digital signal, while other papers focus on the steady part. In this paper, the optimal segment is determined in an empirical way. In addition, the WSST can be applied to the entire complex digital output from RF emissions or only the magnitude (see Figure 2) and phase components in the time domain. Then, we have four degrees of freedom, which must be evaluated to determine the optimal values. Because the analysis of all four degrees of freedom (1 magnitude or phase, 2 segment, 3 scale factor, 4 base wavelet) will be too complex to pursue (the optimization should be conducted in a four-dimensional space), a piecewise approach is adopted. In the first step, the segment and the scale factor \(a\) from Equation (1) are optimized. A simple KNN neighbor algorithm with K = 1 is used to avoid the process of the optimization of the hyperparameters of the machine learning algorithm. The next step is to optimize the scale value \(a\) and the segment of the burst at the same time. In comparison to the preliminary paper [2], where the optimization was performed with a specific scale factor value (\(a=10\)), in this paper, we conduct a more extensive analysis on the bidimensional space of the WSST scale factor and the segment index. In this paper, the WSST representation is divided into 10 segments along the X axis (e.g., the samples of the burst). The reason for this choice is based on two reasons: (1) the visual analysis of Figure 2, which shows that the strongest deviations from the ideal shape of the GSM burst are in the transient region, and (2) the results of [28], which showed an improved accuracy using transients rather than the steady portion of the GSM burst. The result is shown in Figure 4, where it can be seen that the optimal segment is three, which is consistent with the original paper [2], while the optimal scale factor is 20, which provides a slighter improvement to the values of 10 adopted in the original paper. We note that the choice of the segment is the most relevant element to contribute to the performance. Then, a comparison of the Morlet and bump wavelets was performed, and the results are shown in the bar graph of Figure 5. The evaluation was performed using the KNN machine learning algorithm for different values of K (from one to 10). The result showed that the accuracy obtained using the Morlet wavelet in WSST was significantly better than the bump wavelet for all the considered values of K. The results are consistent with the initial findings of [2]. Figure 4: Accuracy for different values of segment Id and the scale factor value. A comparison of the amplitude and phase components of the digitized signal was performed, and the results are shown in the bar graph of Figure 6. The evaluation was performed using the KNN machine learning algorithm for different values of K. The results show that the best accuracy was obtained using the magnitude component in the time domain. The results are consistent for all the considered values of K, and they also confirm the initial findings of [2].