## 4 Materials and Methods
### Methodology  
The overall methodology for the classification of the wireless devices using the WSST is shown in Figure 1. \begin{table}
\begin{tabular}{l l} \hline Sampling frequency & 1 MS/s IQ \\ \hline Sample recording time & 60 s \\ \hline Downlink frequency & 935.2 MHz \\ \hline Uplink frequency & 890.2 MHz \\ \hline Synchronization & GPS only, using GPSDO (min 4 satellites, \\  & min 30 min lock) \\ \hline Distance between DUT and RX & 0.84 m \\ \hline USRP gain & 5 \\ \hline GSM arfcn & 1 \\ \hline OpenBTS version & 3.1.3 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters for signal collection. Figure 1: Overall methodology used in this paper for the identification and authentication of the wireless devices. The methodology to generate the fingerprints from the RF signals consisted of the following steps:  
1. Each of the 12 wireless devices (i.e., GSM mobile phones) were activated, and they started to transmit in a controlled environment where a specific transmission channel is used. 2. The signal in space from the wireless devices was collected using the SDR USRP type N200 receiver with the configuration described in the previous section. 3. The real-valued signal samples were sampled directly in In-phase and Quadrature components (IQ) format and then synchronized and normalized offline to extract the burst of traffic associated with each payload. For each wireless device, a set of 800 bursts was processed for a total of 800 \(\times\) 12 = 9600 bursts. 4. From each burst, the content (payload data associated with the voice communication) was removed. In this way, each burst has only the transients and the preamble, which is the same for all the bursts and all the devices. After the removal, each burst is around 130 samples in length. An image of the normalized magnitude of the GSM bursts after synchronization, normalization and content removal is presented in Figure 2, where the differences among wireless devices can be seen especially near the transients. We note that the granularity of the digitized signal (i.e., number of samples for each burst) used for identification is quite inferior to the granularity of the datasets used by other authors [6; 12; 18], where a very high identification accuracy is obtained. This is intentional because the objective of this paper is to show that the application of WSST provides a better performance than conventional techniques from the literature in difficult datasets like the one used in this paper. 5. WSST was applied to each of the bursts recorded in the test bed. A representation of the burst is shown in Figure 3 for the Morlet mother wavelet, the scale factor \(a=10\) and the entire GSM burst. 6. Different machine learning algorithms are used for classification to implement identification and authentication: Support Vector Machine (SVM), K Nearest Neighbor (KNN) and decision trees. A 10-fold method was used for all the machine learning algorithms. Each collection of statistical fingerprints is divided into ten blocks. Nine blocks from each device are used for training, and one block is held out for classification. The training and classification process is repeated ten times until each of the ten blocks has been held out and classified. Thus, each block of statistical fingerprints is used once for classification and nine times for training. Final cross-validation performance statistics are calculated by averaging the results of all folds. 7. Optimization of the hyperparameters: In the application of WSST, the scale factor \(a\) from Equation (1) is used as a hyperparameter. The window size both for WSST and STFT is set to 10 because this is roughly the size of the transient of the burst. Each of the machine learning algorithms can be optimized on the basis of specific parameters (e.g., K index for the KNN algorithm). The optimization of these parameters is described in detail in Section 5. 8. Metrics definition: For identification, the overall identification accuracy is used as a metric to evaluate the performance of the identification.