## 5 Results
### GMSK Experiments  
In the first part of the process (learning), we start the systems and read the data. For experiments, we use both GMSK and OFDM UL signals in a phone call as the input to the system. For some SNR values, we acquire the time signal and calculate the energy and entropy to identify the signal in a specific frequency. The frequency depends on the technology and operator, and we use a real operator and phone call to acquire these signals in GSM and 4G-LTE cellular systems. We calculate the energy of the signal using the RTLSDR, and these data are transmitted to the PC where there are on average 100 samples. The results for the GMSK signal can be seen in Figure 6, where a periodic pattern can be seen in time. These results show that the energy of the modulated signal is not constant in time. If we take the energy in a time that is low (under \(-90\) dBm), the results will have a wrong interpretation, thus, we calculate the entropy of the averaged energy signal according to [34]. The next step is to calculate the entropy of the received energy signal. There are two stages: in the first one, there is only a noise signal; the second one is where a PUE attacks. These signals are processed and the entropy of the averaged energy received is calculated, as can be seen in Figure 7. The idea to use entropy to classify the signals is explained is this figure. The first 100 samples are the calculation of entropy in the absence of a malicious PUE signal, while the rest of the samples are taken when a modulated PU signal is present in the frequency. This is how the system detects the PUE attack. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Device**} & **Center Frequency** & **Bandwidth** & **Noise Floor** & **Noise Figure** & **Sensitivity** & **IDR (dB)** \\  & **(MHz)** & **(MHz)** & **(dBm)** & **(dB)** & **(dB)** & **(dBm)** & **(dBm)** \\ \hline USRP2922 & 850 & 20 & \(-113\) & 5 & \(-105\) & 50 \\ RTLSDR & 850 & 3.2 & \(-102\) & 3.5 & \(-97.5\) & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Device Parameters. Figure 6: Average energy pattern for the Gaussian minimum shift keying (GMSK) signal. Based on this information, we observe that entropy values are linearly separable and we increase the probability of detection by implementing an SVM in two stages, namely, the learning part and the testing part. We proceed to take 350 samples for each SNR value from \(-25\) dB to \(0\) dB and apply an SVM in the learning stage process to define the hyperplane and predict the values. The idea is to develop an SVM using two parameters, SNR and entropy, which are experimental values in an indoor laboratory. The parameters for this stage are shown in Table 2.  
After the learning process, we test the SVM algorithm with 1250 samples. The results of this achieve 99% effectiveness for the testing data according to the scikit report. The last stage is to test the system with the modulated GMSK signal in the SDR. We capture the energy signal in real-time, calculate the entropy and average 100 values. These values are sent to the SVM which gives a binary result, one if a PUE is present and zero if a PU is present. A sample of the hyperplane calculation is shown in Figure 8, where the support vectors are the green circles, and the hyperplane and working zone are blue, showing the maximization of the margin. The yellow circles correspond to a PU signal and the black circles correspond to malicious PUE signal. We can see the support vectors and the hyperplane margin in the learning process. In the classifying process, when an entropy value is calculated, the software detects the malicious PUE signal according to the previously stored data from the learning process. We take 10,000 samples for different SNRs and energy values with an objective \(P_{fit}\) of 0.1 [28]. With these values, we measure the practical probability of detection as the times of effective detection over all samples.