## 5 Discussion of the Results
### Identification
#### 5.1.1 Optimization of the Hyperparameters
Finally, the optimization of the hyperparameters of the machine learning algorithms was performed. In this paper, we compared the results of three different machine learning algorithms: SVM (using a Radial Basis Function (RBF) kernel), KNN and decision trees. The optimization of the SVM was performed for two hyperparameters: the scaling factor of the RBF kernel and the penalty factor C [29]. A grid approach was adopted to calculate the hyperparameters in the range of \(2^{1}\) to \(2^{12}\) for both hyperparameters. The optimization process was  
Figure 5: Comparison of the performance accuracy with KNN using Morlet and bump wavelets for different values of K.  
Figure 6: Comparison of the performance accuracy with KNN for the magnitude and phase components of the signal in the time domain for different values of K.  
applied to each of the 10 folds, and the results were averaged. The results of the optimization analysis are shown in Figure 7 for a specific fold (where the specific fold result was the same of the average value), where the optimal value is highlighted with a black circle. For WSST and KNN, the optimization results can also be seen from the previous Figures 5 and 6 where K (K = 3) for the KNN algorithm is the optimal value. In the application of the decision tree algorithm, the hyperparameter to optimize is the maximum number of splits for each branch. The optimal value is 12 for WSST. The optimization process was repeated for the other representations of the digital signal (time domain, frequency domain and STFT) by averaging the results from each fold. The summary of the optimal values is shown in Table 2 for all the representations and for all the machine learning algorithms. The optimal values and machine learning algorithms were used in the subsequent sections of this paper. Table 2 shows that the technique based on WSST significantly outperformed the other representations of the digital signal (time domain, frequency domain and STFT) for all the used machine learning algorithms. In other words, the superior performance of WSST was proven in a consistent way regardless of the machine learning algorithm. Table 2 also provides the computation time requested by each machine learning algorithm and for each representation. The times were also based on averaging the results as written above. The computation time was expressed as the ratio with the smallest computation time (i.e., decision tree with time domain representation). The computation time is another metric (together with the identification accuracy) that a user can evaluate to decide the best technique in the practical deployment of the physical layer authentication approach described in this paper. It can be seen that the WSST required a larger computation time than the other techniques, while the most efficient technique was the time domain representation. The results from Table 2 were obtained on the experimental dataset where the RF signal was collected by the SDR in Line Of Sight (LOS) conditions and for high values of SNR. In the next subsection, we evaluate the performance of the WSST-based technique in the presence of AWGN for different values of SNR. Figure 7: Optimization of the scaling factor and the penalty factor for SVM. .1.2 Comparison of the WSST-Based Approach with Other Signal Representations in the Presence of AWGN  
In the preliminary paper [2], an initial comparison was performed for different values of SNR using KNN as a machine learning algorithm with K = 1. The result has shown that the WSST-based techniques outperformed the other techniques for medium and higher values of SNR. The robustness of the identification algorithm in the presence of noise is an analysis commonly performed in the literature [26; 27], to evaluate the impact of attenuation due to the propagation loss or the presence of obstacles (e.g., walls).