## 7 Results
### Training and Testing Data Sets at the Same Level of SNR  
This section aims to describe the result of the comparison of the approach DIFFSNR based on the different TFTs and the one-dimensional representation in the time domain for the data set used in this study. The comparison of the approaches based on the different TFTs are presented in Figure 6 for different values of SNR in dB for the weather radar data set. The accuracy trend for the baseline application of CNN to the 1D time domain representation is also presented in Figure 6. An initial result is that the combination of TFT with CNN has a significantly better performance than the application of CNN directly on the initial 1D time domain representation, in particular for values of SNR \(>\) 10 dB. An additional result is that CWT usually performs better than other TFT in the presence of noise (values of SNR \(<\) 10 dB). In particular, CWT is more robust than WVD and the Smoothed WVD in the presence of noise, even if the Smoothed WVD presents a very minor improvement in comparison to WVD. In low noise conditions (SNR \(>\) 20 dB), all the TFTs combined with CNN have a very high classification accuracy making this approach quite suitable for the identification of wireless propagation channels, at least with the use of pulse-like signals such as the weather radar signal used in this study. This result is consistent with the results in the literature, where pulse-like signals are generally used for channel identification. A detailed report of the accuracy values obtained for the different TFTs and the 1D time domain approach is shown in Table 3 for specific values of SNR in dB. The results are also quite stable in terms of distribution of the accuracy values when we examine the results of the classification algorithm, which (as described in Section 5) are \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**SNR** & **CWT-S** & **CWT-D** & **CWT-M** & **CWT-G** & **WVD** & **SWVD** & **Spectrogram** & **1D** \\ \hline
30 & 0.991 & 0.9851 & 0.9883 & 0.9867 & **0.9918** & 0.9914 & 0.9825 & 0.9652 \\ \hline
10 & **0.9776** & 0.9754 & 0.9684 & 0.9742 & 0.9715 & 0.9701 & 0.9721 & 0.9411 \\ \hline
0 & 0.8891 & 0.8838 & 0.8473 & **0.8965** & 0.8383 & 0.8476 & 0.896 & 0.8405 \\ \hline \(-\)10 & 0.5563 & 0.6085 & 0.5588 & **0.6153** & 0.4832 & 0.4963 & 0.6068 & 0.5981 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Numerical results for accuracy on the weather radar data set. The first column represents the SNR in dB. Then, each column shows the accuracy results for each combination of the TFT and CNN. The row related to the ML is associated to each value of SNR in dB used in this study, and it indicates the choice of the optimal mother wavelet provided by the specific ML (e.g., CWT-G by DT at SNR = 0 dB. Figure 6: Comparison of the different techniques using the weather radar data set in the SAMESNR method. repeated 10 times (the previous figures show the average of the accuracy results). Box plots are used to show the distributions of the results for the radar data set. Figures 7 and 8 show the box plot, respectively, for the CWT (Sombrero) approach and the WVD approach. The distribution of the accuracy results is quite stable (minor spread of the values) in particular for the CWT (Sombrero) approach, while the accuracy results for the WVD approach are more spread out in particular for at lower values of SNR in dB SNR \(<\) 0 dB. A more detailed view of the results of the channel identification is provided by the confusion matrices, which are shown in the following figures. In particular, Figure 9 and the related sub-figures show the confusion matrices for SNR = 30 dB, and SNR = 0 dB for the CWT-S approach. Finally, a comparison with the 1D time domain is done by presenting the confusion matrices in Figure 10 and related sub-figures for SNR = 30 dB and SNR = 0 dB.