## 7 Results
### Training and Testing Data Sets at Different Levels of SNR and Results from the Adaptive Approach  
The following Figure 11 shows the comparison of the different techniques using the weather radar data set with the DIFFSNR method. Figure 11 shows also the application of the adaptive proposed approach. The first finding, which can be extracted from the analysis of Figure 11, is that the act of training the CNN model with a data set at a different SNR than the testing data set usually degrades the classification performance in comparison to the SAMESNR method where the testing and training data sets are the same SNR level. This is to be expected because the presence of noise can change the structure of the data, and the CNN algorithm finds it more difficult to distinguish the fading classes. The second finding is that the choice of the Mother Wavelet (MW) is even more important in DIFFSNR than in SAMESNR because the differences between the different approaches are greater in DIFFSNR. We also note (in a similar way to the findings of SAMESNR) that no approach provides the optimal performance for all the values of SNR in dB. For example, the Smoothed WVD is more robust to noise than the WVD, as expected (because of the smoothing effect), but its accuracy is worst than WVD for values of SNR higher than 15 dB. A similar analysis is valid for the choice of the MW. Then, the application of an adaptive approach to automatically select the optimal wavelet is even more important in the DIFFSNR method than in the SAMESNR method. Figure 11 shows the performance obtained for different values of SNR in dB for the adaptive method using the Decision Tree (DT) algorithm. It can be seen that the adaptive approach is able to select automatically the optimal or the quasi-optimal MW for each value of SNR in dB. The algorithm fails to find the optimal value in the presence of strong noise at SNR = \(-\)15 dB, presumably because the fading conditions are so obscured by the noise that the information on the optimal wavelet is basically lost. On the other hand, at SNR = 15 dB, no TFT combined with CNN is able to classify the fading channels correctly, and most of them achieve an accuracy, which is barely above the random choice (which is accuracy = 1/6 or 0.1(6)). The optimal performance is obtained with the CWT-G and secondly with CWT-S and CWT-D. This is also expected because these wavelets are the  
Figure 10: Confusion matrices for the weather radar data set with 1D time domain representation at different values of SNR in dB. Figure 9: Confusion matrices for the weather radar data set with CWT (Sombrero) at different values of SNR in dB. ones that are more similar to the original pulse-like weather radar signal. On the other hand, the impact of the fading channel conditions is able to distort such pulse-like signal, which is the reason why no approach is able to obtain the perfect classification accuracy of 100 even at SNR = 25 dB. The adaptive curve shown in Figure 11 is obtained using the DT algorithm to choose the MWs. In this study, we have also used the SVM and KNN algorithms. Then, it is interesting to evaluate the related performance of the three algorithms. The results are shown in Figure 12 where the differences between the ground truth (the optimal accuracy among all the approaches) and the value of the accuracy obtained for the MW obtained by the ML algorithm is shown for each value of SNR in dB and for all the three ML algorithms. The overall sum of the differences across the 9 values of SNR in dB is shown in the legend box for each ML algorithm. We can see that the DT algorithm obtains the smaller sum of differences among the three ML algorithms, but the SVM is able to select the optimal MW for most of the values of SNR in dB. On the other hand, SVM is much worst than the other ML algorithms for the lowest value of SNR (SNR = \(-\)15 dB) and the highest value (SNR = 25 dB). Then, there is a potential trade-off to consider.