## 7 Results  
The aim of this section is to provide the results of the application of CNN. As described before, the application of the CNN in the presence of noisy samples can be executed using different approaches. In one approach (SAMESNR), the training and test phase is executed on subsets of the data set with the same level of SNR. In another approach (DIFFSNR), the training set is based on a subset of a data set at one or more specific levels of SNR in dB, and the testing and prediction are based on different levels of SNR in dB. The first approach is simpler to implement, and it is based on a coherent data set because the training and testing samples are extracted from the same data set. On the other hand, it is not consistent with a practical application of the fading channel classification because the SNR values of the data set on which the DL model is trained can be different from the actual SNR value in the field. The second approach addresses this shortcoming, but the different levels of SNR for the training and testing sets must be defined. In this study, for the second approach, we set 30 dB for the SNR of the training data set and progressed lower values of SNR for the testing set. This execution aimed to reproduce a context where the training samples were collected in a relatively high SNR level in a laboratory, and then the fading channel prediction was actually performed in the field with more difficult propagation conditions and a strong presence of noise. The first Section 7.1 provides the results of the optimization process for the CNN, where the impact of the different hyper-parameters is evaluated and optimized using the SAMESNR method. The second Section 7.2 provides the comparison of the results of the different approaches (e.g., 1D against time-frequency representations) for the SAMESNR method in terms of the evaluation metrics identified before (accuracy and confusion matrices). The third Section 7.3 provides the comparison of the results of the different approaches (e.g., 1D against time-frequency representations) for the DIFFSNR method in terms of the evaluation metrics identified before (accuracy and confusion matrices). A more important aspect presented in Section 7.3 is related to the evaluation of the novel adaptive approach proposed in this paper. We have evaluated the adaptive approach for the DIFFSNR methods rather than the SAMESNR method because the differences in performances among the different combinations of the time-frequency transforms and CNN are more evident in the DIFFSNR method. Finally, the fourth Section 7.4 provides computing time estimates to execute the different steps in the proposed approach and highlights the considerable improvement in time efficiency in comparison to the traditional exhaustive approach. Regarding the notation, the approaches based on the different time-frequency representations will be identified for the CWT with CNN as CWT-S, CWT-D, CWT-G, or CWT-M. For the application of CNN to the Wigner Ville distribution, the notation is WVD. For the application of CNN to the Smoothed Wigner Ville distribution, the notation is SWVD or Smoothed WVD. For the application of CNN directly to the 1D time domain representation of the signal, the notation is 1D. Optimization of the Convolutional Neural Network Parameters with Training and Testing Data Set at the Same SNR Level  
As anticipated in Section 5, an assessment of the impact on the classification performance of specific CNN hyper-parameters was implemented, and the optimal values are shown in Table 1 for a specific time-frequency representation: the CWT with the Morlet mother wavelet. The aim of this section is to show how significant can be the improvement in classification accuracy due to the optimal choice of the hyper-parameter value. Note that these results are also based on the optimal values of the voices per octave shown in Table 2.  
The results of the optimization process are shown in Figure 5 for the specific case of CWT-S for the weather radar data set.