## 3 Methodology  
The overall methodology for the generation, processing and input to CNN is provided in Figure 1. In the first phase, a weather radar pulse signal is generated with a signal generator in the JRC radio frequency laboratories as described in Section 4. Then, the signals are transmitted through the channel emulator with different conditions of fading. The output of the channel emulator is recorded in IQ format and the data set is labeled: all the data related to a specific channel condition is labeled as such. Then channel conditions are based on the 3 GPP-TDL models (3 GPP-like channel models) defined in the standard 3 GPP TR 38.901 version 14.0.0 Release 14 standard (page 66 to 70) [20]. Additional details on the adopted 3 GPP-like channel models are provided in Section 4.2. Six classes of labels are defined: No Fading, TDL-A, TDL-B, TDL-C, TDL-D, and TDL-E. The fading conditions are also generated in the channel emulator with different values of SNR in dB to evaluate the robustness of the proposed approach to the presence of noise. The data is then normalized on the basis of the RMS power. Then, different TFTs are applied to the signals. In this study, we have used the WAVELAB library from [21] for the implementation of CWT. In the WAVELAB library, the mother wavelets are real. Then, the output of the application of the CWT is also real as the original raw data is real. The output of the TFTs is normalized between 0 and 1 to be given as an input to the CNN. The architecture of the CNN and related hyper-parameters is described in detail in Section 5. Finally, the output of the CNN is used to evaluate the performance of each TFT using accuracy and confusion matrices. The main hyper-parameter of this approach is the mother wavelet to be chosen. In this study, we use the Gaussian, derivative Gaussian, Morlet, and Sombrero (i.e., Mexican hat wavelet), which are identified in the rest of this paper with the following notations: CWT-S (Sombrero), CWT-D (derivative Gaussian),CWT-G (Gaussian), and CWT-M (Morlet). The problem is still to find the optimal mother wavelet. A method based on the application of the CWT and the CNN classification for each mother wavelet would be cumbersome because the CNN classification takes a considerable amount of computing time and resources, and it should be preferably minimized. Then, a preliminary process is adopted to choose the optimal mother wavelet. The step of applying the CWT with four mother wavelets is still executed, but instead of giving the wavelet representations directly to the CNN, a feature extraction process is implemented where the entire CWT transformed sample (i.e., the weather radar signal) is represented with a significant dimensionality reduction with only three features: its variance, skewness, and kurtosis. These features have been chosen because they are commonly used in literature for feature extraction in wireless communication classification problems [22], and they are simple to compute. Then, a shallow machine learning algorithm is applied for each of the mother wavelets. The mother wavelet, where the classification performance is the best, is chosen for the application of CNN. This adaptive approach is based on the assumption that the extracted features and the machine learning algorithms are able to select the optimal discriminating mother wavelet. This assumption has to be validated by the results of the data set. The advantage of the proposed approach is to save the repeated execution of the CNN with different mother wavelet representations at the cost of performing the feature extraction process and the application of the ML algorithms. Both steps require limited computing resources in comparison to the application of CNN, as shown in Section 7. Finally, another aspect of the proposed approach is related to the addition of Gaussian noise and the composition of the data set described in Section 4.2. Two methods are applied in this study:  
1.