## 2 Materials and Methods
### Synthetic Data Generation
The convolution neural network (CNN) was chosen to solve the regression problem (A) as it is used in common and powerful architectures such as LeNet5, AlexNet, and ResNet: this decision was based on results derived when different NN architectures were studied within the same research project [29; 30]. Several hidden/deep non-linear layers, as well as a convolution layer, were added to improve performance of the model [31; 32]. With the results observed, the CNN showed a preferable learning rate, with only insignificant loss in accuracy performance. Other architectures showed either worse performance or drastically increased training time [29]. The impact of data preprocessing (problem (B)) is crucial to reduce the number of trainable weights and training time, and to improve the prediction accuracy on the evaluation data [33]. In this study, the following data preprocessing methods were tested:  
* Cleaned time domain data;
* Principal component analysis (PCA);
* Amplitude spectrum;
* Phase spectrum;
* Short-time Fourier transform (STFT) [34]. The created data sets with different representations were used to train the proposed CNN architectural model to recognize the dielectric properties of the material, the thickness, as well as the type and structure of the objects in [29,30]. For better comparison, the evaluation/test data sets with identical data signals during the training process on different data representations were chosen. The rest of the data were divided into a 85%/15% ratio, with 85% designated to the training data set, while 15% of the data designated to validation (chosen randomly for each run). In total, 15 runs are performed for every data representation to determine the average performance for lower parameter prediction error. During synthesized data preprocessing, input data dimensions vary, which increases the complexity of the comparison between different NN models. The input data structure varies, and based on the raw input data from a single receiver is the UWB radar signal data, with a length of 500 (\(\times\)2 the length of the data for bistatic and \(\times\)3 for multistatic setup) most significant readings. The data from a single receiver in spectrum representations consist of 200 features, whereas PCA has only 20. All of the data are one-dimensional, while the STFT data are two-dimensional [34]. The output of the neural network is a single value that corresponds to the predicted output of the material parameter (dielectric permittivity or loss tangent). In many cases, the NN model layers and hyperparameters are chosen by the trial-and-error method, which is often time-consuming and may lead to false assumptions for the best performance. To solve problem (C), the _\"Grid search\"_ method was chosen to increase the performance of the NN and to propose the tuning algorithm for the model and hyperparameters [35, 36, 37]. The tool built in the _\"Tensorflow keras\"_ module was used to determine parameters. With the learning rate and batch size determined, the loss functions were studied to propose the favorable function for further model training. The loss function is one of the crucial parameters of the neural network model; it quantifies the distance between the actual and predicted value of the target data. Mean absolute error, mean squared error (MSE), and custom loss function in the form of root mean squared error were evaluated, as they are commonly used to examine regression problems [38]. Therefore, the transmitted synthetic UWB signal data were used to form data sets of different representations with a single-parameter-varying to solve problem (D) (single-parameter/two-parameter-varying data sets with only single/two parameters being non-constant for every ultra-wideband signal or its representation data were used). In addition, the tuner tool was used to implement additional layers into the model to increase performance by tuning the hyperparameters for each individual layer.