## 3 Results and Discussion
### Parameter Estimation Using the NN
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Repres.** & **Signal** & \multicolumn{2}{c}{**Error in**} & \multicolumn{1}{c}{**Training**} & \multirow{2}{*}{**Parameters**} \\  & & **Prediction \(\times\) 10\({}^{-3}\)** & & & \\ \hline \multirow{4}{*}{\begin{tabular}{c} Time \\ domain \\ \end{tabular} } & Refl. & \(1711.83\pm 34.88\) & 17.28 & 16227 \\  & Trans. & \(1231.36\pm 20.11\) & 12.95 & 16227 \\  & Bist. & \(410.81\pm 11.32\) & 11.2 & 7337 \\  & Multist. & \(240.05\pm 5.07\) & 15.59 & 10921 \\ \hline \multirow{4}{*}{PCA} & Refl. & \(170.91\pm 5.31\) & 2.7 & 1619 \\  & Trans. & \(181.88\pm 4.11\) & 2.38 & 1619 \\  & Bist. & \(192.76\pm 3.77\) & 2.69 & 1619 \\  & Multist. & \(141.03\pm 3.31\) & 2.9 & 1619 \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Amplitude \\ spectrum \\ \end{tabular} } & Refl. & \(200.01\pm 5.1\) & 19.62 & 3313 \\  & Trans. & \(3200.1\pm 505.09\) & 23.17 & 3313 \\  & Bist. & \(1310.57\pm 207.31\) & 29.98 & 6033 \\  & Multist. & \(990.22\pm 139.35\) & 54.35 & 8769 \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Phase \\ spectrum \\ \end{tabular} } & Refl. & \(990.1\pm 110.37\) & 12.06 & 689 \\  & Trans. & \(740.9\pm 60.21\) & 8.34 & 689 \\  & Bist. & \(751.33\pm 61.01\) & 12.79 & 1089 \\  & Multist. & \(562.41\pm 40.1\) & 17.67 & 1489 \\ \hline \multirow{4}{*}{STFT} & Refl. & \(532.23\pm 36.5\) & 21.93 & 30839 \\  & Trans. & \(362.65\pm 20.34\) & 26.46 & 30839 \\ \cline{1-1}  & Bist. & \(437.71\pm 40.1\) & 77.46 & 61559 \\ \cline{1-1}  & Multist. & \(521.32\pm 49.21\) & 110.77 & 92279 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Dielectric loss \(tan\delta\) parameter estimation with different representations. signal will not be further studied. The obtained results are shown in the Table 4. For data sets with noise added to the generator signals, two scenes were evaluated to estimate the ability to predict the parameter value. The first scene consisted of data sets with different noise levels, both in training and evaluation data sets. The second scene consisted of UWB signal data with no noise added to the generated signals, while the NN model evaluation was performed on data with different noise levels. Therefore, such evaluation shows  
1. Whether the parameter evaluation is achievable with noisy data;
2. Whether parameter prediction is possible on noisy data while training with synthesized data without any noise added;
3. How the noise level affects the accuracy of the parameter prediction. The noise added to the used data sets in Table 5 was created in OpenEMS by adding random noise to the EDI radar signal used for excitation of the antennas. Testing such types of noise was conducted due to the hardware often not being ideal. Therefore, thermal or flicker noises might occur along with other noises such as crosstalk, interference, capacitive coupling, or ground loops. The results in Table 5 show that it is important to include in training data with noise: the case when NN was trained only on the data set without noise shows worse parameter estimation performance than the case when NN was trained on data with added noise. With the increase in the noise level, prediction error increases due to noise influence on the signal data stability. The prediction errors are satisfactory for the relative permittivity estimation of 0.05, 0.1, and 0.15 noise levels. On the other hand, the loss tangent predictions are chaotic and exhibit large prediction error deviations. Therefore, data with noise is preferable to the training data set as additional information. The results on the synthesized UWB signal data with various noise levels are shown in Figure 9 for dielectric loss parameter estimation (identical behavior was established with relative permittivity). The relative permittivity showed better prediction results with higher accuracy, while loss tangent values were harder to predict (as with previous accuracy performance evaluations).