## 2 Materials and Methods
### Data Accumulation and the Process of the Proposed Method  
By following the aforementioned method, 80 simulated multilayer structures were created. In each simulated structure, 101 X-Band frequency points in the range of 7 GHz to 13 GHz are taken into account as a signal goes through the structure. The MUTs are considered as the low-loss dielectric materials whose relative permeability is around 1 and relative permittivity values are distinct and close to five base values: 2, 2.5, 3, 3.5, and 4. They are closely approximated to the base value. For example, if the base value is 2, the distinct actual value is randomly chosen in the range of 1.9 to 2.1. The MUT thicknesses variating from 7 mm to 10.5 mm with a small increasing step of 0.5 mm result in eight values: 7, 7.5, 8, 8.5, 9, 9.5, 10, and 10.5 mm. Each thickness was combined with ten  
Figure 2: Multilayer structure of simulated measurement. distinct permittivity values extracted by the above random method approximating from all five base values (two permittivities were approximated from each base value for each thickness). As a result, 80 combinations of all thicknesses and permittivities were involved in the simulation. The design of the multilayer structure is shown in Table 1.  
The simulated geometry has been mathematically modeled as three stratified regions, each with differing EM propagation parameters. Figure 2 illustrates that the interested MUT volume is surrounded by two air layers where the extracted scattering parameters of each structure contain both air layers and MUT volume. In order to obtain the exact scattering parameters of the MUT for the further steps, the de-embedding procedure must be implemented [22; 23]. The process of de-embedding the MUT fixture using T-parameters [24] is as follows:  
\[T_{Measured}=T_{air1}T_{MUT}T_{air2} \tag{10}\]  
\[T_{MUT}=T_{air1}^{-1}T_{Measured}T_{air2}^{-1} \tag{11}\]  
where:  
* \(T_{Measured}\) is converted from the scattering parameter of the whole structure;
* \(T_{air}\) is calculated by converting the scattering matrix defined in (12) for an idealized section of air of length \(L\) (\(L\) is the distance from antenna to MUT). \[S_{air}=\left[ \begin{array}{cc}0&e^{-\beta\pi/L}\\ e^{-\beta\pi/L}&0\end{array} \right] \tag{12}\]  
In this study, we conducted a real free space measurement and compared its results with those of the simulation to validate the difference of the de-embedding and NIST iterative methods on both types of data. The free space measurement is depicted in Figure 3, where the bistatic setup is used to measure an acrylic specimen whose permittivity is around 2.5 and thickness is 10 mm. The X-band signal with a frequency range of 8-12.4 GHz is caused by the MUT. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Frequency range & 7–13 GHz \\ Relative permittivity & 2–4 \\ Dielectric dissipation & 0.01 \\ Relative permeability & 1–1.02 \\ Magnetic dissipation & 0.0001 \\ Thickness of MUT & 7–10.5 mm \\ Distance from antenna to MUT & 5 cm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input parameters of simulation procedure. Figure 3: The bistatic experiment setup. Figure 4 below shows the S11 and S21 of one multilayer structure after performing the de-embedding process, which are now ready to be used in the NIST iterative method for the dielectric constants of the MUT. Figure 5 illustrates the dielectric constants of the MUT by applying the NIST iterative method to the de-embedded scattering parameters from the data of the simulation and the real measurement. It can be seen that the dielectric constants attained from simulated and measured data are closed to each other and to the actual values of the MUT. The NIST iterative method provides accurate outputs as well as helps to prevent the inconsistent results caused by the significant deterioration of S11 if using the NRW method [17]. Figure 4: The de-embedded S11 and S21 of MUT from (**a**) measurement and (**b**) simulation.