## 3 Results and Discussion
### Measured Signals  
Regarding the measured signals, Figure 9 shows the mean and standard deviation of the samples from different captures. The first capture presents evident errors, as already explained; thus, it is not shown in Figure 9. For brevity, only the configuration AIR is shown in Figure 9. Despite the efforts in reducing the noises in the experimental setup, some phase noise is still present in the measurements. Much of it, however, is concentrated in specific frequency bands. One can observe that the phase is unstable around the frequencies 0.85, 1.1 and 1.45 GHz. We identified that this can be associated with changes in the RF divider, which is the output divider that divides down the VCO frequency, that is, the oscillator used to synthesize the signal in the transmitter [27]. The ADF4351 VCO operates in the frequency range of 2.2 to 4.4 GHz, as shown in Figure 10, but three dividers have to be used to generate the desired frequencies. More details can be found in [27]. Figure 8: Simulated complex signals for the three configurations, when changing the variable complex \(\varepsilon_{r}\) of the floor and the probes in a total of 336 curves. Magnitudes are on the left and phases are on the right. From top to bottom we have AIR, MUT and MET. Due to the number of curves, the phase is unwrapped [1; 29] for clarity, and the parameter \(w_{0}\) is kept constant, equal to 0.1. The total error between simulated and measured data is shown in Figure 11, considering the AIR and MUT configurations. We can see how the similarity of the data depends on the virtual probe used to obtain the simulated data and on the complex permittivity of the floor, which are the axes of the subfigures. Probes closer to the center of the setup (the first probes) tend to sub-estimate the values of the real part and have a more pronounced slope on the level curves. The more distant probes (the last probes) tend to be more centered and have smoother level curves. In general, there were lower errors when the imaginary part was 0.1 and the real part was 5. The fact that these minimum errors were within the bounds chosen for the variables was an indicator that the actual properties were close to the simulated properties. By the colorbars of Figure 11, one can observe that the lower bound of the scale diminishes as we change the probes (probe 2, probe 4, and so forth). It is consistent with the fact that the positioning of the probes is from the front of the antenna (that is, higher frequencies not used in this work) to behind it (frequencies used). Figure 10: Correspondence between the synthesized frequencies on the transmitter and the three dividers used to generate them, denominated here as VCO 1, VCO 2 and VCO 3. Figure 9: The mean (**top**) and standard deviation (**bottom**) of the frames in the captures of the configuration AIR, both for magnitude (**left**) and phase (**right**). The first capture was omitted because it was always corrupted by errors at the start of the measurement. If the configurations were analyzed separately, AIR and MUT converged to similar values as the probes changed (from the first to the last). This, however, did not happen with the MET, which maintained a real permittivity of about 3 and an imaginary part of 0.1 for all the probes. This is the reason why in Figure 11, the error from MET is not combined with the reported values. An explanation for this difference is based on how the wave reaches the Rx antenna. The direct path (line of sight) does not exist in the MET configuration and the multi-path is considerably longer than the direct path. The algorithm, however, does not have sufficient information about the propagation, that is, whether it is a situation with a line of sight or a reflected wave, for instance. Therefore, similar values could eventually be obtained from another MUT causing the same delay and attenuation observed in the MET.