Figure 6 compares the reflection coefficients of the different materials versus incident angle at selected frequencies. The reflection coefficient of the mirror and glass is generally higher than that of plaster and wood. In addition, all four materials follow the rule that the reflection coefficient increases with the incident angle, which is consistent with the characteristics of vertically polarized waves.

Figure 6 Measured reflection coefficients of four materials as a function of incident angle at 240 (a), 250 (b), 280 (c), 290 (d), 320 (e) and 330 (f) GHz.

Note that there are local deviations from the overall trend. It is possible that this is an error in the experimental process, which may be a consequence of the more complex factors to be considered in the reflection path and power measurements compared to the LOS path. However, we prefer to believe that there are other factors contributing to the fluctuations in the data, such as the complex permittivities, which must be verified by more refined and extensive experiments in the future.

Figure 7 shows the reflection coefficients of the different materials over frequency at an incident angle of 80 degrees. When the incident angle is constant, the reflection coefficient decreases as frequency increases. Generally, the Rayleigh criterion is used to characterize the roughness of a medium surface relative to the wavelength of incident light:18

According to the Rayleigh roughness coefficient theory, when the incident angle is constant, higher frequencies are more likely to be considered rough on the same surface. The experimental results fit well with this theory.

Figure 7 Measured reflection coefficient of different materials as a function of frequency at a fixed incident angle of 80 degrees.

MMSE Method for Estimating the Dielectric Constant of Reflective Surfaces

In the theoretical model, there are four variables that affect the change in the reflection coefficient, namely incident angle θi, wavelength λ, relative dielectric constant εr and surface roughness hrms. The values of θi and λ can be easily determined, but εr and hrms are difficult to measure; so, it is difficult to evaluate the accuracy of the model by comparing the theoretical and measured values. However, the process can be reversed and the relative dielectric constant and surface roughness estimated by measuring the reflection values and employing a theoretical reflection model.

In statistics and signal processing, the MMSE estimator is a function that minimizes the mean square error (MSE), which is usually referred to as the optimal estimator. The MSE represents the degree of match between the predicted value and the true value, as shown in the following equation:

Where represents the predicted value, Yi is the true value, and n is the sample size.

When the model has been established but certain parameters are still unknown, these unknown parameters can be estimated by taking the minimum MSE, which is the MMSE method.

The MMSE method is used to set the ranges of εr and hrms, calculate the corresponding theoretical reflection coefficients, compare them with the actual measured values, calculate the MSE, select the theoretical value closest to the measured value and obtain the best values for εr and hrms. Table I shows the εr and hrms values obtained for different materials at different frequencies using the MMSE method.

TABLE I

εr AND hrms VALUES OBTAINED BY THE MMSE METHOD FOR DIFFERENT MATERIALS AT DIFFERENT FREQUENCIES

From the estimated values in Table I, the estimated surface roughness values of wood, plaster and organic glass are all zero, which can be understood as these surfaces are considered smooth in this range of wavelengths. However, it cannot be ruled out that the influence of surface roughness is not fully reflected due to insufficient data.

The relationship between relative permittivity obtained by MMSE and frequency is plotted in Figure 8. The estimated values of relative permittivity for three materials; wood, plaster and organic glass are concentrated in a small range, which shows that the relative permittivity is an inherent property of the material, consistent with the measurements.

Figure 8 Relationship between relative permittivity and frequency of four materials obtained using the MMSE method.

The estimation of the relative permittivity and surface roughness for the mirror is not ideal, as shown by the large fluctuation in relative permittivity, and the surface roughness only appears at a specific frequency, which is unusual. It is believed that this anomaly is related to the presence of metals in the mirror’s composition. In fact, a similar measurement conducted with an iron plate yielded unexpected results as well. Not only were estimated values inconsistent with those determined through the MMSE method, but the relationship between the reflection coefficient and the angle or frequency did not match the theory. We believe that the reflective properties of metal surfaces are quite different from those of non-metals and other factors must be considered. This requires further exploration in future experiments.

CONCLUSIONS

The reflection characteristics of common materials at THz frequencies are investigated based on measurements from 220 to 330 GHz of the reflection path and analyzing the relationship between reflection coefficients, incident angles and frequencies. The experimental results show that the reflection coefficient depends on the type of material when a vertically polarized wave is incident.

The reflection characteristics of non-metallic materials behave in accordance with theory, increasing with frequency and incident angle. The reflection properties of metallic materials, however, differ significantly from theory and require further investigation.

The use of the MMSE method for estimating the relative dielectric constant and surface roughness of reflective materials introduces a new approach for studying reflection characteristics.

Future work will focus on measuring different types of reflective materials using finer frequency steps and finer spatial densities based on this system to enrich the reflective channel characterization database. The measurement of the dielectric constant and surface roughness of reflective surfaces using this system will also require a finer and more extensive accumulation of measurements. THz reflection characteristics of metal surfaces with multiple/multipath reflections to explore the transmission performance of THz indoor channels in greater depth will be explored as well.

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