Determining real permittivity from fresnel coefficients in GNSS-R

Global Navigation Satellite System Reflectometry (GNSS-R) can be used to derive information about the composition or the properties of ground surfaces, by analyzing signals emitted by GNSS satellites and reflected from the ground. If the received power is measured with linearly polarized antennas, under the condition of smooth surface, the reflected signal is proportional to the modulus of the perpendicular and parallel polarization Fresnel coefficients, which depend on the incidence angle θ, and on the dielectric constant ε of the soil. In general, ε is a complex number; for non-dispersive soils, the imaginary part of ε can be neglected, and a real value of ε is sought. We solve the realvalued problem explicitly giving formulas that can be used to determine the dielectric constant ε and we compare the analytical solution with experimental data in the case of sand soil.