## 5 Signal Processing and Results of an In-Field Test
### Test Campaign Results
In this case, while the elevation of PRN 13 is around 45\({}^{\circ}\), PRN 30 has an elevation lower than 10\({}^{\circ}\), showing reduced power values on the reflected signal. Figure 10: Specular points of PRN 30 over the Avigliana lakes. The color is proportional to the SNR ratio between the left-hand circular polarized (LHCP) reflection and the direct GPS signal. Quantitative measurements validate this expectation: on the water, the SNR ratio assumes values between 0.7 and 1 (the differences are mainly due to the elevation angle and the noise effects), whereas when the specular point is on the terrain, the measured values are very different. Figure 10 shows that for PRN 30, the reflection points out of water are mainly on a forest area (northern points) and on irrigated fields (southern points), showing SNR ratios below 0.2 and between 0.2 and 0.4, respectively. As shown in Figure 11, the reflection points for PRN 13 are southern with respect to PRN 30, and they fall also in the so-called \"Area umida dei Mareschi\", _i.e._, the \"Mareschi humid zone\". In that region, as expected, the SNR ratios oscillate in a range between 0.45 and 0.65, sometimes very close to the values assumed on water basins, due to the swamp effect. Then, in the southern region of irrigated fields, again, the measurement is similar to PRN 30, with values between 0.2 and 0.45, with small differences due to the satellite elevation and specular point positions. Figure 12 shows a comparison between some in-flight real measurements and the expected values of the reflection coefficient for different satellite elevations, _i.e._, different incidence angles, and three types of surface: water (blue), wet soil (green) and dry soil (brown). The expected values of the reflection coefficient, represented by dotted lines, are available in the literature [18,40] and, being the result of accurately calibrated test campaigns, have become the theoretical reference for this kind of measurement. Figure 11: Specular points of PRN 13 over the Avigliana lakes. The color is proportional to the SNR ratio between the LHCP reflection and the direct GPS signal. Note that in the literature, the qualitative expressions dry soil and wet soil are largely used, to indicate poor and abundant water content in the soil, respectively. Since it is correct to think that the expressions wet and dry soil are related to a range of water content values, in Figure 12, a region of values is indicated for the dry and the wet soil, by the dashed bars, brown and green respectively. The circle dots in the figure indicate the measured values, for PRN 13 and 15 respectively. The measurements, as for Figure 11, are taken at a rate of 1 Hz. From Figure 12, it can be seen how the values obtained on the water surface are different for two satellites at different elevation, as expected, as well as in the other regions. Note that different colors are used to plot the circle dots, depending on the region in which the reflection point lays, known from the map. For instance, for the PRN 13, when the reflection point is in the Mareschi humid zone, the reflection index is plotted using the light green color. As is visible from Figure 12, the reflection coefficient over that region has a value that matches the expected one. However, the variance of the measurements, including those obtained on the water surface, which should be expected to be fairly homogeneous, is due to different factors. First, it has to be noted that, in general, the estimate of the SNR of the direct GPS signal, even in static conditions, has a certain variance, in the order of a few dB-Hz, due to several reasons, including the high noise present in the signal. In this environment, in-flight, more effects contribute to the variance, as, in particular, the antenna gain, not being omnidirectional. The use of different antennas being non-co-located, for the direct and the reflected signal, increases the effects of these phenomena.