When we position antennas over soil and propagate the signal any significant distance, it will reflect from soil or water and produce a large multipath signal. Soil is a conductive dielectric that reflects horizontally and vertically polarized signals differently. Typical ground constants are listed in Table 1. Given the grazing angle  measured between the reflected ray and ground, the voltage reflection coefficients are
 (1)where  .
Figure 1-9 gives the reflection coefficient for the two polarizations versus grazing angle. Horizontal polarization reflects from soil about the same as a metal surface. Vertical polarization reflection produces a more interesting curve. The graph shows that the reflection is low over a region of grazing angles. The minimum reflection direction is called the Brewster angle. At this angle the reflected wave is absorbed into the soil. At high grazing angles  has a phase near  and  a phase of  . When the grazing angle decreases and becomes less than the Brewster angle, the vertical polarization reflection changes from to . Remember that for most general response nulls, the signal phase changes by 180◦ when passing through the transition. As the grazing angle approaches zero both reflection coefficients approach −1 and multipath is independent of polarization.
TABLE 1 Typical Ground Constants
FIGURE 1 Average soil reflection for horizontal and vertical polarization.
The electric field at the receiving antenna height
is the sum of the direct wave plus the reflected wave, which traveled along a longer path:
We compute the magnitude
for the small phase difference between the two equal-amplitude signals. The received power is proportional to . The path loss for this multipath link is modified from the free-space equation:
 (2)
Equation (2) states that the power received is proportional to  and increases by  for either antenna. We can approximate the propagation over soil by a region for closely spaced antennas when the results consist of the free-space transmission with  average transmission with significant variation due to multipath and a second region proportional to with small multipath variations. The breakpoint between the two models occurs at a distance . Experiments at mobile telephone frequencies showed that Eq. (2) overestimates the received power when the receiving antenna height is less than 30m and a more correct model modifies the exponent of [11, p. 38]:
 (3)Below 10 m, C = 1 and the exponent varies linearly between 10 and 30 m: C =.
On a narrow-beam terrestrial propagation path, scattering from an object along a path an odd multiple of produces a signal that reduces the main path signal. Given an obstacle at a distance h radial from the direct ray path and located from the transmitter and a distance from the receiving antenna, we determine the differential path length as
 (4)We call these Fresnel clearance zones of order n. The direct path should clear obstacles by at least one clearance zone distance h to prevent the scattered signal from having a negative impact on the communication link. The first Fresnel zone touches ground when  is the breakpoint distance between and propagation models. |
