Ground Wave Propagation
1 Interference Zone
In this zone, the total field is composed of the sum of the direct and reflected waves (see Figure 3.6). The field strength E0 of the direct wave at a distance d is given by geometric optics as in equation (3.1). The field strength of the reflected wave differs from that of the direct wave in four main respects:
a) The propagation distance to the receiver is longer. This means that the field strength is reduced and there is a phase difference between the direct and reflected wave.
b) The gain of the transmitting antenna may be different for the two component waves since their directions of propagation are different.
c) The reflected wave is modified by a complex reflection coefficient R, which depends upon the angle of incidence of the wave, its polarisation and the ground characteristics. Reflection from a lossy ground produces changes in both magnitude and phase of the reflected signal.
Fig. 3.4 Height gain factors over good ground
HF COMMUNICATIONS: A SYSTEMS APPROACH 27
d) Reflection from the Earth’s spherical surface produces a divergence of ray paths. This has the effect of further reducing the reflected wave strength. The ratio of the field strength after reflection from a spherical surface to that after reflection from a plane surface is known as the divergence coefficient D.
Taking into account these differences, the field strength of the reflected wave ER compared to the direct wave E0 then becomes
(3.8) where GR, GD are the antenna gains and dR, dD the total path lengths for the reflected and direct waves respectively. When the phase factor due to path difference is included, the total field then becomes
(3.9) In practice the situation is rather more complicated than (3.9) shows since the radio ray trajectories may not be linear.
Tropospheric refraction has the effect of bending the ray paths, further complicating the computation.
2
Radio Horizon Zone
Reflection theory in geometric optics is valid only when diffraction has a minor effect, i.e. for cases when the waves are not too grazing in incidence.
Suppose the grazing angle is less than
(3.10) where a=Earth’s radius
m=parameter between unity and 4/3 used to modify Earth’s radius resulting from tropospheric effects.
Under these conditions ray theory becomes invalid and the surface wave may contribute appreciably to the total field strength.
In this zone, the field strength must be fitted to that in the interference zone and the diffraction zone. The exact calculation of Fig. 3.5 Zonal relationships for elevated antennas
Fig. 3.6 Direct and reflected wave components of the space wave 28 GROUND WAVE PROPAGATION
this fit is rather difficult[6], since absorption and diffraction are combined in a complex fashion. The total attenuation is obtained by a series expansion which has terms that are tedious to calculate and converge slowly.
3 Diffraction Zone
Beyond the radio horizon, the diffraction zone is entered. Here the attenuation settles to the value 0.62/ dB/km as mentioned on page 38.
3.3.2
Effect of Antenna Height
Consider the case for which the reflection angle (see Figure 3.6) is greater than the limiting angle defined in equation (3.
10), but is small enough to ensure a reflection coefficient of approximately −1. The difference in path length between the reflected wave and the direct wave is approximately 2h1h2/d when both h1 and h2 are much less than d. There is a series of maxima equal to twice the field in free space (see equation (3.5)) when
(3.11) and a series of minima when
where n is an integer.
When the angle is increased the effects produced are different depending upon wave polarisation.
a) For horizontal polarisation, the modulus of the reflection coefficient decreases and the minima are less pronounced.
b) For vertical polarisation, the effects become complicated because both the phase angle and the modulus of the reflection coefficient change rapidly with changes in .
3.4
Deviations from Simplified Model 3.4.1
General Considerations
The theory outlined above must be modified to account for a number of other physical effects and influences that are imposed upon the radio wave as it propagates over the surface of the Earth.
The extent to which the lower strata influence the effective Earth constants depends upon the depth of penetration of the radio energy. The penetration depth is defined as that depth at which the wave has been attenuated to 1/e (or 37%) of its value at the surface. The penetration depth for a frequency of 10 MHz is shown for different types of ground in Table 3.1. For frequencies in the HF band only the surface of the ground usually needs to be considered since , even for poor conductivity soil, is no more than a few metres; for sea water it is much less than a metre.
The radio energy received at a point travels not only by the direct path from the transmitter but also by a large number of indirect paths distributed on either side of the direct path. It is necessary, therefore, to consider the constants of the ground over the area covered by the lateral spread of the wave paths as well as along the direct path itself. The most important region is the first Fresnel (half-wave) zone. This is the ellipse having the transmitter and receiver positions as its foci and axes of (d+ / 2) and (d )½ respectively, where d is the length of the direct path and is the wavelength.
Just beyond the radio horizon of a transmitting antenna the observed signal strength results from a variety of propagation mechanisms. These may include diffraction over ridges and hills as well as diffraction by the Earth’s curvature. At one extreme, the case of diffraction over high, isolated obstacles, knifeedge diffraction theory gives theoretical results that agree fairly well with observations[7]. Field strengths are similar to near free-space values, showing a low rate of attenuation with distance. At the other extreme is diffraction over a smooth spherical Earth. This condition results in low field strengths which are soon exceeded, beyond the horizon of a transmitting antenna, by radio fields produced by reflection from elevated layers or by forward-scatter radio waves.
HF COMMUNICATIONS: A SYSTEMS APPROACH 29
Table 3.1 Penetration depth of 10 MHz wave as a function of terrain
TERRAIN TYPE PENETRATION DEPTH (m)
Sea Water 0.1
Wet Ground 3
Fresh Water 10
Medium Dry Ground 15
Theoretical methods[7] have been developed to handle certain idealisations of terrain features, such as bluffs, cliffs and knife-edge obstacles in a transmission path. However, in most cases of propagation over land it is extremely difficult to take into account the roughness and irregularities of terrain features and environmental clutter such as vegetation, buildings, bridges and electric power lines.
It is not possible to make simple general statements regarding the influence of the terrain and the vegetation on propagation.
It is a complex function of frequency, ground constants, tropospheric variations, path geometry, season and vegetation density.
3.4.2 Ground Conductivity A number of physical factors influence the effective conductivity of the ground:
1