MoPro Chapter 9.3.2

9.3.2 Prediction Method of Karasawa and Shiokawa

We describe here the prediction model of Karasawa and Shiokawa [1988] (also adopted by the ITU-R [1994, pp. 352-354]) for evaluating the fading depth due to sea surface multipath reflections. The individual steps in executing this model follow:

Step 1: Confirm the applicable parameters for which the method is valid. These are:

Frequency range from 1 to 2 GHz (nominal frequency is 1.5 GHz).
Polarization is circular or horizontal. Vertical polarizations may be used for elevation angles above 8°. Below 8°, noticeable errors may exist for vertical polarization due to Brewster angle complications.
Elevation angle is within the interval given by

(9-15)

The sea condition is such that the roughness parameter u defined as:

(9-16)

is given by

(9-17)

where

is the wavelength in m,

is the elevation angle to the satellite, h₀ is the RMS wave height in m related to the significant wave height H by

(9-18)

Employing Figure 9-2, (9-17) implies for instance, at 5° elevation

(9-19)

Step 2: Find the relative antenna gain D_r (in dB) in the direction of the specular reflection point on the sea. The relative antenna gain is approximately given by

,
(9-20)

where G₀ is the antenna gain in dBi (dB above isotropic), and

(9-21)

when the beam center is in the direction of the satellite. The factor of 1.5 (as opposed to 2) is used since a significant portion of the multipath energy comes from the region between the true specular reflection point and the horizon [Karasawa and Shiokawa, 1984a].

Step 3: Obtain the Fresnel reflection coefficient R_ij (in dB), where i represents the polarization of the incident wave and j is the polarization of the reflected wave. These reflection coefficients are tabulated for the sea at 1.5 GHz in Table 9-1 for horizontal polarization R_HH, vertical polarization R_VV, and circular polarization R_CC. The Fresnel reflection coefficients may also be calculated using the formulas of Beckmann and Spizzichino [1963].

Step 4: Calculate the correction factor in dB given by

(9-22)

and

.
(9-23)

Step 5: Find the mean power of sea reflected waves P_r (in dB) relative to the direct power. This is given by

(dB)
(9-24)

Step 6: Find the fading depth A (relative to the direct power) from Figure 9-1 by setting the multipath power calculated from (9-24) to the abscissa. Least square fits of the individual curves in Figure 9-1 follow the form

(dB),
(9-25)

where the parameters , in (9-25) are tabulated in Table 9-2 for different exceedance percentages.

In Figure 9-3 through Figure 9-9 are given the fading depths versus the elevation angle for antenna gains of 0, 5, 10, 15, 18, 20, and 25 dBi, respectively. These curves were derived executing the above-described steps at 1.5 GHz, assuming circular polarization.

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