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9.5 Multipath from Rough
Seas and Frequency Dependence on Multipath Fading
9.5.1 Rough
Sea Model
Karasawa
et al. [1990] executed an analysis in which multipath fading from very
rough seas (with significant wave heights H greater than 3 m) is
examined. They developed a model which takes account of the effect of smaller-scale
waves superimposed onto the dominant wave. They make use of the fact that
the spectrum of ocean waves caused by wind may be approximated by the Pierson-Moskowitz
spectrum [1964]
and that ocean waves have the characteristics of gravity waves. The RMS
slope of the sea surface is calculated and applied to a theoretical model
for estimating fade depths. A series of curves is presented of the 99th
percentile of fading depth versus significant wave height H for
the following combinations of antenna gain and elevation angle (15 dBi,
5°), (21 dBi, 5°), and (15 dBi, 10°). The analytically derived
multipath fading for "wind-wave" and "swell" conditions are compared with
results derived from the experiments of Karasawa
et al. [1986]; Matsudo
et al., [1987], and Ohmori
et al. [1985]. They show that the fading depth tends to reach a peak
for H between 1 and 2 m. The multipath fading peaks are approximately
8 dB, 5 dB, and 4 dB for the above combinations of antenna gain and elevation
angle, respectively, consistent with their wind-wave model. For larger
H,
the multipath fading decreases slightly for wind-waves conditions and remains
relatively unchanged for swell conditions. The multipath fading due to
swell gives greater contributions by as much as 4 dB, 2 dB, and 1 dB (for
the different combinations of gain and elevation angle) vis-à-vis
the wind-wave contribution.
9.5.2 Dependence on Frequency
The analysis by Karasawa
et al. [1990] alluded to above enable a computation of the relation
between frequency, significant wave height and fading depth. A set of fade
isopleths at the 99% probability exceedance level were calculated by them
and have been depicted in Figure 9-18 for an
elevation angle of 5°, circular polarization, and antenna gain of 15
dBi assuming wind-wave conditions
[CCIR,
1990 (p.525-526)]. The left side of the dashed line denotes the region
where both coherent and incoherent multipath may contribute whereas the
right side of the dashed line is the region where the coherent component
is negligible.
In the region where incoherent multipath is dominant, (e.g., to the
right of the dashed line), the fading depth versus significant wave height
decreases with increasing significant wave height. This is evident in Figure
9-19, which represents a plot of fading depth versus significant wave
height at 10 GHz, 5 GHz, and 3 GHz extracted from the curves of Figure
9-18.
Figure 9-18: Calculation of contours of fading depth at the 99% probability
exceedance level for variable frequencies and significant wave heights
assuming an elevation angle of 5°, circular polarization, antenna gain
of 15 dBi, and wind-wave sea conditions are assumed dominant. The region
to the left of the dashed line corresponds to where the coherent and incoherent
components of multipath reflections may contribute.
Figure 9-19: Fading depth versus significant wave height at 3
GHz, 5 GHz, and 10 GHz extracted from Figure 9-18
in the region where incoherent multipath dominates.
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