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9.4 Model of Fade Durations
Due to Sea Reflections
Karasawa
and Shiokawa [1987] analyzed multipath fading due to sea surface reflections
at L-Band (1.54 GHz) and determined mean values of fade durations
TD
and fade occurrence intervals TI from the fading power
spectrum. The fade duration TD is defined as the time
interval between the instant the signal amplitude falls below a particular
level and the instant it reaches that level again (Figure
9-10). The fade occurrence interval TI is defined
as the interval of time between the instant the signal intensity drops
below a specified level
Rp to the instant it falls below
that same level again (Figure 9-10). The signal
level Rp in Figure 9-10 is
assigned the exceedance percentage P.
Karasawa
and Shiokawa [1987] arrived at a simple model for the mean values of
TD
and TI which was also adopted by the ITU-R
[1994, pp. 354-356]. The mean value of the fade occurrence interval
at the fade exceedance percentage
P is denoted by 
and is given by
 ,
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where 
is
the mean value of the fade occurrence interval at the fade exceedance percentage
of 50% and m(P) is given by (9-31). The mean
value of the fade duration at the fade exceedance P or 
may be calculated by
 .
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The mean fade occurrence interval at P = 50% may be calculated
using
 ,
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Where f-10 is called the "-10 dB
spectral bandwidth." This corresponds to the bandwidth over which the power
density decays to –10 dB relative to the peak power density (characterized
in Figure 9-11). The parameter m(P)
in (9-28) is evaluated using the following equations.
The bandwidth f-10 was derived from a theoretical fading
model of Karasawa
and Shiokawa [1984b] and is plotted as a function of elevation angle
in Figure 9-11 at 1.5 GHz for two maritime
conditions. The upper bound (denoted by f-10U)
corresponds to a significant wave height of 5 m, ship velocity of 20 knots,
with a roll of 30°. The lower bound (f-10L)
corresponds to a significant wave height of 1 m, ship velocity of 0 knots,
with 0° roll. Least square fits of the lower and upper curves in Figure
9-11 have the form
The values of a,b,c are tabulated in Table
9-3 for the upper bound f-10U
and lower bound f-10L.
Figure 9-10: Definitions of "fade duration"
TD
and "fade occurrence interval" TI.
These are defined at the signal level Rp that is exceeded
P(%)
of the time.
Figure 9-11: Spectral bandwidth f-10 of 1.5
GHz multipath fading due to sea surface reflection based on a theoretical
model [Karasawa
and Shiokawa; 1984b]. The upper bound f-10U corresponds
to a significant wave height of 5 m, ship velocity of 20 knots, with a
roll of 30°. The lower bound f-10L corresponds to
a significant wave height of 1 m, ship velocity of 0 knots, with 0°
roll.
Table 9-3: Values of parameters a,
b, c
for upper and lower bounds of –10 dB spectral bandwidth (9-32).
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f-10
|
a
|
b
|
c
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Upper Bound
f-10U
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-1140489.7
|
1140489.4
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-2129739.7
|
Lower Bound
f-10L
|
-0.99312632
|
0.97234278
|
-16.718273
|
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