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3.3 Extended
Empirical Roadside Model
3.3.1 Background
The empirical roadside shadowing (ERS) model gives estimates of cumulative
fade distributions due to roadside trees over the frequency range UHF (870
MHz) through S-Band (3 GHz), elevation angles to the satellite from 20°
to 60°, and percentages from 1% to 20% [Goldhirsh
and Vogel, 1992; Vogel
et al., 1992; Vogel
and Goldhirsh, 1990]. This model has been adopted as a recommendation
of the ITU-R [1994]. The extended
empirical roadside shadowing model (EERS) enhances the ERS model in the
following ways: (1) It may be used for elevation angles as low as 7°,
(2) it includes the frequency of 20 GHz, and (3) it may be applied at a
percentage range of 1% to 80% [Goldhirsh
and Vogel, 1995a]. This model has been validated at UHF (870 MHz),
L-Band (1.5 GHz), S-Band (3 GHz), and K-Band (20 GHz). It is offered as
a candidate formulation at frequencies in-between 3 GHz and 20 GHz and
at higher frequencies (e.g., 30 GHz) until data becomes available for validation.
This revised model has been adopted by the ITU-R in 1997 [ITU-R,
1997].
The ERS model was derived from the median of cumulative UHF and L-Band
fade distributions systematically obtained from helicopter-mobile and satellite-mobile
measurements in central Maryland. The measurements were made over approximately
600 km of driving distance comprising path elevation angles of 21°,
30°, 45° and 60°. The 21° case was executed employing the
geostationary satellite MARECS-B2 [Vogel
and Goldhirsh, 1990], whereas the measurements for the other angles
were obtained employing a helicopter as the transmitter platform [Goldhirsh
and Vogel, 1987; 1989].
The configuration corresponds to a shadowing condition in which the helicopter
flew parallel to the moving vehicle and the propagation path was approximately
normal to the line of roadside trees (e.g., azimuth of the satellite relative
to the vehicle direction was 90°). Tree heights ranged from approximately
5 to 30 m. The satellite path directions were such that these were also
predominantly along 90° shadowing orientation, although some of the
roads sampled had a number of bends in them and deviations from this aspect
did arise. The measurements were performed on two-lane highways (one lane
in each direction), and a four-lane highway (two lanes in each direction),
where the roadside trees were primarily of the deciduous variety. In order
to assess the extent by which trees populate the side of the road, a quantity
called percentage of optical shadowing (POS) was defined. This represents
the percentage of optical shadowing caused by roadside trees at a path
angle of 45° for right side of the road driving, where the path is
to the right of the driver and the vehicle is in the right lane. The POS
values for the roads driven were predominantly between 55% and 75% implying
tree populations of at least these amounts.
In deriving the EERS model, use was made of the original previously
developed body of data at UHF and L-Band in central Maryland as well as
more recent developed data bases. These correspond to mobile L-Band measurements
of transmissions from MARECS B-2 in the western United States [Vogel
and Goldhirsh, 1995], static K-Band (20 GHz) measurements in Austin,
Texas [Vogel
and Goldhirsh, 1993a; 1993b],
and mobile K-Band measurements employing transmissions from ACTS [Goldhirsh
and Vogel, 1995a; 1995b].
These latter measurements were performed during the first six months of
1994 during which a series of four 20 GHz mobile-ACTS campaigns were executed.
The campaigns were performed in central Maryland (March, elevation = 39°),
Austin, Texas (February and May, elevation = 55°) and Fairbanks, Alaska
and environs (June, elevation = 8°). The mobile measurements in Austin,
Texas during February and May enabled a determination of 20 GHz fading
probability distributions for no-foliage and foliage conditions, respectively.
3.3.2 EERS Formulation
In the following paragraphs is given an overview of the EERS formulation
followed by examples of its validation.
For 
and 
 .
|
|
and for 
and 
 .
|
(3-2)
|
where
is the
attenuation (in dB) at the frequency f (in GHz) exceeded at P
(in %) which represents the percentage of the driving distance for an Earth-satellite
path angle 
(in degrees), and
is the corresponding attenuation (in dB) at 
= 1.5 GHz. The attenuation is defined relative to non-shadowed and negligible
multipath conditions.
The L-Band attenuation at 
= 1.5 GHz (i.e., 
)
for and
is given by,
 ,
|
|
where
 ,
|
|
 ,
|
(3-5)
|
and where
In Equation (3-3), P is in %,
is in degrees, f is in GHz, and 
is in dB. Substituting (3-4) through (3-6)
into (3-3), 
may alternately be expressed by
 , |
|
where 
are tabulated in Table 3-1 for a series of fixed
percentages in the interval between 1% and 80%.
Table 3-1: Listing of parameter values of 
in Equation (3-7).
|
Percentage, P
|
|
|
|
|
1
|
34.7600
|
-0.4430
|
0.0
|
|
2
|
32.3756
|
-0.5106
|
1.3863X10-3
|
|
5
|
29.2235
|
-0.5999
|
3.2189X10-3
|
|
10
|
26.8391
|
-0.6675
|
4.6052X10-3
|
|
20
|
24.4547
|
-0.7351
|
5.9915X10-3
|
|
30
|
17.3022
|
-0.5201
|
4.2391X10-3
|
|
40
|
12.2273
|
-0.36754
|
2.9957X10-3
|
|
50
|
8.2910
|
-0.2492
|
2.0313X10-3
|
|
60
|
5.0748
|
-0.1525
|
1.2433X10-3
|
|
70
|
2.3556
|
-7.0805X10-2
|
5.7711X10-4
|
|
80
|
0.0
|
0.0
|
0.0
|
For the case in which 
,
the distribution derived using the formulations (3-1)
or (3-7) is first calculated at 
.
This distribution for 
is subsequently assumed to be invariant at the smaller elevation angles.
That is,
for 
and 
 .
|
|
Equation (3-8) implies that the probability distributions
at elevation angles smaller than 20° are the same as those at 20°.
Extending the model to elevation angles smaller than 20° is a complex
task for the following reasons: (1) The EERS model tacitly assumes that
the canopies of single trees shadow the Earth-satellite path. At lower
angles, there may be a greater likelihood that the path cuts the canopies
of multiple trees or multiple tree trunks. (2) At smaller angles, there
may also be a greater likelihood that the terrain itself blocks the Earth-satellite
path creating high attenuation. (3) Ground multipath may also influence
the distribution considerably. Based upon empirical experience for cases
where the above caveats did not arise, it has been found that with good
approximation the EERS model at 20° elevation is representative of
results at 7° or 8°. The rationale for this assumption is characterized in
Figure 3-4. At 20° elevation, the Earth-satellite
path is already passing through the lower part of the tree canopies. Reducing
the path elevation angle is likely to result in attenuation caused by tree
trunks which may tend to mitigate the signal degradation. On the other
hand, attenuation effects may increase because of fading from those tree
canopies which are further offset from the road (as was the case in Alaska).
The combination of these two effects generally results in the median fade
statistics to be relatively invariant to angles below 20°, although
larger deviations about the median are expected because of the breakdown
of the aforementioned underlying assumptions.
Figure 3-4: Cartoon depicting the mechanism by which the fades are statistically
invariant at angles smaller than 20° (down to 7°).
At angles smaller than 20°, Earth-satellite paths tend to fall below
the canopy of nearby trees but intersect more distant tree canopies.
3.3.3
Step by Step Implementation of the EERS Model
We presume that it is desired to determine the percentage P of distance
traveled over which a fade is exceeded for a LMSS tree shadowing scenario
at frequency f (in GHz) and elevation angle to the satellite
(in degrees). We present here the step-by-step approach of determining
this distribution using the EERS model given by (3-1)
through (3-8). Initially, consider the angular interval 
.
We will return to the extension of the formulation outside these angle
bounds shortly.
Step 1: Calculate the fade distribution at
,
valid for percentages of distance traveled of 
,
at the desired path elevation angle, :
 ,
|
(3-9)
|
where
|
(3-10)
|
|
(3-11)
|
Step 2: Convert the fade distribution at 
,
valid for ,
to the desired frequency, f (GHz), where 
.
|
(3-12)
|
Step 3: Scale the fade distribution to percentages of distance
traveled 
:
Step 4: For path elevation angles in the range 
,
the fade distribution is assumed to have the same value as at 
:
|
(3-14)
|
In Section
3.7.4, a methodology is outlined for extending the EERS model at L-
and S-Bands to elevation angles greater than 60°.
3.3.4 Example Plots
Applying the above steps, we show plotted in Figure
3-5 to Figure 3-8 a family of curves describing
the cumulative fade distributions at UHF (870 MHz), L-Band (1.5 GHz), S-Band
(3.0 GHz), and K-Band (20 GHz). In Figure 3-9
is given the fade exceeded versus elevation angle for a family of constant
percentages at L Band using (3-7) and the constants
in Table 3-1. These curves may be used for establishing
fade-margin design criteria for LMSS scenarios.
Figure 3-5: Family of cumulative fade distribution curves derived from
the extended empirical roadside shadowing model (EERS) at UHF (870 MHz).
The curve labeled "
"
is applicable at angles smaller than 20 degrees as described in the text.
Figure 3-6: Family of cumulative fade distribution curves derived from
the extended empirical roadside shadowing model (EERS) at L-Band (f
= 1.5 GHz).
Figure 3-7: Family of cumulative fade distribution curves derived from
the extended empirical roadside shadowing model (EERS) at S-Band (3 GHz).
Figure 3-8: Family of cumulative fade distribution curves derived from
the extended empirical roadside shadowing model (EERS) at K-Band (f
= 20 GHz).
Figure 3-9: L-Band (1.5 GHz) fade values exceeded versus elevation angle
for a family of fixed percentages using the EERS model.
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