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3.4
Validation of the Extended Empirical Roadside Shadowing Model
3.4.1 Central Maryland
at L-Band
In Figure 3-10
is shown a comparison of the above EERS model at 1.5 GHz for distributions
derived from measurements in Central Maryland using a helicopter as the
transmitter platform for an elevation angle of 45° [Goldhirsh
and Vogel, 1989]. Shown are eight cumulative distributions corresponding
to eight runs with different scenarios pertaining to three roads in central
Maryland. The first legend item refers to the EERS model curve (solid black
line) which is shown to approximate the median of the distributions whose
fade values at any given probability are within ±
5 dB of the measured distributions. The next item in the legend refers
to Route 295 driving south (295 S), right lane driving (RL), with the helicopter
on the right (HR). The other items in the legend have analogous definitions.
Sets of other distributions were derived for elevation angles of 20°,
45°, and 60° with similar results associated with the EERS model
[Goldhirsh
and Vogel, 1995b].
Figure 3-10: Comparison of EERS (solid black curve) model distribution
with cumulative distributions for eight runs in central Maryland at 1.5
GHz and elevation angle of 45°.
3.4.2
Australian Fade Distributions at L-Band
In Figure 3-11
is shown a comparison of the EERS model with measurements made in Australia
by the authors at 1.55 GHz [Vogel
et al., 1992]. The Australian cumulative distribution reflects measurements
made over a distance of 403 km comprising 15 individual runs in the Sydney
region using the Japanese ETS-V geostationary satellite. The elevation
angle to the satellite was 51°. Two major vegetation zones were traversed;
forests along the coastal roads and woodlands further inland. Forests ranged
from dry sclerophyll, in which the crowns of contiguous trees did not touch
each other to tropical rain-forests, in which the leafy crowns of the trees
intermingled. The dominating tree genus in the forests was Eucalyptus.
Other than tree types, general similarities existed between the roads traveled
in Australia and those in central Maryland (e.g., tree heights, POS, setbacks).
Shown also is the EERS model at 51°. We note that the maximum difference
between the two distributions is less than 2 dB which occurs at 14%. The
differences reduce monotonically above and below this percentage.
Figure 3-11: Comparison of Australian fade distribution with EERS model
at elevation angle of 51° at a frequency of 1.55 GHz.
3.4.3 Austin, Texas
at K-Band
In Figure 3-12
is shown a K-Band (20 GHz) distribution (elevation angle = 55°) for
an approximate 10 km run along an evergreen (Loblolly Pine) tree-lined
road in Bastrop, Texas derived from the ACTS campaign. This distribution
corresponds to the fade time-series plot in Figure
3-3 and was alluded to in Section
3.2. The Earth-satellite paths cut the line of roadside trees on average
at an angle of 57°. The population of trees was in excess of 55%, and
there were considerable segments of road where the trees formed a tunnel
with branches and foliage overhead. Also shown plotted is the EERS model
(dashed curve). We note that the EERS model underestimates the fade by
at most 5 dB for probabilities between 1% and 20%. This deviation is within
the variability expected in comparing the EERS model with measured distributions
as exemplified for L-Band in Figure 3-10. The
underestimation of the EERS model at the smaller probabilities is most
likely caused by the prevalence of foliage tunnels giving a greater likelihood
of fading at the higher elevation angles.
Figure 3-12: Distribution (solid) from ACTS 20 GHz measurements made in
Bastrop, Texas at an elevation angle of 54.5°. The dashed curve represents
the corresponding EERS model.
3.4.4
Low Angle Measurements in Washington State at L-Band
In Figure 3-13
is shown an L-Band (1.5 GHz) cumulative fade distribution corresponding
to a tree-lined road along an approximate 16 km stretch of road in Washington
State (elevation angle = 7°), where the satellite path was orthogonal
to the line of trees [Vogel
and Goldhirsh, 1995]. Also plotted (dashed curve) is the EERS model
employing the assumption that the 20° fade is the same as that at 7°
as described by (3-8). The EERS distribution
agrees with the measured distribution to within 2 dB for percentages smaller
than 10% and larger than 50%, and is within 5 dB for the other percentage
levels. The above deviations are comparable to those obtained when comparing
the ERS model with L-Band distributions from multiple runs in central Maryland
(Figure 3-10).
Figure 3-13: Cumulative fade distribution (solid curve) derived from L
Band (1.5 GHz) measurements in Washington State over an approximate 16
km stretch of road (elevation = 7°). The dashed curve corresponds to
the EERS model distribution.
3.4.5
Low Elevation Angle Measurements at K-Band in Alaska
In Figure 3-14
are shown a set of K-Band distributions (elevation = 8°) derived from
ACTS measurements in Alaska corresponding to different roads in which the
Earth-satellite path was orthogonal to the line of roadside trees. Also
shown is the EERS model. We note that the EERS model maintains its median
characteristic, although the variability about the median is large. The
low angle distributions are shown to vary considerably because of the reasons
enumerated in Section
3.3.2, with the high probability fades caused by terrain blockage and
multiple trees along the Earth-satellite path.
Figure 3-14: K-band (20 GHz) distributions (elevation = 8°) derived
from ACTS measurements in Alaska. The solid red curve is the EERS model
distribution.
3.4.6
K-Band Measurements in Central Maryland
In Figure 3-15
are shown several plots which validate elements of the EERS model. The
solid curve to the left (with circled points) represents the measured distribution
derived from ACTS 20 GHz measurements in March 1994 for Route 108 (traveling
south-west) for the case in which the deciduous trees were without leaves.
For this case, the satellite was on the left and the Earth-satellite path
frequently cut the line of roadside trees at or near orthogonal angles.
Shown also (green solid line) is the distribution derived by applying the
foliage adjustment formulation described in the next section. This adjusted
distribution thus represents a predictor of the full foliage case. Also
shown is the EERS distribution at K-Band (dashed curve). We observe that
the EERS distribution deviates from the adjusted measured distribution
by less than 5 dB.
The red dot-dashed curve in Figure 3-15 was derived from previous L-Band
helicopter measurements in June 1987 [Goldhirsh
and Vogel, 1989] employing the following procedures: (1) Distributions
were examined which corresponded to the same scenario as for the K-Band
measurements; namely, the vehicle was traveling in the southwest direction
and the helicopter was on the left, (2) a resultant 39° distribution
was derived by interpolating the 45° and the 30° distributions
at L-Band, and (3) the L-Band distribution was extended to K-Band employing
the frequency scaling factor given by the exponential term in (3-1). We
note that relatively close agreement exists between the adjusted distribution
(based on helicopter measurements; dot-dashed curve), the foliage adjusted
ACTS distribution (right solid curve), and the EERS model (dashed curve)
[Goldhirsh
and Vogel, 1995a; 1995b].
Figure 3-15: Plots of K-Band (20 GHz) cumulative fade distributions from
measurements in central Maryland at elevation angle of 39°.
3.4.7
Comparison with ESA K-Band Measurements
We compare here EERS model distributions at 18.7
GHz with measured distributions by Murr
et al. [1995] obtained in a series of campaigns supported by the European
Space Agency (ESA). The campaigns used a radiating source on board the
geostationary satellite Italsat F1 [Paraboni
and Giannone, 1991] and a mobile van with a tracking antenna [Joanneum
Research, 1995]. The elevation angles were between 30° and 35°
and a number of runs in four European countries were executed for different
driving directions relative to the satellite position. In Figure
3-16 are shown two measured distributions (solid curves) made along
tree shadowed roads in Munich, Germany [Murr
et al., 1995]. Also shown is the corresponding EERS model distribution
(dashed curve). We note that the two measured distributions generally flank
the EERS model between percentage values of 5% to 30% with fade deviations
in excess of 10 dB occurring at percentages smaller than 5%. Murr
et al. [1995], in these measurements, found that a 90° relative
satellite azimuth scenario did not always represent a worst case fading
situation. Some distributions showed larger fades at the 45° relative
satellite azimuths. This was explained as follows: For some 90° cases,
the Earth-satellite path encountered clear spaces between adjacent trees
giving rise to minimal fade conditions during the corresponding time intervals.
On the other hand, at 45°, the tree canopies overlapped and the incidence
of optically non-shadowed Earth-satellite path scenarios was not as prevalent
as for the 90° case. Hence the 45° case sometimes gave rise to
longer periods with extended shadowing.
Figure 3-16: Measured cumulative distributions for tree shadowed environments
at 18.7 GHz and elevation angle of 32.5°, where the satellite azimuth
was 90° relative to the driving direction [Murr
et al., 1995]. The dashed curved represents the EERS model.
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