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3.7
Comparison of EERS Model with Other Empirical Models
3.7.1
Modified Empirical Roadside Shadowing Model (MERS)
This model is an outgrowth of campaigns carried out by the European Space
Agency (ESA) [Jongejans
et al., 1986] and is described by Sforza
et al. [1993a; 1993b]
and Butt
et al. [1995]. It is called the Modified Empirical Roadside Shadowing
(MERS) and is representative of mobile-satellite attenuation from deciduous
trees corresponding to POS values from 35% to 85%. The formulation has
the same form as the ERS model (3-3)
and is given by
 ,
|
|
where
 ,
|
(3-22)
|
and where
 .
|
(3-23)
|
In the above, 
is
the L-Band (1.5 GHz) fade in dB, P is the percentage of fade exceeded
applicable in the range 1% to 30%, and 
is the elevation angle (in degrees) valid from 20° to 80°. In Figure
3-24, the above MERS formulation is compared with the EERS model at
30°, 45°, and 60°. The two models at the different angles generally
agree with one another to approximately 1 dB at the equal percentage levels.
The 60° MERS distribution appears shifted to the right relative to
the EERS model by approximately 1 dB. Although the above formulation is
described for L-Band, it may be used for S-Band frequencies applying the
frequency scaling relation (3-20)
[Butt
et al., 1995].
Figure 3-24: Comparison of EERS model (solid) with MERS (dashed)
results at L-Band (1.5 GHz).
3.7.2 Empirical
Fading Model (EFM)
This model was derived from measurements made by the Centre for Satellite
Engineering at the University of Surrey, UK. It is based on simultaneous
measurements at L, S, and Ku bands at the higher elevation angles
from 60° to 80° [Butt
et al., 1993; 1995].
This model also has a form similar to the ERS model (3-3)
and is given by
 ,
|
|
with
 ,
|
|
and where 
is the attenuation (in dB) at the percentage 
(in %) valid from 1% to 20%, 
is the elevation angle (in degrees) applicable from 60° to 80°,
and the frequency 
(in GHz) may be applied in the range 1.3 GHz to 10.4 GHz. The multiplying
constants on the right hand side of M in (3-25) are
the negative of those presented by Butt
et al. [1993, 1995]
because M in (3-24) is preceded by a negative sign
to maintain consistency with the EERS model. (Their multiplying coefficient
was positive). Figure
3-25 shows a comparison of the above model distribution at 60°
elevation with those corresponding to the EERS, MERS, and CEFM (to be described
shortly). It is interesting to note that the other three models cluster
about one another, whereas the EFM model deviates considerably from the
grouping; especially at percentages smaller than 5%.
Figure 3-25: Comparison of various models at 60° elevation with EERS
(solid) at 1.5 GHz.
3.7.3
Combined Empirical Fading Model (CEFM)
The Combined EFM (CEFM) model extends the above high elevation angle results
with those contained in the ERS model. It is described by Parks
et al. [1993a] and Butt
et al. [1995] and is given as follows:
with
 ,
|
(3-27)
|
and where the units are the same as described previously. This formulation
may be applied in the angular range 20° to 80°, over the frequency
interval from 1.3 GHz to 3 GHz, and percentage range from 1% to 20%. Here
again, the constants in M are the negative of those presented by Parks
et al. [1993a; 1993b]
because M in (3-26) is preceded by a negative sign. The
CEFM distributions are shown plotted at L-Band (1.5 GHz) in Figure
3-26 (dashed curves) and are compared with the EERS model (solid curves)
at 30°, 45°, and 60°. Agreement at the three angles are generally
within 1 dB.
In order to obtain a handle on the behavior of
the distributions at the higher elevation angles (above 60°), we show
plotted the distributions for the MERS and CEFM models in Figure
3-27 at 70° and 80°. The MERS model at the higher elevation
angles is shown to exhibit more self consistency, whereas the CEFM model
distributions are noted to cross over at approximately 10%.
Figure 3-26: Comparison of EERS model (solid) with CEFM model (dashed)
results at L-Band (1.5 GHz).
Figure 3-27: EFM and MERS model values at 70° and 80° elevations
at L-Band (1.5 GHz).
3.7.4
ITU-R Fade Model at Elevation Angles above 60°
The ITU-R has recommended that for elevation angles
greater than 60°, the ERS model be linearly interpolated with the fade
values listed in Table
3-2 (at 80°) and plotted in Figure 3-28
for the frequencies of 1.6 GHz or 2.6 GHz at the indicated percentages
[ITU-R, 1994]. The tabulated
values in the right two columns of Table
3-2 were derived from measurements described by Smith
et al. [1993]. We have extended this methodology below to apply to
the formulation (3-1) employing the
following steps:
-
Apply equation (3-1) at the frequency
of 1.6 GHz and 2.6 GHz at an elevation angle of 60° (values in the
second and third columns).
-
Linearly interpolate between the fade calculated for an angle of 60°
and the fade for an elevation angle of 80° provided in Table
3-2 (second and fourth columns) at 1.6 GHz.
-
Linearly interpolate between the value calculated for an angle of 60°
and the fade values for an elevation angle of 80° provided in Table
3-2 at 2.6 GHz (third and fifth columns) only for percentages of 15%
and smaller.
-
Linearly interpolate between the values in the fourth and fifth columns
in Table
3-2 and a value of zero at 90° to arrive at fade levels at elevation
angles between 80° and 90°.
The above methodology is self-consistent
at 1.5 GHz for percentages between 1% and 30% in that the 60° elevation
fade values derived from the EERS model are larger than the respective
tabulated 80° fade values at the same percentages. On the other hand,
this is not the case at 2.6 GHz for percentages of 20% and larger (see
columns three and five of Table
3-2 showing values with *). It is therefore suggested that at 2.6 GHz
the above methodology be used at percentages of 15% and smaller as stated
in Step 3 above. In Figure 3-29 is shown plotted
the L-Band (1.5 GHz) fade exceeded versus elevation angle showing linear
interpolation of fades between angles 60° and 90°.
Table
3-2: Fades exceeded at elevations of 60° and 80°.
|
Percentage, P
|
EERS Fade (dB) at Elevation = 60°
|
Fade (dB) at Elevation = 80°
|
|
|
f = 1.6 GHz
|
f = 2.6 GHz
|
f = 1.6 GHz
|
f = 2.6 GHz
|
|
1
|
8.2
|
11.0
|
4.1
|
9.0
|
|
5
|
4.8
|
6.5
|
2.0
|
5.2
|
|
10
|
3.4
|
4.5
|
1.5
|
3.8
|
|
15
|
2.6
|
3.4
|
1.4
|
3.2
|
|
20
|
1.9
|
2.6*
|
1.3
|
2.8*
|
|
30
|
1.4
|
1.8*
|
1.2
|
2.5*
|
Figure 3-28: Cumulative distributions at 80° for frequencies of 1.6
and 2.6 GHz.
Figure 3-29: Fade versus elevation angle at L-Band (1.5 GHz) with ITU-R
extension to 90°.
3.7.5 Comparative
Summary of Model Limits
In Table 3-3
is given a comparative summary of the above competing models and their
domains of validity. The EERS model covers a wider range of percentages
than the other models (1% to 80%) and includes angles as low as 7°.
The other models are limited to 20° elevation. It also covers the greatest
range of frequencies (e.g., 0.87 to 20 GHz). The EERS model limitation
vis-à-vis the other models is that it does not include elevation
angles greater than 60°. The ITU-R model extends the EERS model from
60° to 90° at 1.6 GHz and 2.6 GHz. The EFM, CEFM, and MERS models
include elevation angles up to 80°.
Table 3-3:
Summary of empirical models and their domains of validity.
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