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6.5 Antenna
Separation Diversity Gain
A space diversity simulation has been carried out employing the data base
corresponding to 400 km of roadside tree shadowing measurements taken during
the Australian campaign [Vogel
et al., 1992]. Space diversity operation for LMSS configurations may
be envisaged by the scenario of two spaced antennas mounted atop a vehicle
where each antenna is fed to a separate receiver system. Because the signal
levels at the two antennas are expected to be different at any instant
of time, rapid switching between the two receiver outputs followed by subsequent
processing should enable the larger signal to be accessed. Such a system
should therefore require smaller fade margins for the same "signal access
distance" than single terminal systems. The "signal access distance" represents
that distance over which the received signal level operates within the
designed fade margin.
Questions addressed here are: (1) what is the increase in "signal access
distance" as a function of antenna spacing along the driving direction,
and (2) what is the improvement in terms of reduced fading (enhanced signal)
for a given "signal access distance" as a function of antenna spacing?
The first question is addressed employing the concept of "diversity improvement
factor, DIF" and the second "diversity gain, DG", both of
which are characterized in the following paragraphs.
6.5.1 Joint Probabilities
In Figure 6-6 are shown a family of cumulative
fade distribution functions derived from the above mentioned simulation.
The curve labeled d = 0 represents the single terminal cumulative
fade distribution corresponding to data acquired from over 400 km of driving
in Australia. The curves labeled d = 1 to 10 m represent the individual
joint probability cumulative fade distribution for the indicated antenna
separations (in the direction of vehicle motion). Such a distribution represents
the joint probability that two antennas spaced a distance d mutually
exceed the abscissa value of fade. Finally, the curve labeled "independent
fading" corresponds to the joint distribution of two links with single
terminal fading, assuming that the two are independent. We note that the
joint probabilities tend to coalesce with increasing antenna separation
at about 2/3 the dB-distance to the independent fading case. That is, the
fade distributions for 8 m and 10 m separations have insignificant differences.
6.5.2 Diversity
Improvement Factor, DIF
The DIF is defined as
 ,
|
|
where P0(A) represents the single terminal probability
distribution at the fade depth A, and Pd(A) represents
the joint probability distribution for an antenna spacing d assuming
the same attenuation A is exceeded. These probabilities may be obtained
from Figure 6-6.
Employing the above results, a least square estimate of DIF was
derived given by,
 ,
|
|
where d is the antenna separation expressed in m and A
is the fade depth in dB. In Figure 6-7 are plotted
a family of curves of DIF as a function of fade depth for antenna
separations between 1 and 10 m. We note, for example, that DIF(8,1) 
3. This implies that when the antennas are separated 1 m, the distance
over which the signal is received above noise is three times greater for
diversity operation relative to the single terminal case assuming an 8
dB fade margin. At the larger separations for any given fade depth, the
rate at which DIF increases is shown to diminish rapidly.
Figure 6-6: Single and joint probability fade distributions for mobile
communications operating in a space diversity mode with antennas separated
by the distance, d.
Figure 6-7: Diversity Improvement Factor (DIF) as a function of
fade depth for a family of antenna separation distances.
6.5.3 Diversity Gain
Diversity gain is a concept defined by Hodge
[1978] for an earth-satellite communications system involving two spaced
antennas operating in a diversity mode in the presence of precipitation.
This concept may also be applied to separated antennas atop a vehicle for
LMSS scenarios. The diversity gain is defined as the fade reduction experienced
while operating in the diversity mode at a given fade margin. It is equal
to the difference in fades between the single terminal and joint probability
distributions at a fixed probability level. For example, from Figure
6-6 we note that the diversity gain at a probability of 1% for a 1
m antenna separation is 4 dB. Hence, while the single terminal operation
at 1% probability will experience a 12 dB fade, the diversity pair for
a 1 m separation will experience only an 8 dB fade.
In Figure 6-8 are plotted the diversity gains
versus antenna separations for a family of single terminal fade levels.
Each single terminal fade uniquely defines a probability level. For example,
an 8 dB fade occurs at a probability level of 3% as is noted from Figure
6-6 (for d = 0). Figure 6-8 shows
that for any given fade margin, the effect of the antenna separation is
dramatic the first 2 meters, whereas at larger spacing, relatively little
additional fade reduction ensues.
Figure 6-8: Diversity gain versus antenna separation distance for a family
of single terminal fade levels.
6.5.4
Space Diversity for Expressway and Trunk Road Driving in Japan
Ryuko and
Saruwatari [1991] describe 1.5 GHz cumulative fade distributions derived
from road measurements in Japan using the Japanese Engineering
Test Satellite V (ETS-V) as the transmitter platform. Using these measurements,
joint probability distributions were calculated as a function of antenna
spacing on the roof of a mobile vehicle. Measurements were made on roads
labeled "expressways" and "trunk roads." The "expressways" in Japan run
through mountainous areas and have many overpasses with local roads. The
"trunk roads" are not as wide and run through urban areas. The major fading
for "expressway" measurements was observed to depend primarily on the density
of overpasses. On the other hand, "trunk road" fades are primarily caused
by tall buildings. Table 6-4 summarizes the fading
and diversity gain results for the Kan-etsu Expressway and the trunk road
which correspond to measurements at an elevation angle of 46° to 47°.
The Kan-etsu Expressway has a total length of 150 km between Tokyo and
Yuzawa. The trunk road runs alongside the Kan-etsu Expressway, passes through
local urban areas, suburbs, farming areas and has many bridge crossings
for pedestrians. Fading for this road was caused by pedestrian-bridge crossings,
tall buildings, trees, utility poles and road signs. Since this route runs
approximately in the same direction as the satellite path, fading along
other trunk roads not so favored by direction is expected to be more severe.
The expressway case shows that a diversity gain of 4 dB exists at the 1%
probability level. Negligible diversity gain differences exist when the
antenna spacing is increased from 5 m to 10 m over the percentage interval
shown. The trunk road exhibits similar results at the higher percentages.
At the 0.5% fade (13 dB), diversity gains of 5 dB and 8 dB occur at an
antenna spacing of 5 m and 10 m, respectively.
Table 6-4: Single terminal fade distribution and
diversity gain values for Japan roads, Ryuko
and Saruwatari [1991]
|
Road Type
|
Single Terminal
|
Diversity Gain for Given Antenna Separation (dB)
|
| |
Prob (%)
|
Fade (dB)
|
d = 5 m
|
d = 10 m
|
|
Expressway
|
2.0
|
3
|
1
|
1
|
| |
1.0
|
6
|
4
|
4
|
| |
0.5
|
14
|
11
|
11.5
|
|
Trunk Road
|
2.0
|
3
|
1
|
1
|
| |
1.0
|
6
|
3
|
4
|
| |
0.5
|
13
|
5
|
8
|
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