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S.R. Saunders, 1999, 1
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S.R. Saunders, 1999, 2
Source of shadowing
Shadowing statistics Impact of shadowing on cell size andsystem availability
At cell edge Over cell area
Measured shadowing variability
Shadowing correlations Serial (auto) correlation
Site-to-site (cross) correlation
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S.R. Saunders, 1999, 3
Path 1 Path 2
Path 3
Basestation
1 2
3 MobileLocation
Geometry of
individual pathprofiles varies atfixed distance
Path loss modelspredict themedianlevel,exceeded at
50% of locations
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S.R. Saunders, 1999, 4
0 50 100 150 200 250 300 350 400 450 500
-20
-15
-10
-5
0
5
10
15
20
25
Distance [m]
Signallevelrelativetomedian[dB]
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30 20 10 0 10 20 30 400
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Shadowing Level[dB]
ProbabilityDensity
MeasuredNormalDistribution
Power in dB isapproximatelynormally distributed
Hence power in
watts is lognormal Typical standard
deviation (location
variability) of 5-12dB
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S.R. Saunders, 1999, 6
Assume contributions to the path loss aremultiplicative and independent:
In decibels:
If N is large, central limit theorem gives Lnormal, so A is lognormal
NLLLL +++= 21
NAAAA = 21
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sLLL += 50Total
path loss
Median
path loss(from
models)
Medianpath loss(from
models)
Probability density function (zero meannormal):
( )
= 2
2
2exp2
1
L
S
L
S
L
Lp
L is location variability
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S.R. Saunders, 1999, 8
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
-140
-130
-120
-110
-100
-90
-80
-70
-60
Distance from Base Station [m]
TotalPath
Loss[-dB
]
Maximum
AcceptablePath Loss
Median
Path Loss
FadeMargin, z dB
Maximum CellRange
Reducedradius foravailabilityabove 50%
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S.R. Saunders, 1999, 9
[ ]
=
=>
= L
zx
S
zQdx
xzL
L
2exp
2
1Pr
2
( )
=
=
= 2erfc
2
1
2exp
2
1 2 tdx
xtQ
tx
Probability shadowing exceeds fade margin
z [dB]:
where Q(.) is complementary cumulativenormal distribution:
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0 1000 2000 3000 4000 5000 6000 7000 800030
40
50
60
70
80
90
100
Distance from Base Station [m]
Percentage
ofLocations
Adequately
Covered[%]
L=6dB
8dB
10dB
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S.R. Saunders, 1999, 12
r
rmax
r
Availability decreases with distance
Compute at all distances and average
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S.R. Saunders, 1999, 13
pe= 0.5
pe= 0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0.55
Cell edge availability:
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S.R. Saunders, 1999, 14
1 dB
10 dB
Fade Margin:
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S.R. Saunders, 1999, 15
1 00 2 00 3 00 4 0 05 00 7 00 1 00 0 2 00 0 3 0 00 5 00 0 70 00 1 00 00 2 00 002
3
4
5
6
7
8
9
10
11
12
Frequency [MHz]
StandarddeviationL
Egl iOkumura Suburban Rolling HillsOkumura UrbanReudinkOttBlackIbrahim 2kmIbrahim 9kmUrban EmpiricalModelSuburban EmpiricalModel
UrbanSuburban
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S.R. Saunders, 1999, 16
Base 1
Base 2
Mobile 1
Mobile 2
S11
S12
S21
S22
rm
[ ]
21
2111
SSEc =
( ) [ ]
21
1211
SSErms =
Serial (auto) correlation:
Site-to-site (cross) correlation:
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S.R. Saunders, 1999, 17
Rateof power variation Affects power control
Handover (handoff) measurements Automatic gain control in receivers
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S.R. Saunders, 1999, 18
0
0.2
0.4
0.6
0.8
1
Distance Moved by Mobile between Shadowing Samples, r[m]
S(d)
1/ e
ShadowingCorrelationDistance, rc
ShadowingA
utocorrela
tions(rm)
m
First order negative exponential
Correlation distance 10s-100s metres
Corresponds to obstruction sizes
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S.R. Saunders, 1999, 19
a T
IndependentGaussian
Samples
x
+ 10x/20S (dB)
LinearVoltage
x
L a1
2
c
rvT
ea
=
speedsamplinginterval
correlation distance
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S.R. Saunders, 1999, 20
0 10 20 30 40 50 60 70 80 90 10015
10
5
0
5
10
15
20
25
Time [seconds]
RelativePower[dB]
Speed 50 km h-1
Correlation distance 100m
Location variability 8 dB
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S.R. Saunders, 1999, 21
-20 -15 -10 -5 0
10
10
10
10
10
10
Difference between threshold and mean C/I
ProbabilityofinadequateC/I
12
12
-5
-4
-3
-2
-1
0
c
c
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S.R. Saunders, 1999, 22
Sectorisation gain Soft handoff, site diversity, simulcast
performance
Handover algorithm performance
Frequency planning
Adaptive antenna performance
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S.R. Saunders, 1999, 23
=
T2
1
T
2
1
for
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S.R. Saunders, 1999, 24
0 20 40 60 80 100 120 140 160 180
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Sha
dowingCorrelation,
12
Angle-of-arrival Difference, [degrees]
Measurements
Model
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S.R. Saunders, 1999, 27 C/I threshold = 9dB
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Shadowing makes coverage predictionstatistical (predict availabilityrather thansignal level)
Affects both coverage and capacity Can be predicted using simple statistics
without specific knowledge of variability of
path profiles Overall impact dependent on correlations