9 Shadowing

7/25/2019 9 Shadowing

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S.R. Saunders, 1999, 1


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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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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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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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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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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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[ ]

=

=>

= 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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r

rmax

r

Availability decreases with distance

Compute at all distances and average


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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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1 dB

10 dB

Fade Margin:


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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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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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Rateof power variation Affects power control

Handover (handoff) measurements Automatic gain control in receivers


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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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a T

IndependentGaussian

Samples

x

+ 10x/20S (dB)

LinearVoltage

x

L a1

2

c

rvT

ea

=

speedsamplinginterval

correlation distance


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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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-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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Sectorisation gain Soft handoff, site diversity, simulcast

performance

Handover algorithm performance

Frequency planning

Adaptive antenna performance


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=

T2

1

T

2

1

for


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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

Documents

9 Shadowing