Cellular Network Planning and Optimization Part2

Cellular Network Planningand Optimization

Part II: FadingJyri Hämäläinen,

Communications and Networking Department, TKK, 17.1.2007

2

Outline

� Modeling approaches� Path loss models

� Shadow fading� Fast fading

3

Modeling approaches

4

Fading seen by moving terminal

Modeling approach:

1. Distance between TX and RX =>

path loss2. Shadowing by

large obstacles => shadow fading

3. Multi-path effects => fast fading

Time

Power

+20 dB

Path loss

- 20 dB Lognormal fading

Fast fading

Path loss

5

Path Loss

� Path loss is distance dependent mean attenuation of the signal.

� Once the allowed path loss of a certain system is known we can solve the maximum distance between transmitter and receiver and compute the relative coverage area.

� Suitable path loss model depends on the environments (macro-cell, micro-cell, indoor)� Outdoor to outdoor models � Outdoor to indoor models� Indoor models

6

Shadow Fading

� Shadow fading is used to model variations in path loss due to large obstacles like buildings, terrain conditions, trees.

� Shadow fading is also called as log-normal fading since it is modeled using log-normal distribution

� In cell dimensioning/link budget shadow fading is taken into account through a certain margin (=shadow fading margin)

7

Path loss + shadow fading

Distance between TX and RX in logarithmic scale

Sig

nal s

tren

gth

in d

B’s

Log-normal distribution

Standard deviation e.g. +/-8 dB

Path loss

8

Fast Fading

� Fast fading is also called as multi-path fading sin ce it is mainly caused by multi-path reflections of a transmitted w aves by local scatterers such as human build structures or natural obstacles

� Fast fading occurs since MS and/or scatterers nearby MS are moving� Signal strength in the receiver may change even ten s of decibels

within a very short time frame� Signal coherence distance = separation between loca tions where fast

fading correlation is negligible. Signal coherence distance is half of the carrier wavelength

� f = 2GHz => coherence distance = c/(2*f) =7.5 cm� Coherence time = time in which MS travels coherence distance

� Coherence time depends on MS speed.

� In cell dimensioning/link budget fast fading is tak en into account through a certain margin (=fast fading margin)

9

Fast Fading

)(01

01)( ttjetta ++ φ

)(05

)(010

0501 )(...)()( ttjttj ettaettattS ++ ++++=+ φφ

)(5

)(1

51 )(...)()( tjtj etaetatS φφ ++=

Scatterers

Especially the changes in component signal phases create rapid variations in sum signal

)(1

1)( tjeta φ

Sum signal at time t

Sum signal at time t+t0

10

Path loss models

11

Content� We recall first two important path loss models for macro- and micro-cell

environments � I Model: Classical Okumura-Hata

� Okumura-Hata is based on only few parameters but it works well and is widely used to predict path loss in macro-cell environments

� II Model: COST 231 or Walfisch – Ikegami� This model is suitable for both macro- and micro-cel l environments and it is mode

general than Okumura-Hata. Walfisch – Ikegami models propagation phenomena more accurately but in cost of increased complexity.

� Then we consider path loss in urban environment whe n both transmitter and receiver are below the rooftop (Berg model)

� Outdoor to outdoor model� Path loss of RS – MS signal in street canyon II Mod el: BRT – BRT, NLOS

(Berg model)� Finally, we discuss shortly on outdoor-to-indoor mo deling� Terminology

� ART= Above Roof Top� BRT = Below Roof Top� LOS = Line-of-Sight� NLOS = Non Line-of-Sight

12

General path loss model/outdoor

� Outdoor path loss models are usually given in the f orm

Here� R is the distance between TX and RX� A and n are constants. Values of these constant are

depending on the various parameters such as carrier frequency, antenna heights etc

� An other form for formula (*)

)(log10 10 RnAL ⋅⋅+= (in decibels)

nnAL RARL ⋅=⋅== ~1010

~ 10/10/

(*)

Note that n defines the exponential attenuation of the signal. Typically its value is 3-4 in urban environment. In free spac e n=2.

13

Okumura-Hata

� Okumura-Hata propagation loss model � Based on measurements in Tokyo� May be the most widely used path loss model for

attenuation of cellular transmissions in built up a reas.� Most suitable for large macro-cells

( ) ( )10 10 10 10log 13.82log 6.55log logc b m bL A B f h a h C h d= + − − + −

A and B constants

33.926.16B

44 – 47, default 44.9C

46.369.55A

1500 –2000 MHz

150-1000 MHz

cf

bh

mh

Carrier frequency (MHz)Base station antenna height

Mobile station antenna height

Mobile antenna gain function

C constant gives distance dependency and should be fitted tolocal measurements

( )ma h

30 200bm h m≤ ≤

1.5mh m≈

14

Okumura-Hata

mhha

MHzfha

mm

cm

5.1,0)(

1500,0)(

==>=

� Mobile station antenna gain function� Small/Medium size city

� Large city

� Antenna gain function can be in most cases be ignor ed!

( ) ( ) ( )10 101.1log 0.7 1.56log 0.8m c m ca h f h f= − − −

( )( )( )

( )( )

2

10

2

10

8.29 log 1.54 1.1 200

3.2 log 11.75 4.97 400

m

m

m

h f MHza h

h f MHz

− ≤= − ≥ MHzfMHz c 1500200 ≤<

15

Okumura-Hata: Example

� Path loss according to Okumura-Hata model in large city when

� f = 450 MHz (□)� f = 900 MHz (*)� f = 1800 MHz (o)� f = 1950 MHz (x)

� Flash-OFDMA (NMT-450), GSM900, GSM1800, WCDMA

0 1 2 3 4 5 6 7 870

80

90

100

110

120

130

140

150

160

170

Range [km]

Pat

h Lo

ss [

dB]

(Oku

mur

a-H

ata

Mod

el)

Note: There would be huge differences in coverage i f allowed path losses would be the same for different systems

BS height = 30m, MS height = 1.5m

16

Okumura-Hata: Example

� Impact of base station antenna height:

� Distance = 3.0 km� Distance = 2.0 km� Distance = 1.0 km� Distance = 0.5 km

� Distance measured between TX and RX

10 15 20 25 30 35 40 45 50120

125

130

135

140

145

150

155

160

165

Base Station Antenna Height [m]

Pat

h Lo

ss [

dB]

(Oku

mur

a-H

ata

Mod

el)

1.5mh m=

1950cf Mhz=

d

bh

17

COST231-Walfisch-Ikegami path loss model

In the following we also use notations:

Note: we consider only NLOS case

18


The rooftop-to-street diffraction loss term determines the loss which occurs on the wave coupling into the street where the receiver is located

φ

19


b

20


Comparison with some measurements made by Nortel in 1996 for a base antenna deployed in Central London well above the a verage rooftop height revealed that the COST 231 W-I model did not correctly model the variation of path loss with mobile height. This pro blem was solved by the above correction factor.

21

COST231-Walfisch-Ikegami path loss model: Impact of rooftop height

Parameters:

BS antenna height = 30m

Carrier frequency = 1950MHz

Street width = 12m

Building spacing = 60m

Street orientation = 90 degrees

Roof top heights:

6m (□),12m (*)

18m (o), 24m (x)0 1 2 3 4 5 6 7 8

90

100

110

120

130

140

150

160

170

180

190

Range [km]

Pat

h Lo

ss [

dB]

Remarks: � W-I and Okumura-Hata give approximately the same pat h loss curve when roof top height is 12m � Impact for rooftop height is crucial for cell cover age

22

COST231-Walfisch-Ikegami path loss model: Impact of MS height

1 2 3 4 5 6 7 8 9 10 11105

110

115

120

125

130

135

140

145

150

Relay Height [m]

Pat

h Lo

ss [

dB]

BS - RS distance = 1 kmParameters:

Roof top height = 12m

Carrier frequency = 1950MHz

Street width = 12m

Building spacing = 60m

Street orientation = 90 degrees

BS antenna height = 15m (o), 20m (*), 25m (x), 30m (+)

Notice:- BS antenna 20m -> 30m => 10 dB gain- MS antenna 1.5m -> 5m => 10 dB gain

MS height [m]

23

Berg model

BS

Scenario:Both BS and MS antennas are below rooftop.Model takes the minimum of an over-the-rooftop signal component and a round-the streets component.This scenario will be increasingly important in future since density of network elements is increasing and macro-cell site costs are high

24

Berg model

Check how to use this modelNote: Path loss depends heavily on corners (how man y, how sharp)

25

Berg model: Example

RS

Red marks = range along the dashed routeViolet marks = range without penetration loss

*

+

x

o

o

*x

o

o

+∇∇∇∇∇∇∇∇

30 m200 m

0 1 00 20 0 30 0 40 0 5 00 6 0050

60

70

80

90

1 00

1 10

1 20

1 30

D is ta nc e fro m re la y [m ]

Pat

h Lo

ss [

dB]

0 100 200 300 400 500 60040

60

80

100

120

140

160

Distance from relay [m]

Pat

h Lo

ss [d

B]

Remarks:- This model is quite pessimistic (high path

loss)- Signal is dying soon round the corner- BS location planning is important

26

Outdoor-to-indoor modeling: Example

Remark:- Path loss depends on number of walls

27

Shadow fading

28

General remarks

� In urban areas macro-cell ranges are from few hundred meters up to few kilometers

� Shadowing by big buildings etc can be critical on cell edge. It may create large coverage holes

� Example: Allowed total signal fading in system is 155dB and shadow fading margin is 8dB. How much larger (in %) would the coverage be without shadow fading margin? Use figure of the slide for range comparison.

� Answer: Cell range would increase from 1.35 km up to 2.2 km which leads to 267% increase in coverage

� Remark: the impact of shadow fading can be really large

0 0.5 1 1.5 2 2.5 3100

110

120

130

140

150

160

170

Range [km]

Pat

h Lo

ss [

dB]

W-I with parameters:BS antenna height = 25mRoof top height = 15mCarrier frequency = 1950MHzStreet width = 12mBuilding spacing = 60mStreet orientation = 90 degrees

29

Shadow fading model

� Shadow fading is modeled by log-normal distribution, i.e. signal strength in decibels is of the form

where first term is the mean path loss and latter term follows the normal distribution,

with zero mean and standard deviation σ.

XLL +=

)(2

1~

2

2

2 xfeXx

=−

σ

σπ

(1)

(2)

30

Cell edge coverage probability

� In link budget shadow fading is taken into account through a certain shadow fading margin (SFM). In ce ll border we require that the signal strength plus SFM is larger than mean signal level by a certain probabil ity, denoted by . Then we compute the corresponding SFM. Hence, we require that

covP

)(log10 10 RnAL ⋅⋅+=

{ }{ }{ }SFMXP

LSFMXLP

LSFMLPP

−>=>++=

>+=cov

)(log10 10 RnAL ⋅⋅+=

-SFM

31


� Using the distribution (2) we find that

From this equation we can solve SFM for given and σ:

{ }

)/(1)/(2

1

2

1

/

2

2cov

2

2

2

σσπ

σπ

σ

σ

SFMQSFMQdte

dxeSFMXPP

SFM

t

SFM

x

−=−==

=−>=

∫

∫∞

−

−

∞

−

−

)1( cov1 PQSFM −⋅= −σ

covP

32


� Function 1-Q is the cumulative density function (CDF) of normal distribution with zero mean and standard deviation 1. Moreover,

)(12

1

2

1

2

1

2

1

2

1)(

,1)(,0)(

22

222

22

222

xQdtedte

dtedtedtexQ

QQ

x

tt

x tt

x

t

−=−=

−==−

=−∞=∞

∫∫

∫∫∫∞ −∞

∞−

−

−

∞−

−∞

∞−

−∞

−

−

ππ

πππ

33


� We can estimate the value of SFM by using the inversion curve of Q.

0 0.5 1 1.5 2 2.5 3 3.5 410

-5

10-4

10-3

10-2

10-1

100

x

Q(x

)

( )1cov1 Pr 1.6449Q − − ≈

Example: Let =0.95 and let σ=6dB. Then wefind from the curve that

and hence, SFM=11.6dB

covP

Outdoors: σ=5-8dB. Indoors: σ=10-12dB.

34

Single cell coverage probability

� Next we compute the cell coverage probability in case of a single cell.

� Analytical computation is pretty technical but result shows the relation between path loss exponent n, standard deviation σ of shadow fading and the required cell coverage probability

35


� Let us compute the single cell coverage probability. We use assumptions:� Mean path loss follows the general formula, i.e.

� Cell radius is R� Users are uniformly distributed in the cell, i.e.

2( , ) , 0 , 0 2

rp r r R

Rϕ ϕ π

π= ≤ ≤ ≤ ≤

)(log10)( 10 rnArL ⋅⋅+=

36


� The cell coverage probability is obtained by averag ing the local coverage probability over all possible mo bile positions. Hence, we must compute the integral

First we need to find formula for coverage probabil ity within a certain distance r.

∫ ∫=π

ϕϕ2

0 0

cov ),()(R

u drdrprPF

37


� The coverage probability at distance r is given by

where lower bound is defined by the maximum allowed path loss. We use now the equations:

XrLrL += )()(

{ }rSFMRLXrLPrP |)()()(cov −>+=

=

+−+=−

r

Rn

rnARnArLRL

10

1010

log10

))(log10()(log10)()(

38


� We obtain a form

and thus, there holds

Next task is to compute this integral

( ){ }( )( )( )σ/log10

|log10)(

10

10cov

Rr

Rr

nSFMQ

rnSFMXPrP

+−=−−>=

( )( )( )∫ ⋅+−=R

Rr

u rdrnSFMQR

F0

102/log10

2 σ

39


� By using the substitution

we obtain

and

10

1, 10 log

SFMa b n e

σ σ= − = − ln

rx a b

R = +

exp

1exp

x ar R

b

x adr R dx

b b

− =

− =

0r x

r R a

= ⇒ → −∞= ⇒

( ) ( )22exp

a

u

x aF Q x dx

b b−∞

− =

∫

40


� We proceed using integration by parts

now

and we get

( )21 1

' exp22

u Q x

u xπ

=

= −

( )

( )

2' exp

2exp

2

x av

b

x abv

b

− =

− =

' 'uv dx uv u vdx= −∫ ∫

( ) ( )

( )

2

2

2 22 1( ) exp exp

2 2 22

21( ) exp

22

x aa

u

x

a

x a x ab b xF Q x dx

b b b

x axQ a dx

b

π

π

=

−∞=−∞

−∞

− − = + − +

− = + − +

∫

∫

41


� We can still go forward by completing the squares:

Then cell coverage probability admit the form

( )

( )

2 222 2

2 2

2

2

2 1 4 2 1 2 2 2 22

2 2 2

1 2 1 2 2

2 2

2 11 2

2

x ax a ax x x x

b b b b b b b

ax

b b b

abx

b b

− − + = − − − = − − + − −

= − − + −

− = − − +

( ) 2

2

2 1 1 1 2( ) exp exp

22

a

u

abF Q a x dx

b bπ −∞

− = + − − ∫

42


� We still need to substitute Then

and finally we are able to write the

( ) ( )2

22 2

2 1 2 11 1 2( ) exp exp ( ) exp 1

22

ab

u

ab abF Q a t dx Q a Q a

b b bπ

−

−∞

− − = + − = + − −

∫

2t x

b= −

Coverage probability on the edge of the cell

( )2

2 1 2( ) exp 1u

abF Q a Q a

b b

− = + − −

10

1, 10 log

SFMa b n e

σ σ= − = −

43


� Path loss exponent n=3

� Shadow fading margin is� 6dB (x)� 9dB (o)� 12dB (*)

� Remark: The SFM difference between 95% and 80% coverage requirements is large

-5 0 5 10 150.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Shadow Fading Margin [dB]

Cel

l cov

erag

e pr

obab

ility

44


-5 0 5 10 150.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Shadow Fading Margin [dB]

Cel

l cov

erag

e pr

obab

ility

� Path loss exponent n=4

� Shadow fading margin is� 6dB (x)� 9dB (o)� 12dB (*)

� Remark: The SFM difference between 95% and 80% coverage requirements is even larger than in case n=3.

45

Fast Fading

46

Recall: Fast Fading

)(01

01)( ttjetta ++ φ

)(05

)(010

0501 )(...)()( ttjttj ettaettattS ++ ++++=+ φφ

)(5

)(1

51 )(...)()( tjtj etaetatS φφ ++=

Scatterers

Especially the changes in component signal phases create rapid variations in sum signal

)(1

1)( tjeta φ

Sum signal at time t

Sum signal at time t+t0

47

Fast fading

� In link budget a fast fading margin is needed because� If fast power control is applied, then

some headroom is needed especially in uplink since MS power reservations are limited. If power control fails, the whole uplink may beak down

� Although link adaptation (=adaptation of channel coding and modulation) would be used instead of fast power control, there can be need for fast fading margin; fast fading can be crucial for slowly moving users

Fading time scale depends on the user speed.

48

Ideal fast power control

� Fast power control aims to convert the channel so that mean power of the signal in the receiver is constant

Transmitted power from MS

Response of the physical channel

Channel seen by BS receiver (AWGN channel)

Ideal case

Time

49

Limited power control dynamics

� At the cell edge MS power control starts to hit its maximum value. => Number of erroneous frames is increasing => Data rate is decreased when QoS degrades => in the worst case connection breaks down

MS travels towards cell edge/coverage hole => mean transmission power needs to be increased

Maximum TX power value

Longer and longer times with ‘bad connection’ tempor al length of the fades depends on the user speed

Documents

Cellular Network Planning and Optimization Part2