propagation models in wireless communications

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Propagation models for wireless mobilecommunications

D. Vanhoenacker-Janvier,Microwave Lab. UCL, Louvain-la-Neuve,

Belgium

AT1-Propagation in wired, wireless and optical communications

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Content of the presentation

- Free space losses- Plane earth losses- Models for wireless channel

macrocellsshadowingnarrowband fast fadingwideband fast fadingmegacells

This presentation is based on the following reference:S.R. Saunders, Antennas and propagation for wirelesscommunication systems, Wiley, 1999.

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Free space losses

emitter receiver

GT GR

LPT PR

RT

RTTR LLL

GGPP =

LT LR

Where PR is the power at the receiver terminal PT is the power at the emitter terminal GT is the gain of the emitter antenna (dBi) GR is the gain of the receiver antenna (dBi) L is the path loss LT,E are the feeder losses (emitter, receiver)

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Free space losses

TIT

TT PLGPEIRP ==

Effective isotropic radiated power:

Effective isotropic received power:

R

RRRI G

LPP =

Path loss:�

��

�=��

�=TRR

RTT

RI

TI

LLPGGP

PPL log10log10

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Free space losses

Assuming 2 antennas, with their polarisation matched,the power density arriving to the receiving antenna is(feeder losses are neglected)

24 rGPS TTπ

=

The power received by the antenna is

24 rAGPP eRTT

R π=

where AeR is the effective aperture of thereceive antenna:

eRR AG 24λπ=

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Free space losses

And finally

2

4�

��

�=r

GGPP

TRT

R

πλ Friis formula

The free space loss becomes:

24 ��

�==λπr

PGGPL

R

RTT

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Plane earth loss

Wireless environment is not governed by free space losses,due to the presence of the ground.

Base station

mobile

This is not multipath!

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Plane earth loss

Assumption: flat reflecting ground

( )( ) 22

2

221

rhhr

rhhr

mb

mb

++=

+−=

The lengths of the direct and reflected rays are:

The amplitude of the fields is assumed to be the same, onlythe phase difference is taken into account:

�

��

�+�

�

��

−−+��

��

+=− 1122

12 rhh

rhhrrr mbmb

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Plane earth loss

In most of the practical cases: rhh mb <<,

And the amplitude of the electric field is

( )ψ∆+= jREEtot exp10

Then

( )rhhrr bm2

12 ≈−

E0 is the amplitude of the direct field

rhhk bm2=∆ψ

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Plane earth loss

( )22

exp14

ψπλ ∆+�

��

�= jRrP

PT

R

If the angle of incidence is small, the reflection coefficient isclose to -1.

22

sincos14

ψψπλ ∆−∆−�

��

�= jr

PP TR

The phase difference is small so that

ψψψ

∆≅∆≅∆

sin1cos

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Plane earth loss

222

2 444

��

��

��

�≅∆��

��

�≅d

hhr

Pr

PP bmTTR λ

ππλψ

πλ

2

2�

��

�≅d

hhPP bmTR

The loss is increasing with the distance by 40 dB per decadeand decreasing with the antenna heights.

This is not an accurate model of propagation; it is sometimesused as a reference case.

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Models for wireless channel

Various types of models for the wireless channel:- empirical models,

based on measurementslinked to the environment and the parameters of themeasurement campaign

- deterministic modelsbased on a fixed geometry (buildings, streets,…)used to analyse particular situations

- physical-statistical modelscombination of deterministic models and statistics ofvarious parameters (building heights, street width,…)

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Models for wireless channel

- Models for macrocells

- Shadowing

- Narrowband fast fading

- Wideband fast fading

- Megacells

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Macrocells

Macrocell geometry

Definition: hb>h0

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Macrocells

Macrocell models are used by system designers to placethe base stations.

They are- simple- dependent on distance from the base station only- based on measurement (empirical models)

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Macrocells-empirical models

Example of measurements taken in a suburban area.

Each measurementrepresents anaverage of a set ofsamples (localmean)

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Macrocells-empirical models

Simplest form for an empirical path loss model:

kKKrndBL

rk

LPP

nT

R

log10;log10)(

1

=+=

==

PR and PT are the effective isotropic transmitted andpredicted isotropic received power, K and n are constants ofthe model.

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Macrocells -empirical models

Measurements taken in urban and suburban area usuallyfind a path loss exponent close to 4, but with losses higherthan predicted.

( )( ) refref LrrndBL

KrndBL+=

+=log10)(log10

Represented by the clutter factor

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In urban andsuburban areas

J. Egli, “Radiowave propagation above 40 Mc over irregular terrain”, Proc. IRE, pp. 1383-1391, 1957.G. Delisle, J. Lefèvre, M. Lecours, J. Chouinard, ‘Propagation loss prediction : a comparative study withapplication to the mobile radio channel”, IEEE Trans. Veh. Techn., vol.26, n)4, pp. 295-308, 1985.

10log203,7610log103,76≥−=<−=

mmm

mmm

hforhLhforhL

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Fully empirical model, based on an extensive series ofmeasurements made around Tokyo city between 200 MHzand 2 GHz1 .

Predictions are based on a series of graphs; the mostimportant ones have been approximated in a set offormulae by Hata2.

1 Y. Okumura, E. Ohmori, T. Kawano, K. Fukuda, “Field strength and its variability in VHF andUHF land mobile radio service”, Rev. Electr. Communic. Lab., vol.16, pp. 825-873, 1968.2 M. Hata, “Empirical formula for propagation loss in land mobile radio services”, IEEE Trans.Vehic. Techn., vol 29, pp. 317-325, 1980.

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The terrain categories proposed by Okumura are the following:

- Open area: open space, no tall trees or buildings in the path,land cleared for 300-400m ahead, e.g. farmlands, rice fields,open fields- Suburban area: village or highway scattered with trees andhouses, some obstacles near the mobile but not very congested- Urban area: built up city or large town with large buildingsand houses with two or more storeys, or larger villages withclose houses and tall, thickly grown trees.

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Lee model is a power law model with parameters taken frommeasurements in a number of locations

( ) ��

�++−+��

�+��

�=

+��

�−−−=

+��

�−−−=

+��

�−−−=

10log106

10log10

100log20

900loglog1.4364

900loglog8.3670

900loglog4.387.61

0

0

0

0

mmb

Tb

R

R

R

hGGPh

NewarkfnRP

iePhiladelphfnRP

suburbanfnRP

α

α

α

α

hb,hm in feet; PT in Watts, f in MHz, R in miles (R>1mile)

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W.C.Lee, Mobile design fundamentals, John Wiley, New York, 1993.

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Limitations of the empirical models:

- they can only be used over parameter ranges included in theoriginal measurement set.- environment must be classified subjectively accordingcategories, which may be different in different countries.- they provide no physical insight into the mechanisms bywhich propagation occurs.

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Macrocells-Physical models

S. R. Saunders, F. Bonar, “Prediction of mobile radio wave propagation aver buildings ofirregular heights and spacings, IEEE Trans. Ant. Prop., vol. 42, n°2, pp. 137-144.

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Macrocells-Physical models

S. Saunders, F; Bonar, “Explicit multiple building diffraction attenuation function for mobileradio wave propagation”, Electr. Let., vol. 27, n°14, pp. 1276-1277, 1991.

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Macrocells-base station antennas

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Shadowing

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Shadowing

Typical variation of shadowing with mobile position, at a fixed distance of thebase station.

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Shadowing

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Shadowing

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Narrowband fast fading

After path loss and shadowing, there is still significantvariation in the signal as mobile moves over distances whichare small compared with the shadowing.

This phenomenon is

Fast fading

and can be described bydeterministic modelsstatistical models

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Non-line-of-sight

Line-of-sight

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Deterministic model: ray-tracing method

The built-up area is composed of parallelepipedic blocswith plane faces representing buildings either vegetation.

The field arriving at the receiver results from thecombination of all components arriving at the terminal:- direct component (if it exists)- reflected components (various orders of reflection)- diffracted components (various orders of diffraction)- scattered components (d∼λ).It is necessary to know the√electrical characteristics of theblocs (ε and σ) at the frequency of interest.

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3-D bloc model for “place du Levant”

T

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30 40 50 60 70 80 90−60

−55

−50

−45

−40

−35

−3012.5 GHz

Distance from Maxwell building, [m]

Rec

eive

d po

wer

, [dB

]

30 40 50 60 70 80 90−65

−60

−55

−50

−45

−40

−35

−3030 GHz

Distance from Maxwell building, [m]

Rec

eive

d po

wer

, [dB

]

+Simulation winter

Simulation summer

Meas. winter

Meas. summer

Comparison between simulation and measurement

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LOS path (simulated, without trees)

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Path under the balcony

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T

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Statistical model for the multipath signal

A sum of enough independent variables approaches veryclosely a normal distribution.

In the NLOS case, the real and imaginary parts of the electricfield components are composed of a sum of a large number ofwaves

they have a normal distribution

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Complex baseband signal (Ricerepresentation)

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Pdf of r is a Rayleigh function

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filtered

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Doppler effect on the direct wave

vϑ

( )( )

��

��

��

� −=

��

��

��

��

� −=

−=

tvfjE

vttfjE

kxtjEEr

ϑλ

π

ϑλ

π

ϑω

cos2exp

cos12exp

cosexp

00

00

00

xavv =

xa

df

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Effect of Doppler spread on signal spectrum:

a different doppler shift affects all the multipaths

λvffm 0±=

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Statistics of the angle of arrival of the multipaths

Pdf of the arrival angle

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The mean power arriving from an element of angle dα

( ) ( ) αααα dpGP =)(

has a given Doppler shift (G(α) is the antenna gain for α).The power spectrum of the received signal, S(f), is found byequating the power in an element of α to the power in anelement of spectrum

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

α

αααααααααα

ddf

pGpGfS

dpGdpGdffSfP−−+=

−−+==

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Assuming a short dipole antenna:

( ) 5.1=αG

and the spectral density becomes

( ) m

mm

fffor

fff

fS <��

��−

=2

1

5.1

π

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Classical Doppler spectrum

Very difficult to measure due to the small bandwith!

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Limited angle of arrival :

−π/2 π/2

β β1/2β

p(α)

β β

( )( )( )215.1

mm ffffS

−=β

22 mm fff ≤≤−

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Other measurable parameters linked to the Doppler spectrum

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LCR

Jakes

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AFD

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Exemple:Soit un système mobile à 900 MHz et un mobile se déplaçant à 100km/h, combien de fois le signal sera-t-il de 20dB inférieur à savaleur rms en 1 minute?Dans ce cas,

Hzcvff c

m 33.83103

360010100109008

36=⋅==

( )1.020

25.099.01.05.2exp2 2

=−=

≅⋅⋅=−=

dBrcar

rrfN

m

R π

Cela fait secondeparfois2125.0 == mR fNEn doublant la fréquence et en divisant la vitesse par deux, onobtient le même lcr.

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Importance of interleaving

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Another way to see Doppler effect is to work in time domain.The inverse Fourier Transform of the power spectral density isthe autocorrelation function. It expresses correlation between asignal at t and its value at t+τ. The autocorrelation function ofthe received signal writes down

( ) ( ) ( )[ ] [ ]2* αταατρ EttE +=

For the classical spectrum, one obtains( ) ( )τπρ mfJt 20=

The coherence time is defined as the time during which tehchannel can be considered as constant. The signals, shorter thenthe coherence time are not affected by the Doppler shift nor thespeed of the mobile.

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In the time domain:

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Exemple:Quel est le débit maximum pour éviter les effets de l’étalementDoppler dans un système mobile à 900 MHz pour une vitessemaximum du mobile de 100 km/h?La fréquence Doppler maximum est

Hzcvff c

m 33.83103

360010100109008

36=⋅==

Le temps de cohérence est

msf

Tm

c 15.233.8316

916

9 ===ππ

C’est donc la durée maximum d’un symbole, cela fait un débitsymbole minimum de 465 bits/sec.

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Wideband fast fading

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Megacells

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Megacells

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Megacells

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Megacells

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Megacells

Local multipath effects

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Megacells

Empirical narrowband modelsEmpirical Roadside Shadowing model (ERS)

Statistical modelsLoo model (shadowing due to roadside trees)Corazza model Lutz model (2 states: LOS and NLOS)

Physical-statistical model for built up area

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Megacells

dm

w

hm

hb

hbh2

h1L

A'

A

Basic physical parameters:

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Megacells

Fade statistics:

( ) ( )

( ) ( ) ( ) ( ) ϑφϑϕ ϑφ

π πφθ

dddwdddhTTwTdT

hTTaT

mbWmD

wbHWDHAA

m

bmb

⋅⋅⋅

⋅⋅=∞ ∞2/

0

2/

0 0 0 0

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Megacells

0 2 4 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

0.25

0.3

Building height, [m]

Pro

babi

lity

dens

ity fu

nctio

n

Guildford

Building height distribution

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Megacells

5 15 25 35 45 55 65 75 850

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Elevation angle, [deg.]

Pro

babi

lity

dens

ity fu

nctio

n

Maximum elevation anglefor Iridium constellationat London

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Megacells

0 10 20 30 40 50 600

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Street width, [m]

Pro

babi

lity

dens

ity fu

nctio

n

Street width distribution inGuildford

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Megacells

0 1 2 3 4 5 60

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Satellite azimuth angle, [rad.]

Pro

babi

lity

dens

ity

Distribution of the nearest satellite azimuthangle (relative to earth parallels) for Iridium atLondon

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Megacells

0 1 2 3 4 5 60.15

0.152

0.154

0.156

0.158

0.16

0.162

0.164

0.166

0.168

0.17

Satellite azimuth angle, [rad.]

Pro

babi

lity

dens

ityDistribution of the global azimuth angle (relative tostreet axis) for Iridium constellation at London

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Megacells