Propagation Model
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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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Macrocells -empirical models
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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Macrocells -empirical models
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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Macrocells -empirical models
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Macrocells -empirical models
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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Macrocells -empirical models
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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Macrocells -empirical models
W.C.Lee, Mobile design fundamentals, John Wiley, New York, 1993.
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Macrocells -empirical models
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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Narrowband fast fading
Non-line-of-sight
Line-of-sight
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Narrowband fast fading
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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Narrowband fast fading
3-D bloc model for “place du Levant”
T
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Narrowband fast fading
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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Narrowband fast fading
LOS path (simulated, without trees)
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Narrowband fast fading
Path under the balcony
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Narrowband fast fading
T
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Narrowband fast fading
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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Narrowband fast fading
Complex baseband signal (Ricerepresentation)
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Narrowband fast fading
Pdf of r is a Rayleigh function
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Narrowband fast fading
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Narrowband fast fading
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Narrowband fast fading
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Narrowband fast fading
filtered
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Narrowband fast fading
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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Narrowband fast fading
Effect of Doppler spread on signal spectrum:
a different doppler shift affects all the multipaths
λvffm 0±=
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Narrowband fast fading
Statistics of the angle of arrival of the multipaths
Pdf of the arrival angle
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Narrowband fast fading
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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Narrowband fast fading
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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Narrowband fast fading
Classical Doppler spectrum
Very difficult to measure due to the small bandwith!
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Narrowband fast fading
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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Narrowband fast fading
Other measurable parameters linked to the Doppler spectrum
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Narrowband fast fading
LCR
Jakes
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Narrowband fast fading
AFD
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Narrowband fast fading
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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Narrowband fast fading
Importance of interleaving
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Narrowband fast fading
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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Narrowband fast fading
In the time domain:
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Microwaves UCL
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Narrowband fast fading
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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Microwaves UCL
63
Wideband fast fading
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Microwaves UCL
64
Wideband fast fading
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Microwaves UCL
65
Wideband fast fading
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Microwaves UCL
66
Wideband fast fading
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Microwaves UCL
67
Wideband fast fading
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Microwaves UCL
68
Wideband fast fading
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Microwaves UCL
69
Wideband fast fading
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Microwaves UCL
70
Wideband fast fading
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Microwaves UCL
71
Wideband fast fading
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Microwaves UCL
72
Wideband fast fading
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Microwaves UCL
73
Megacells
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Microwaves UCL
74
Megacells
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Microwaves UCL
75
Megacells
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Microwaves UCL
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Megacells
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Microwaves UCL
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Megacells
Local multipath effects
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Microwaves UCL
78
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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Microwaves UCL
79
Megacells
dm
w
hm
hb
hbh2
h1L
A'
A
Basic physical parameters:
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Microwaves UCL
80
Megacells
Fade statistics:
( ) ( )
( ) ( ) ( ) ( ) ϑφϑϕ ϑφ
π πφθ
dddwdddhTTwTdT
hTTaT
mbWmD
wbHWDHAA
m
bmb
⋅⋅⋅
⋅⋅=∞ ∞2/
0
2/
0 0 0 0
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Microwaves UCL
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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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Microwaves UCL
82
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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Microwaves UCL
83
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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Microwaves UCL
84
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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Microwaves UCL
85
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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Microwaves UCL
86
Megacells