This document summarizes key concepts in propagation models for wireless mobile communications. It discusses free space losses, plane earth losses, and models for the wireless channel including macrocells, shadowing, narrowband fast fading, and wideband fast fading. Empirical and physical statistical models are described for modeling propagation in different environments like urban, suburban, and rural areas. Deterministic and statistical models are presented for modeling narrowband fast fading effects.
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Propagation models for wireless mobile
communications
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
macrocells
shadowing
narrowband fast fading
wideband fast fading
megacells
This presentation is based on the following reference:
S.R. Saunders, Antennas and propagation for wireless
communication systems, Wiley, 1999.
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Free space losses
emitter receiver
GT GR
LPT PR
RT
RTT
R
LLL
GGP
P =
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
TI
T
TT P
L
GP
EIRP ==
Effective isotropic radiated power:
Effective isotropic received power:
R
RR
RI
G
LP
P =
Path loss:
ö
ç
è
æ
=÷
ö
ç
è
æ
=
TRR
RTT
RI
TI
LLP
GGP
P
P
L 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)
2
4 r
GP
S TT
π
=
The power received by the antenna is
2
4 r
AGP
P eRTT
R
π
=
where AeR is the effective aperture of the
receive antenna:
eRR AG 2
4
λ
π
=
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Free space losses
And finally
2
4
ö
ç
è
æ
=
r
GG
P
P
TR
T
R
π
λ Friis formula
The free space loss becomes:
2
4 ö
ç
è
æ==
λ
πr
P
GGP
L
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
22
1
rhhr
rhhr
mb
mb
++=
+−=
The lengths of the direct and reflected rays are:
The amplitude of the fields is assumed to be the same, only
the phase difference is taken into account:
ù
ê
ê
ë
é
+÷
ø
ö
ç
è
æ −
−+÷
ø
ö
ç
è
æ +
=− 11
22
12
r
hh
r
hh
rrr 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
( )
r
hh
rr bm2
12 ≈−
E0 is the amplitude of the direct field
r
hh
k bm2
=∆ψ
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Plane earth loss
( )2
2
exp1
4
ψ
π
λ
∆+
ö
ç
è
æ
= jR
rP
P
T
R
If the angle of incidence is small, the reflection coefficient is
close to -1.
2
2
sincos1
4
ψψ
π
λ
∆−∆−
ö
ç
è
æ
= j
r
PP TR
The phase difference is small so that
ψψ
ψ
∆≅∆
≅∆
sin
1cos
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Plane earth loss
22
2
2
4
44
ö
ç
è
æ
÷
ö
ç
è
æ
≅∆÷
ö
ç
è
æ
≅
d
hh
r
P
r
PP bm
TTR
λ
π
π
λ
ψ
π
λ
2
2
ö
ç
è
æ
≅
d
hh
PP bm
TR
The loss is increasing with the distance by 40 dB per decade
and decreasing with the antenna heights.
This is not an accurate model of propagation; it is sometimes
used as a reference case.
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Models for wireless channel
Various types of models for the wireless channel:
- empirical models,
based on measurements
linked to the environment and the parameters of the
measurement campaign
- deterministic models
based on a fixed geometry (buildings, streets,…)
used to analyse particular situations
- physical-statistical models
combination of deterministic models and statistics of
various 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 models are used by system designers to place
the 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
Simplest form for an empirical path loss model:
kKKrndBL
r
k
LP
P
n
T
R
log10;log10)(
1
=+=
==
PR and PT are the effective isotropic transmitted and
predicted isotropic received power, K and n are constants of
the model.
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Macrocells -empirical models
Measurements taken in urban and suburban area usually
find a path loss exponent close to 4, but with losses higher
than predicted.
( )
( ) refref LrrndBL
KrndBL
+=
+=
log10)(
log10
Represented by the clutter factor
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Macrocells -empirical models
In urban and
suburban 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 with
application to the mobile radio channel”, IEEE Trans. Veh. Techn., vol.26, n)4, pp. 295-308, 1985.
10log203,76
10log103,76
≥−=
<−=
mmm
mmm
hforhL
hforhL
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Macrocells -empirical models
Fully empirical model, based on an extensive series of
measurements made around Tokyo city between 200 MHz
and 2 GHz1 .
Predictions are based on a series of graphs; the most
important ones have been approximated in a set of
formulae by Hata2.
1 Y. Okumura, E. Ohmori, T. Kawano, K. Fukuda, “Field strength and its variability in VHF and
UHF 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
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 and
houses, some obstacles near the mobile but not very congested
- Urban area: built up city or large town with large buildings
and houses with two or more storeys, or larger villages with
close houses and tall, thickly grown trees.
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Macrocells -empirical models
Lee model is a power law model with parameters taken from
measurements in a number of locations
( ) ö
ç
è
æ++−+÷
ö
ç
è
æ+÷
ö
ç
è
æ=
+÷
ö
ç
è
æ−−−=
+÷
ö
ç
è
æ−−−=
+÷
ö
ç
è
æ−−−=
10
log106
10
log10
100
log20
900
loglog1.4364
900
loglog8.3670
900
loglog4.387.61
0
0
0
0
m
mb
Tb
R
R
R
h
GG
Ph
Newark
f
nRP
iePhiladelph
f
nRP
suburban
f
nRP
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
Limitations of the empirical models:
- they can only be used over parameter ranges included in the
original measurement set.
- environment must be classified subjectively according
categories, which may be different in different countries.
- they provide no physical insight into the mechanisms by
which propagation occurs.
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Macrocells-Physical models
S. R. Saunders, F. Bonar, “Prediction of mobile radio wave propagation aver buildings of
irregular 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 mobile
radio wave propagation”, Electr. Let., vol. 27, n°14, pp. 1276-1277, 1991.
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Narrowband fast fading
After path loss and shadowing, there is still significant
variation in the signal as mobile moves over distances which
are small compared with the shadowing.
This phenomenon is
Fast fading
and can be described by
deterministic models
statistical models
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Narrowband fast fading
Deterministic model: ray-tracing method
The built-up area is composed of parallelepipedic blocs
with plane faces representing buildings either vegetation.
The field arriving at the receiver results from the
combination 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 the
blocs (ε and σ) at the frequency of interest.
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Narrowband fast fading
Statistical model for the multipath signal
A sum of enough independent variables approaches very
closely a normal distribution.
In the NLOS case, the real and imaginary parts of the electric
field components are composed of a sum of a large number of
waves
they have a normal distribution
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Narrowband fast fading
Doppler effect on the direct wave
v
ϑ
( )( )
ö
ç
è
æ
÷
ö
ç
è
æ
−=
÷
ö
ç
è
æ
÷
ö
ç
è
æ
−=
−=
t
v
fjE
vttfjE
kxtjEEr
ϑ
λ
π
ϑ
λ
π
ϑω
cos2exp
cos
1
2exp
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
λ
v
ffm 0±=
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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 by
equating the power in an element of α to the power in an
element of spectrum
( ) ( ) ( ) ( ) ( ) ( )
( )
( ) ( ) ( ) ( )
α
αααα
αααααα
d
df
pGpG
fS
dpGdpGdffSfP
−−+
=
−−+==
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Narrowband fast fading
Assuming a short dipole antenna:
( ) 5.1=αG
and the spectral density becomes
( ) m
m
m
fffor
f
ff
fS <
öç
è
æ−
=
2
1
5.1
π
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Narrowband fast fading
Exemple:
Soit un système mobile à 900 MHz et un mobile se déplaçant à 100
km/h, combien de fois le signal sera-t-il de 20dB inférieur à sa
valeur rms en 1 minute?
Dans ce cas,
Hz
c
vf
f c
m 33.83
103
36001010010900
8
36
=
⋅
==
( )
1.020
25.099.01.05.2exp2
2
=−=
≅⋅⋅=−=
dBrcar
rr
f
N
m
R
π
Cela fait secondeparfois2125.0 == mR fN
En doublant la fréquence et en divisant la vitesse par deux, on
obtient le même lcr.
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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 is
the autocorrelation function. It expresses correlation between a
signal at t and its value at t+τ. The autocorrelation function of
the 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 teh
channel can be considered as constant. The signals, shorter then
the coherence time are not affected by the Doppler shift nor the
speed of the mobile.
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Narrowband fast fading
Exemple:
Quel est le débit maximum pour éviter les effets de l’étalement
Doppler dans un système mobile à 900 MHz pour une vitesse
maximum du mobile de 100 km/h?
La fréquence Doppler maximum est
Hz
c
vf
f c
m 33.83
103
36001010010900
8
36
=
⋅
==
Le temps de cohérence est
ms
f
T
m
c 15.2
33.8316
9
16
9
===
ππ
C’est donc la durée maximum d’un symbole, cela fait un débit
symbole minimum de 465 bits/sec.
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Megacells
Empirical narrowband models
Empirical Roadside Shadowing model (ERS)
Statistical models
Loo 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
5 15 25 35 45 55 65 75 85
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Elevation angle, [deg.]
Probabilitydensityfunction
Maximum elevation angle
for Iridium constellation
at London
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Megacells
0 10 20 30 40 50 60
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Street width, [m]
Probabilitydensityfunction
Street width distribution in
Guildford
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Megacells
0 1 2 3 4 5 6
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Satellite azimuth angle, [rad.]
Probabilitydensity
Distribution of the nearest satellite azimuth
angle (relative to earth parallels) for Iridium at
London
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Megacells
0 1 2 3 4 5 6
0.15
0.152
0.154
0.156
0.158
0.16
0.162
0.164
0.166
0.168
0.17
Satellite azimuth angle, [rad.]
Probabilitydensity Distribution of the global azimuth angle (relative to
street axis) for Iridium constellation at London