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1
MOBILE PROPAGATION CHANNEL:
LARGE-SCALE PATH LOSS
2
Introduction
Mobile radio channel is an important controllingfactor in wireless communication systems
Transmission path between transmitter and receivercan vary in complexity LOS (Line-Of-Sight) - simplex
Wired channels are stationary and predictable, radiochannels are extremely random and have complex
models Modeling of radio channels is done in statistical
fashion based on measurements for each individualcommunication system or frequency spectrum
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Propagation Models To predict the average received signal
strength at a given distance from thetransmitter - large scale propagationmodels, hundreds or thousands of meters
To predict the variability of the signalstrength, at close spatial proximity to aparticular location -Small scale or fading
models
4
Free Space Propagation Model
The free space propagation model is used topredict received signal strength when thetransmitter and receiver have a clear,unobstructed line-of-sight path between them
The free space model predicts that receivedpower decays as function of the transmitter-receiver (T-R) separation distance raised tosome power
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Free Space Propagation Model
6
Free Space Propagation Model
Free space power received by a receiver antennawhich is separated from a radiating transmittingantenna by a distance d (Friis free space equation):
P t is the transmitted power
P r (d) is the received powerG t , G R is the transmitter and receiver antenna giand is the T-R separation distance in metersL is the system loss factor not related to propagation (L ≥1)λ is the wavelength in meters
2
2 2
. . .( )
( 4 ) . .
t t r r
P G G P d
d L
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Free Space Propagation Model The gain of an antenna is related to its
effective aperture, A e
A e is related to the physical size of theantenna
λ is related to the carrier frequency
2
4 e AG
8
Free Space Propagation Model
The effective isotropic radiated power (EIRP )represents the maximum radiated power availablefrom a transmitter in the direction of maximumantenna gain, compared to an isotropic radiator
In practice, effective radiated power (ERP ) is used
instead of EIRP to demonstrate the maximumradiated power as compared to a half-wave dipoleantenna
t t IRP PG
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Free Space Propagation Model The path loss for the free space model when
antenna gain are included is given by
When antenna gains are excluded, theantennas are assumed to have unity gain andpath loss is given by
2
2 210 log 10 log
4
t t r
r
P GG PL dB
P d
2
2 210 log 10 log
4
t
r
P PL dB
P d
10
Free Space Propagation Model
The Friis free space model is a only validpredictor for P r for values of which are in thefar-field of the transmitting antenna
The far-field, or Fraunhofer region, of atransmitting antenna is defined as the regionbeyond the far-field distance d
f , related to
the largest linear dimension of the transmitterantenna aperture and the carrier wavelength
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Free Space Propagation Model The Fraunhofer distance is given by
D is the largest physical linear dimension of the antenna
d f must satisfy , and
22
f
Dd
f d Df d
12
Free Space Propagation Model
Large-scale propagation models use a close-in distance,d 0 , as a known received power reference point
The received power, P r (d) , at any distance d > d 0 , maybe related to P r at P 0
The reference distance must be chosen such that it lies inthe far-field region, that is, d 0 ≥ d f , and d 0 is chosen to besmaller than any practical distance used in the mobilecommunication system
The received power in free space at a distance greaterthan d 0 is given by
2
00 0,r r f
d P d P d d d d
d
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Free Space Propagation Model Large dynamic range of received power
levels, often dBm or dBW units are usedto express received power levels
P r (d) is in dBm
P r (d 0 ) is in watts
( ) 10 log 20 log
0,001,r o o
r o f
P d d P d d d d
W d
14
Example
Given a transmitter produces 50 W of power. If this
power is applied to a unity gain antenna with 900MHz carrier frequency, find the received power at afree space distance of 100 m from the antenna. Whatis P r (10 km). Assume unity gain for the receiverantenna
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Example The received power at 100m
The received power at 10Km
W Ld
GG P md P r t t
r
6
22
2
22
2
10.5,31.100.)4(
)3/1.(1.1.50
)4(100
63,5.10
100 10 log 24, 50,001
r d m dBm
100( 10 ) 24,5 20 log 64,5
10000r P d km dBm
16
Propagation Mechanisms
Receiving power is generally the mostimportant parameter predicted by large-scale propagation model based on thephysics of reflection, scattering, anddiffraction
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Propagation Mechanisms Reflection occurs when a propagating
electromagnetic wave impinges upon an object whichhas very large dimensions when compared to thewavelength of the propagating wave.
Diffraction occurs when the radio path between thetransmitter and receiver is obstructed by a surfacethat has sharp irregularities
Scattering occurs when the medium through whichthe wave travels consists of objects with dimensionsthat are small compared to the wavelength and
where the number of obstacles per unit volume islarge
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Reflection
Reflection occur from the surface of theearth and from buildings and walls
When a radio wave propagating in onemedium impinges upon anothermedium having different electrical
properties, the wave is partiallyreflected an partially transmitted
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Reflection The electric field intensity of the reflected and
transmitted waves may be related to theincident wave the medium of origin throughthe Fresnel reflection coefficient (Γ)
The reflection coefficient is a function of thematerial properties, and generally depends onthe wave polarization, angle of incidence, and
the frequency of the propagation wave
20
Law Of Reflection At TheBoundary Between 2 Dielectrics
Reflection coefficient
Transmission coefficient
r
i
E
E
1t
i
E T
E
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Ground Reflection (2-ray)
Model In mobile radio channel, the 2-ray ground
reflection model is a useful propagationmodel that is based on geometrics optics, andconsiders both direct path and a groundreflected propagation path betweentransmitter and receiver
This model has been found to be reasonablyaccurate for predicting the large-scale signal
strength over distance of several kilometersfor mobile radio systems
22
Ground Reflection (2-ray)Model
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Ground Reflection (2-ray)
Model In mobile communication systems, the
maximum T-R separation distance is atmost only a few tens of kilometers, andthe earth may be assumed to be flat
The total received E-field, E TOT , is thena result of the direct line-of-sight
component, E LOS , and the groundreflected component, E g
24
Ground Reflection (2-ray)Model
If E 0 is the free space E-field (V/m) at thereference distance d0 from the transmitter,then for d > d 0 , the free space propagatingE-field is given by
where represents the envelope of
the E-field at d distance from the transmitter
0 0, cos c
E d d E d t t
d c
0 0( , )d t E d d
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Ground Reflection (2-ray)
Model Two propagating waves arrives at the receiver: the
direct wave that travel a distance d ’ ; and thereflected wave that travel a distance d ”
The direct LOS component at the receiver can beexpressed
The E-field for the ground reflected wave can beexpressed
0 0'
( ', ) cos'
LOS c
E d d E d t t
d c
0 0 ''( '', ) cos
'' g c
E d d E d t t
d c
26
Ground Reflection (2-ray)Model
According to laws of reflection in dielectrics:
Where Γ is the reflection coefficient for ground
For small values of θ i , the reflected wave isequal in magnitude and 1800 out of phasewith the incident wave
i o
g i E E (1 )t i E E
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Ground Reflection (2-ray)
Model The resultant E-field, assuming perfect
ground reflection (i.e. Γ = 1 and E t = 0) is thevector sum of ELOS and Eg
TOT LOS g E E E
0 0 0 0' ''( , ) cos[ ( 1) cos
' ''TOT c c
E d E d d d E d t t t
d c d c
28
Ground Reflection (2-ray)Model
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Ground Reflection (2-ray)
Model The path difference between line-of-sight and the
ground reflected paths can be expressed
The phase difference θ Δ between the two E-fieldcomponent and the time delay τ d between the
arrivals of the components
2 2 2 2" ' ( ) ( )t r t r d d h h d h h d
2" ' t r h h
d d d
2 c
c
2d
cc f
30
Ground Reflection (2-ray)Model
As d becomes large, the difference between the distanced ’ and d ” becomes very small, and the amplitudes of E LOS
and E g is virtually identical and differ only in phase
The E-field at the receiver at the distance d from the
transmitter can be written as
0 0 0 0 0 0
' "
E d E d E d
d d d
2sin2cos22
0000
d
d E
d
d E E
TOT
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Ground Reflection (2-ray)
Model
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Ground Reflection (2-ray)Model
If θ Δ < 0.3 radian
E-field can be approximately as
K is constant related to E 0 , the antenna height and thewavelength
2sin 0, 3
2 2
t r h hrad
d
20 20
3
t r t r h h h hd
0
2
2 2( / )o t r
TOT
E d h h k E V m
d d d
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Ground Reflection (2-ray)
Model The received power at the distance d from the
transmitter can be expressed as
Path loss 2-ray model (with antenna gains) can beexpressed in dB as
When θ Δ = Π , then d = (4h t h r )/λ is where the ground appears inthe first Fresnel zone between the transmitter and receiver
2 2
4( ) t r
r t t r
h h P d P G G
d
( ) 40log 10log 10log 20log 20logt r t r PL dB d G G h
34
Example
A mobile is located 5 km away from a base station.and uses a vertical /4 monopole antenna with a gainof 2.55 dB to receive cellular radio signals. The Efield at 1 km from the transmitter is measured to be10-3 V/m. The carrier frequency used is 900 MHz.
(a) Find the length and gain of the receiving antenna
(b) Find the received power at the mobile using the
2-way ground model assuming the height of thetransmitting antenna is 50 m and receiving antenna
is 1.5 m above the ground.
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Example Wavelength:
Length of the antenna:
Gain of antenna:
Since
Received power
m f
c33,0
10.900
10.36
8
4 8.33 L cm
2.55 1.8G dB
r t hhd
mV
mV d
k
d
hh
d
d E d E r t
R
/10.1,113)10.5.(33,0
5,1.50.2
10.5
10.1.10.2
)/(22
)(
633
33
2
00
dBmdBW
W kmd P r
68,9268,122
10.4,54
33,08,1
377
10.1,113)5( 13
226
36
Diffraction
Diffraction allows radio signals to propagatearound the curved surface of the earth,beyond horizon, and to propagate behindobstructions
The received field strength decreases rapidlyas a receiver moves deeper into obstructed(shadow) region.
The diffraction field still exists and often hassufficient strength to produce a useful signal
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Diffraction – Fresnel Zone
Geometry Consider a transmitter and receiver separated
in free space as shown in below figure
Let an obstructing screen of effective height h with infinite width be placed between them ata distance d 1 from the transmitter and d 2
from the receiver
The wave propagating from the transmitter to
the receiver via the top of the screen travelsa longer distance than if a direct line-of-sightpath existed.
38
Diffraction – Fresnel ZoneGeometry
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Diffraction – Fresnel Zone
Geometry Assuming h << d 1 , d 2 and h >> λ
The difference between the direct path andthe diffracted path, called the excess pathlength ( Δ ) can be obtained as
The corresponding phase difference is given
2
1 2
1 2
( )
2
h d d
d d
2
1 2
1 2
( )2 2
2
h d d
d d
40
Diffraction – Fresnel ZoneGeometry
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Diffraction – Fresnel Zone
Geometry
42
Diffraction – Fresnel ZoneGeometry
When
Fresnel Kirchoff diffraction parameter v is given by
Where has units of radians, the corresponding phasedifference can be expressed as
tgx x
21
21
d d
d d h
1 2 1 2
1 2 1 2
2 2d d d d v h
d d d d
2
2v
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Diffraction – Fresnel Zone
Geometry In practical diffraction problems, it is advantageous to reduce all
heights by a constant, so that the geometry is simplified withoutchanging the values of the angles
The concept of diffraction loss as a function of the pathdifference around an obstruction is explained by Fresnel zones.
The Fresnel zones represent successive regions wheresecondary waves have a path length from the transmitter toreceiver which are nλ/2 greater than the total path length of aline-of-sight path
The successive Fresnel zone have the effect of alternatelyproviding constructive and destructive interference to the totalreceived signal
The radius of the nth Fresnel zone circle is denoted by r n and beexpressed in terms of n , λ, d 1 , and d 2
1 21 2
1 2
,n n
n d d r d d r
d d
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Diffraction – Fresnel ZoneGeometry
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Diffraction – Fresnel Zone
Geometry In mobile communication systems, diffraction loss
occurs from the blockage of secondary waves suchthat only a portion of the energy is diffracted aroundan obstacle
That is, an obstruction causes a blockage of energyfrom some of the Fresnel zones, thus allowing onlysome of the transmitted energy to reach the receiver.
Depending on the geometry of the obstruction, thereceived energy will be a vector sum of the energy
contributions from all unobstructed Fresnel zones.
46
Diffraction – Fresnel ZoneGeometry
If an obstruction does not block the volumecontained within the first Fresnel zone, thediffraction loss will be minimal, and diffractioneffects may be neglected
In fact, a rule of thumb used for design of line-of-sight microwave links is that as longas 55% of the first Fresnel zone is kept clear,then further Fresnel zone clearance does notsignificantly alter the diffraction loss
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Diffraction – Fresnel Zone
Geometry
48
Diffraction – Fresnel ZoneGeometry
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Diffraction – Fresnel Zone
Geometry
50
Knife-edge Diffraction Model
It is impossible to make very precise estimates of thediffraction losses
In practice, prediction is a process of theoreticalapproximation modified by necessary empiricalcorrections
The limiting case of propagation over a knife-edgevies good insight into the order of magnitude of diffraction loss
When shadowing is caused by a single object such asa hill or mountain, the attenuation caused bydiffraction can be estimated by treating theobstruction as a diffracting knife-edge
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Knife-edge Diffraction Model
52
Knife-edge Diffraction Model
Consider a receiver at point R , located in theshadowed region
The field strength at point R is a vector sumof the fields due to all of the secondaryHuygen’s source in the plane above the knife-edge
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Knife-edge Diffraction Model The E-field strength, E d , of a knife-edge
diffracted wave is given by
E 0 is the free space field strength in the absenceof both the ground and the knife-edge
F(v) is the complex Fresnel integral and is a function of theFresnel-Kirchoff diffraction paremeter v
2
2
0
(1 )( )
2
j t
d
v
E jv e dt
E
54
Knife-edge Diffraction Model
The diffraction gain due to the presence of a knife-edge, as compared to the free space E-field, is givenby
The approximate solution is given
( ) 20 log ( )d
G dB F v
0.95
2
( ) 0 1
( ) 20 log(0, 5 0, 62 ) 1 0
( ) 20 log 0.5 0 1
( ) 20 log 0.4 0,1184 (0, 38 0,1 ) 1 2, 4
0,225( ) 20 log 2, 4
d
d
v
d
d
d
G dB v
G dB v v
G dB e v
G dB v v
G dB vv
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ExampleCompute the diffraction loss between the
transmitter and receiver assuming, = 1/3m, d 1 = 1 km, d 2 = 1 km and h = 25m
56
Knife-edge Diffraction Model
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Example Given
= 1/3 m,
d 1 = 1 Km,
d 2 = 1 Km
h = 25 m
Fresnel diffraction parameter
Diffraction loss is 21.71 dB
1 2
1 2
2 2 1 0 0 0 1 0 0 02 5 2 .7 4
1 / 3 1 0 0 0 * 1 0 0 0
d d v h
d d
( ) 20log 0.225 2.74 21.71v dB
58
Multiple Knife-edge Diffraction
In many practical situations, especially in hill terrain,the propagation path may consist of more than oneobstruction, in which case the total diffraction lossdue to all of the obstacles must be computed
Bullington suggested that the series of obstacles bereplaced by a single equivalent obstacle so that thepath loss can be obtained using single knife-edge
diffraction model This method oversimplifies the calculations and often
provides very optimistic estimates of received signalstrength
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Multiple Knife-edge Diffraction
60
Multiple Knife-edge Diffraction
Millington gave a wave-theory solution for thefield behind two knife edges in series
This solutions is very useful and can beapplied easily for predicting diffraction lossdue to two knife edges.
However, extending this to more than twoknife edges becomes a formidable
mathematical problem Many models that are mathematically less
complicated have developed to estimate thediffraction losses due to multiple obstruction
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Scattering A radio wave impinges on a rough
surface, the reflected energy is spreadout (diffused) in all directions due toscattering
The actual received signal is oftenstronger than what is predicted by
reflection and diffraction models alone
62
Practical Link Budget Design
Most radio propagation models are derived using acombination of analytical and empirical models
Empirical approach is based on fitting curves oranalytical expressions that recreate a set of measured data Advantages: Takes into account all propagation factors, both
known and unknown
Disadvantages: New models need to be measured fordifferent environment or frequency
Over many years, some classical propagation modelshave been developed, which are used to predictlarge-scale coverage for mobile communicationsystem design
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Log-Distance Path Loss Model The average large-scale path loss for an arbitrary T-R
separation is expressed as a function of distance byusing a path loss exponent, n
n is the path loss exponent
d 0 is the close-in distance which is determined frommeasurements close to the transmitter
d is the T-R separation distance
0
( )
n
d PL d
d
0
0
( )[ ] ( ) 10 logd
PL d dB PL d nd
64
Log-Distance Path Loss Model
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Log-normal Shadowing Log-distance path loss model does not
consider the fact that the surroundingenvironmental clutter may be vastly differentat two different location having the same T-R separation
This leads to measured signals which arevastly have shown that at any value d, thepath loss at a particular location is random
and distributed log-normal (normal in dB)about the mean distance dependent value
66
Log-normal Shadowing
That is
And (antenna gains included in PL(d) )
X б is a zero-mean Gaussian distributed random variable (indB) with standard deviation б (also in dB)
0
0
( )[ ] ( ) ( ) 10 logd
PL d dB PL d X PL d n X d
( )[ ] ( )[ ] ( )[ ]r t P d dBm P d dBm P L d dB
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Log-normal Shadowing Since PL(d) is a random variable with a normal
distribution in dB about the distance dependentmean, so is P r (d) , and Q -function or error function(erf ) amy be used to determine the probability thatthe received signal level will exceed a particular level
The Q -function2
21 1
( ) 1
2 2 2
x
z
z Q z e d x e r f
( ) 1 ( )Q z Q z
68
Log-normal Shadowing
The probability that the received signal level willexceed a certain value γ can be calculated from thecumulative density function
Similarly, the probability that the received signal levelwill be belowγ is given by
( )
Pr ( ) r r
P d P d Q
( )
Pr ( ) r r
P d P d Q
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Determination of Percentage
of Coverage Area For a circular coverage area having radius R
from a base station, let there be somedesired received signal threshold γ
We are interested in computing U(γ) , thepercentage of useful service area, i.e. thepercentage of area with a received signal thatis equal or greater than γ
70
Determination of Percentageof Coverage Area
Let d = r represent the radial distance from thetransmitter
It can be shown that Pr[P r (r) > γ] is the probabilitythat the random received signal at d = r exceeds thethreshold γ within an incremental area dA
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Determination of Percentage
of Coverage Area U(γ) can be found by
2
2 2
0 0
1 1P r ( ) P r ( )
R
r r U P r d A P r r d r d
R R
0
0
( ) ( )1 1Pr ( )
2 2 2
[ ( ( ) 10 lg )]1 1
2 2 2
r r r
t
P r P r P r Q erf
r P PL d n
d er f
72
Determination of Percentageof Coverage Area
In order to determine the path loss as referenced tothe cell boundary (r = R ), it is clear that
0
0
( ) 10 log 10 log ( ) R r
PL r n n PL d d R
0
0( ) 10 log 10 log
1 1P r ( )
2 2 2
t
r
R r P PL d n nd R
P d erf
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Determination of Percentage
of Coverage Area If we let
Then
0
0
( ) 10 log
2
t
R P PL d n
d a
1 0 lo g
2
n eb
2
0
1 1ln
2
R r U r erf a b dr
R R
74
Determination of Percentageof Coverage Area
By substituting
By choosing the signal level such that
(i.e. a = 0)
log( )t a b r R
2
1 21 1
1 ( ) 12
ab
bab
U erf a e erf b
( )r P R
2
11 1
1 12
bU e erf b
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Determination of Percentage
of Coverage Area
76
Example
Four received power measurements were taken at the distances
of 100m, 200m, 1 km and 3 km from a transmitter. Thesemeasured values are given in the following table.
The path loss equation model for other measurements followslog normal shadowing model where d0 = 100 m.
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Example(a) Find the minimum mean square error
(MMSE) estimate for the path lossexponent n.
(b) Calculate the standard deviation aboutthe mean value
(c) Estimate the received power at d = 2 kmusing the resulting model
(d) Predict the likelihood that the receivedsignal at 2 km will be greater than -60dBm.
78
Example
The MMSE estimate may be found using the followingmethod: Let p i be the received power at a distance d i and let be the estimate for pi using the (d/d 0 )
n
path loss model. The sum of squared errors betweenthe measured and estimated is given by
The value of n which minimizes the mean squareerror can be obtained by equating the derivative of
J (n ) to zero, and then solving by n
i p̂
k
i
ii p pn J
1
2ˆ)(
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Example We find
Since P (d 0 ) = 0 dBm, the following estimates for in dBm
The sum of squared errors is then by
Setting
0ˆ ( ) 10 log
100
ii i
d p p d n
i p̂
1ˆ 0 p 2
ˆ 3 p n 3ˆ 10 p n 4
ˆ 14.77 p n
2 2 2 2
2
( ) (0 0) (20 ( 3 )) ( 35 ( 10 )) ( 70 (14.77 ))
65.25 2887.8 327.153
J n n n n
n n
( )654.306 2887.8 0 4.4
dJ nn n
dn
80
Example
The variance at n = 4.4 can be obtained2 ( )
4
J n
2 2 2 2( ) (0 0) (20 13.2) ( 35 44) ( 70 64.988) 152.36 J n
2 152.36 4 38.09
6.17dB
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Example The estimate of the received power at d = 2Km is
given by
The probability that the received signal level will begreater than -60dBm is given by
2000ˆ 0 10.4, 4 log 57, 24
100 p dBm
%4,6717,6
)24,57(60
)(60)(Pr
Q
d P QdBmd P r r
82
Outdoor Propagation Model
Longley-Rice Model
Okumura Model
Hata Model
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83
Longley-Rice Model Applicable to point-to-point communication systems
in frequency range from 40MHz to 100GHz, overdifferent kind of terrain
Longley-Rice propagation prediction model is alsoreferred to as the ITS irregular terrain model
Longley-Rice model is also available as a computerprogram calculate large-scale median transmissionloss relative to free space loss over irregular terrainfor frequencies between 20MHz to 10GHz
There have been many modifications and corrections
to the Longley-Rice model to deal with radiopropagation in urban area – this is particularlyrelevant to mobile radio
84
Okumura Model
It is one of the most widely used models forsignal prediction in urban area.
This model is applicable for frequencies inrange 10MHz to 1920MHz (although it istypically extrapolated up to 3000MHz) anddistance of 1Km to 100Km
It can be used for base station antennaheight ranging from 30m to 1000m
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Okumura Model Okumura developed a set of curves giving the
median attenuation relative to free space ( A m u) , inan urban area over a quasi-smooth terrain with abase station effective antenna height (h te ) of 200mand a mobile antenna height (h r e) of 3 m
To determine path loss using Okumura’s model, thefree space loss between the points of interest is firstdetermined, and then the value of A mu(f,d) (as readfrom the curves) is added to it along with correction
factors to account for the type of terrain.
86
Okumura Model
The model can be expressed as
Where L 50 is the 50th percentile (i.e. median) value of propagation path loss
L F is the free space path loss
A mu is the median attenuation relative to free space
G (h re ) is the base station antenna height gain factor
G (h re ) is the mobile antenna height gain factor
G area is the gain due to the type of environment
50( ) ( , ) ( ) ( )
F mu te re area L dB L A f d G h G h G
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Okumura Model
88
Okumura Model
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Okumura Model Okumura found that G (h te ) varies at a rate of
20dB/decade and G (h re ) varies at a rate of 10dB/decade for height less than 3m
( ) 20 lg 1000 30200
( ) 10 lg 33
( ) 20 lg 10 33
tete te
re
re re
rere re
hG h m h m
hG h h m
hG h m h m
90
Okumura Model
Other corrections may also be applied to Okumura’smodel
Okumura’s model is wholly based on measured dataand does not provide any analytical explanation
Okumura’s model is considered to be among thesimplest and best in terms of accuracy in path lossprediction for mature cellular and land mobile radio
systems in cluttered environment It is very practical and has become a standard for
system planning in modern land mobile radio systemin Japan
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Okumura Model The major disadvantage with the model
is its slow response to rapid changes interrain, therefore the model is fairlygood in urban and suburban area, butnot good as in rural area
Common standard deviations between
predicted and measured path lossvalues are around 10dB to 14dB
92
Example
Find the median path loss using Okumura’smodel for d = 50Km, h t e = 100m, h re = 10m inan urban environment. If the base stationradiated an EIRP of 1KW at a carrierfrequency of 900MHz. Find the power at thereceiver (assume a unity gain receiving
antenna)
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Example The free space path loss L F can be calculated as:
From the Okumura curves
A mu (900MHz, 50Km) = 43 dB
G area = 9 dB
22
2 22 3 2
1 / 310 lo g 10 lo g 12 5.5
4 * 4 * (50 *1 0 ) F L d B
d
10 0( ) 20 log 20 log 6
200 20010
( ) 20 log 20 log 10.463 3
tete
rere
hG h dB
hG h dB
94
Example
The total mean path loss is
The average received power is
50( ) ( , ) ( ) ( ) 155.04
F mu te re area L dB L A f d G h G h G dB
50( ) ( ) ( ) ( )60 155.04 0 95.04
r r P d EIRP dBm L dB G dBdBm dB dB dBm
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Hata Model Hata model is an empirical formulation of the
graphical path loss data provided by Okumura
Applicable form frequencies range from150MHz to 1500MHz
Hata presented the urban area propagationloss as a standard formula and suppliedcorrection equations for application to other
solutions
96
Hata Model
The standard formula for median path loss in urbanarea is given by
f c is the frequency (in MHz) from 150MHz to 1500MHz
h te is the effective transmitter (base station) antenna height(in meters) ranging from 30m to 200m
h re is the effective receiver (mobile) antenna height (inmeters) ranging from 1m to 10m
d is the T-R separation distance (in Km)
a(hre) is correction factor for effective mobile antenna heightwhich is the function of the size of the coverage area
50 ( )( ) 69.55 26.16 log 13.82 log ( )
(44.9 6.55log )log
c te re
te
L urban dB f h a h
h d
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Hata Model For a small to medium sized city, the mobile antenna
correction factor is given by
For a large city, it is given by
( ) (1.1log 0.7) (1.56 log 0.8)re c re ca h f h f
2( ) 8.29(log1.54 ) 1.1 300re re ca h h dB f MHz
2
( ) 3.2(log11.75 ) 4.97 300re re ca h h dB f MHz
98
Hata Model
The path loss in a suburban area the standard Hataformula is modified as
The path loss in open rural areas is modified as
2
50 50( ) ( ) 2 log 28 5.4c L dB L urban f
2
50 50( ) ( ) 4.78(log ) 18.33log 40.98c c L dB L urban f f
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Hata Model Although Hata’s model does not have any of
the path specific corrections which areavailable in Okumura’s model, theexpressions have significant practical value
The predictions of Hata model compare veryclose with the original Okumura model, aslong as d exceeds 1Km.
This model is well suited for large cell mobilesystems, but no personal communicationssystems (PCS) which have cells on the orderof 1Km radius
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PCS Extension to Hata Model
European Co-operative for Scientific andTechnical research (EURO-COST) formed theCOST-231 working committee to develop anextended version of Hata model
COST-231 proposed the following formula toextend Hata model to 2GHz
The COST-231 extension of the Hata model is
restricted to the following parameters: f : 1500MHz – 2000MHz h te : 30m to 200m h re : 1m to 10m d : 1Km to 10Km
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Walfisch and Bertoni Model In dB, the path loss is given
L 0 represents free space loss
L rts represents the rooftop-to-street diffraction andscatter loss
L ms denotes multiscreen diffraction loss due to the
rows of buildings
0( )
rts msS dB L L L
104
Walfisch and Bertoni Model
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Indoor Propagation Models The indoor radio channel differs from the traditional
mobile radio channel in two aspects – the distancescovered are much smaller, and the variability of theenvironment is much greater for a much smaller of T-R separation distances.
Propagation within buildings is strongly influenced byspecific features such as the layout of the building,construction materials and the building type
Indoor radio propagation is dominated by the samemechanisms as outdoor: reflection, diffraction, and
scattering In general, indoor channels may be classified either
as line-of-sight (LOS) or obstructed (OBS) withvarying degrees of clutter
106
Partition Losses (Same Floor)
Buildings have a wide variety of partitionsand obstacles which form the internal andexternal structure
Partitions that are formed as part of thebuilding structure are called hard partitions,and partitions that may be moved and whichdo not span to the ceiling are called soft
partition Partitions vary widely in their physical and
electrical characteristics, making it difficult toapply general models to specific indoorinstallation
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Partition Losses (Same Floor)
108
Partition Losses (BetweenFloor)
The losses between floors of a building aredetermined by the external dimensions andmaterials of the building, as well as, the typeof construction used to create the floors andthe external surroundings
The following table illustrated values for floorattenuation factor (FAF) in three buildings
It can be seen that for all three buildings, theattenuation between one floor of the buildingis greater than the incremental attenuationcaused by each additional floor
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Partition Losses (Between
Floor)
110
Log-distance Path Loss Model
Indoor path loss obeys the distance powerlaw
Where the value of n depends on thesurroundings and building type
X б represents a normal random variable in dBhaving a standard deviation of б dB
0
0
( ) ( ) 10 logd
PL dB PL d n X d
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Log-distance Path Loss Model
112
Ericsson Multiple BreakpointModel
The Ericsson radio system model obtained bymeasurement in a multiple floor office building
The model has four breakpoints and considers bothan upper and lower bound on the path loss
The model also assumes that there is 30dBattenuation at d0 = 1m, which can be shown to beaccurate for f = 900MHz and unity gain antenna
Rather than assuming a log-normal shadowingcomponent, the Ericsson model provides adeterministic limit on the range of path loss at aparticular distance
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Ericsson Multiple Breakpoint
Model
114
Attenuation Factor Model
An in-building propagation model thatincludes the effect of building type as well asthe variations caused by obstacles
This model provides flexibility and was shownto reduce the standard deviation betweenmeasured and predicted path loss to around4dB, as compare to 13dB when only a log-distance model was used in two differentbuildings
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Attenuation Factor Model The attenuation factor model is given
Where n SF represents the exponent value for thesame floor measurement. If a good estimate for nexists on the same floor, then the path loss on a
different floor can be predicted by adding anappropriate value of FAF
0
0
( ) ( ) 19 logSF
d PL d dB PL d dB n FAF dB
d
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Attenuation Factor Model
FAF may be replace by an exponent whichalready considers the effects of multiple floorseparation
When n MF denotes a path loss exponent based onmeasurements through multiple floor
0
0
( ) ( ) 19 log MF
d PL d dB PL d dB n
d
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Attenuation Factor Model
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Attenuation Factor Model
Devasirvatham, et. al. found that in-building pathloss obeys free space plus an additional loss factorwhich increase exponentially with distance as infollowing table
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Attenuation Factor Model Path loss is possible to modify as follows
Where is the attenuation constant for thechannel with units of dB per meter (dB/m)
0
0
( ) 20 logd
PL d dB PL d dB d FAF dBd
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Measured Indoor Path Loss
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Measured Indoor Path Loss
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Measured Indoor Path Loss
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Signal Penetration into
Buildings The signal strength inside of a building due to an external
transmitter is important for wireless systems that sharefrequencies with neighboring buildings or with outdoor systems
As with propagation measurements between floors, it is difficultto determine exact models for penetration as only a limitednumber of experiments have been published, and they aresometimes difficult to compare
Some generalizations can be made from the literaturemeasurements reported: signal strength received inside abuilding increase with height. At the lower floors of a building,the urban clutter induces greater attenuation and reduces thelevel of penetration. At the higher floor, a LOS path may exist,
thus causing a stronger incident signal at the exterior walls of the building