Wireless Communication
Channels: Large-Scale Pathloss
The Three Basic Propagation Mechanisms
Three basic mechanisms that impact propagation in a
mobile communication system

Reflection



Diffraction


A propagating electromagnetic wave impinges upon an object which has
very large dimension compared to the wavelength
Reflection occurs from surface of earth and from buildings and walls
The radio path between the transmitter and receiver is obstructed by a
surface that has sharp irregularities
Scattering

When the medium consists of objects with dimensions that are small
compared to the wavelength
© Tallal Elshabrawy
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Reflection
Reflection from Dielectrics
Normal Incidence
Parallel Incidence
Er
Ei
Hi
Hr
i
r
t
Er
Ei
Hr
Hi
1 , 1 , 1
i
2 , 2 , 2
t
1 , 1 , 1
2 , 2 , 2
Et
Et
i  r
r
E r   Ei
E t   1    Ei
Snell’s Law
11 sin  90  i   2 2 sin  90  t 
© Tallal Elshabrawy
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Reflection from Dielectrics
Normal Incidence
Parallel Incidence
Er
Ei
Hi
Hr
i
Er
Ei
Hr
Hi
1 , 1 , 1
r
i
2 , 2 , 2
t
t
1 , 1 , 1
2 , 2 , 2
Et
Et
 
r
E r  2 sin  t  1 sin  i

E i  2 sin  t  1 sin  i
 
E r  2 sin  i  1 sin  t

E i  2 sin  i  1 sin  t
First Medium is Free space and μ1 = μ2
 
 r sini   r  cos 2 i
 r sini   r  cos i
© Tallal Elshabrawy
2
 
sini   r  cos 2 i
sini   r  cos 2 i
5
Reflection from Dielectrics
Normal Incidence
Parallel Incidence
Er
Ei
Hi
Hr
r
i
t
Et
Er
Ei
1 , 1 , 1
2 , 2 , 2
Hr
Hi
i
r
t
1 , 1 , 1
2 , 2 , 2
Et
First Medium is Free space and μ1 = μ2 , θi approaches 0
 1
   1
This shows that the ground may be modeled as a perfect reflector with
a reflection coefficient of unit magnitude when an incident wave grazes the
earth regardless of the polarization or dielectric properties
© Tallal Elshabrawy
6
Ground Reflection (Two-Ray) Model
Transmitter
ETOT=ELOS+Eg
ELOS
Receiver
ht
Ei
Er= Eg
i
hr
r
d



A single direct path between the base
station and a mobile is seldom the only
means for propagation
Friis equation is most likely inaccurate
Two ray ground reflection model has
been found to be reasonably accurate for
predicting large scale strength over
distances of several Kms for mobile radio
systems that use tall towers
© Tallal Elshabrawy
Power Flux Density
R 
E TOT

2

E TOT
2
120
W m2
7
Ground Reflection (Two-Ray) Model
E0 d0
  d 
E d,t  
cos  c  t    ,d  d0
d
  c 
E0 d0
  d'  
E LOS  d ', t  
cos  c  t   
d'
c 
 
E0 d0
  d ''  
E g  d '', t   
cos  c  t   
d ''
c 
 
Assuming grazing incidence Γ=-1 for normal incidence
E TOT  E LOS  E g
E0 d0
E0 d0
  d'  
  d ''  
E TOT  d , t  
cos  c  t      1
cos  c  t   
d'
c 
d ''
c 
 
 
© Tallal Elshabrawy
8
Ground Reflection (Two-Ray) Model
Transmitter
d’
ETOT=ELOS+Eg
Receiver
ELOS
ht
Ei
Er= Eg
d’’
i
hr
r
hr
ht
d
© Tallal Elshabrawy
9
Ground Reflection (Two-Ray) Model
d '' 
 h t  hr   d2  d 1 
d' 
ht  hr 
2
2
 d  d 1 +
where 1  x  1 
© Tallal Elshabrawy
2
x
for x
2
ht  hr 
d2
ht  hr 
<<
2
d2
1
2
  h t  h r 2
 d 1

2d 2


 ,d < <  h t  h r 


  h t  h r 2
 d 1
2

2
d


 ,d < <  h t  h r 


  d''  d'  2
ht hr
c
, 
d
c
10
Ground Reflection (Two-Ray) Model
E TOT  d , t  
E0 d0
Ed
  d'  
  d ''  
cos  c  t      1 0 0 cos  c  t 

d'
c 
d ''
c 
 
 
Slide 9
Let evaluate ETOT at t=d’’/c
E0 d0
d ''  E0 d0
  d '' d '  

E TOT  d , t 
cos  c 
     1
cos 0 

c 
d'
c 
d ''

  c
ETOT
E0 d0
sin
d'
E0 d 0
d ''
© Tallal Elshabrawy
E0 d 0
d'

E0 d0 E0 d0

cos 
d''
d'
11
Ground Reflection (Two-Ray) Model
E0 d0
E0 d0
E0 d0


d'
d ''
d
Assume for large d
2
2
2
 E0 d 0 
 E0 d0 
2
E TOT  d   
cos


1

sin







 d 
 d 
 E0 d0 
E TOT  d   
2  2 cos  

 d 
E d  
E TOT  d   2  0 0  sin 
2
 d 
Note that rather than using 2 sin   
 2
phasors, we could also use


 
 sin  c t  2
 

  cos c t   cos c t    

Important Note:
The significance of the path difference Δ appears in the phase difference θΔ
between the two waves (LOS and Reflected Wave)
© Tallal Elshabrawy
12
Ground Reflection (Two-Ray) Model
Under the assumption

2
 0.3 rads  sin

2


2
2 h t h r

 
 0.3rad
2 
d
20 h t h r 20 h t h r
d

3


 E0 d0
E TOT  d   2 
 d
 E0 d0
E TOT  d   2 
 d
2
R 
© Tallal Elshabrawy
E TOT

2
 
 sin 2

 2 h t h r
 d

  E0 d0  2 h t h r 
E0 d0 

2
 d 
 d  4 h h 2
d







t r 


120
120   d 
2
13
Ground Reflection (Two-Ray) Model
2
R 
E TOT

2
  E0 d0  2 h t h r 
 E0 d0 
2
 
 d 
 d  4 h h 2
d


 
 
t r 

120
120   d 
2
2
But from LOS
analysis
 E0 d 0 
 d 

  PT G T
120
4 d 2
2
PT G T  4 h t h r 
R 


4 d 2   d 
PR  d    R  A e dir   R G R  A e iso
E TOT
2
PT G T  4 h t h r 

PR  d  
GR


2 
4
4 d   d 
2
© Tallal Elshabrawy
2
PT G T G R  h t h r 
2
d4
14
Ground Reflection (Two-Ray) Model Notes
 The received power falls off with distance raised to the
fourth power, 40 dB/decade
 Much rapid than free space
 The received power and path-loss are no longer dependent
on frequency

PL(dB)=40logd-(10logGT+10logGR+20loght+20loghr)
© Tallal Elshabrawy
15