Wireless Communication Channels: Large-Scale Pathloss.

Wireless Communication Channels: Large-Scale Pathloss

© Tallal Elshabrawy 2

Three basic mechanisms that impact propagation in a mobile communication system

Reflection 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

Diffraction 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

The Three Basic Propagation Mechanisms

Reflection


Reflection from Dielectrics

Snell’s Law

i t1 1 2 2sin 90 sin 90

i r r i t iE E E E1

i r

t

Ei

1 1 1, ,

2 2 2, ,

Er

Hi Hr

Et

i r

t

Ei

1 1 1, ,

2 2 2, ,

Er

HiHr

Et

Normal IncidenceParallel Incidence



t ir

i t i

E

E2 1

2 1

sin sin

sin sin

i tr

i i t

E

E2 1

2 1

sin sin

sin sin

First Medium is Free space and μ1 = μ2

r i r i

r i r i

2

2

sin cos

sin cos

i r i

i r i

2

2

sin cos

sin cos

i r

t

Ei

1 1 1, ,

2 2 2, ,

Er

Hi Hr

Et

i r

t

Ei

1 1 1, ,

2 2 2, ,

Er

HiHr

Et



First Medium is Free space and μ1 = μ2 , θi approaches 0

i r

t

Ei

1 1 1, ,

2 2 2, ,

Er

Hi Hr

Et

i r

t

Ei

1 1 1, ,

2 2 2, ,

Er

HiHr

Et


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



Ground Reflection (Two-Ray) Model

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

TOT TOTR

E EW m

2 2

2

120

Power Flux Density

ht

hr

ELOS

EiEr= Eg

i r

Transmitter

Receiver

ETOT=ELOS+Eg

d



c

E d dE d t t d d

d c0 0

0, cos ,

LOS c

E d dE d t t

d c0 0 '

', cos'

g c

E d dE d t t

d c0 0 ''

'', cos''

Assuming grazing incidence Γ=-1 for normal incidence

TOT LOS g

TOT c c

E E E

E d E dd dE d t t t

d c d c0 0 0 0' ''

, cos 1 cos' ''



ht

ELOS

EiEr= Eg

i r

Transmitter

Receiver

ETOT=ELOS+Eg

d

ht

hr

hr

d’

d’’



t r t rt r t r

t r t rt r t r

h h h hd h h d d d d h h

d d

h h h hd h h d d d d h h

d d

xwhere x for x

2 22 2

2 2

2 22 2

2 2

'' 1 1 ,2

' 1 1 ,2

1 1 12

t r ch hd d

d c'' ' 2 ,

+

<<

<<

<<



TOT c c

E d E dd dE d t t t

d c d c0 0 0 0' ''

, cos 1 cos' ''

TOT c

E d E dd d dE d t

c d c c d0 0 0 0'' '' '

, cos 1 cos 0' ''

Let evaluate ETOT at t=d’’/c

Slide 9

E d

d0 0

'

E d

d0 0

''

ETOT

E d

d0 0 sin'

E d E d

d d0 0 0 0 cos'' '


c c ct t t2 sin sin cos cos2 2


E d E d E d

d d d0 0 0 0 0 0

' ''

Important Note:The significance of the path difference Δ appears in the phase difference θΔ between the two waves (LOS and Reflected Wave)

TOT

TOT

TOT

E d E dE d

d d

E dE d

d

E dE d

d

2 22 20 0 0 0

0 0

0 0

cos 1 sin

2 2cos

2 sin2

Assume for large d

Note that rather than using phasors, we could also use



Under the assumption

t r

t r t r

rads

h hrad

dh h h h

d

0.3 sin2 2 2

20.3

220 20

3

TOT

t rTOT

E dE d

d

E d h hE d

d d

0 0

0 0

2 sin2

22

t r

TOT t rR

E d h h E dE d d h hd

d

2 20 0 0 0

2 2

22

4

120 120



t r

TOT t rR

E d h h E dE d d h hd

d

2 20 0 0 0

2 2

22

4

120 120

But from LOS analysis T T

E dP Gd

d

2

0 0

2120 4

TOT t rT TR

R R e R R edir iso

T T R t rt rT TR R

E h hP G

dd

P d A G A

P G G h hh hP GP d G

dd d

2 2

2

22 2

2 4

4

4

4

44


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)

Ground Reflection (Two-Ray) Model Notes

Wireless Communication Channels: Large-Scale Pathloss.

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