Large scale path loss 1

9/28/2013MIT, MEERUT1
UNIT-1
Mobile Radio Propagation
Large-Scale Path Loss

•Electromagnetic wave propagation
•reflection
•diffraction
•scattering
•Urban areas
•No direct line-of-sight
•high-rise buildings causes severe diffraction loss
•multipath fading due to different paths of varying lengths
•Large-scale propagation models predict the mean signal strength for an arbitrary
T-R separation distance.
•Small-scale (fading) models characterize the rapid fluctuations of the received
signal strength over very short travel distance or short time duration.
Introduction to RadioWave Propagation

3
transmitted
signal
received
signal
Ts
max
LOS
LOS
Reflection
Diffraction
Scattering

• Small-scale fading: rapidly fluctuation
– sum of many contributions from different directions with
different phases
– random phases cause the sum varying widely. (ex: Rayleigh
fading distribution)
• Local average received power is predicted by large-scale model
(measurement track of 5 to 40 )

• Free Space Propagation Model
• The free space propagation model is used to predict received
signal strength when the transmitter and receiver have a clear
line-of-sight path between them.
– satellite communication
– microwave line-of-sight radio link
• Friis free space equation
: transmitted power :T-R separation distance (m)
: received power : system loss
: transmitter antenna gain : wave length in meters
: receiver antenna gain
Ld
GGP
dP rtt
r 22
2
)4(
)(
t
P
)(dPr
t
G
r
G
d
L

• The gain of the antenna
: effective aperture is related to the physical size of the antenna
• The wave length is related to the carrier frequency by
: carrier frequency in Hertz
: carrier frequency in radians
: speed of light (meters/s)
• The losses are usually due to transmission line
attenuation, filter losses, and antenna losses in the communication
system.A value of L=1 indicates no loss in the system hardware.
2
4 e
A
G
e
A
c
c
f
c 2
f
c
c
L )1( L

• Isotropic radiator is an ideal antenna which radiates power with unit
gain.
• Effective isotropic radiated power (EIRP) is defined as
and represents the maximum radiated power available from transmitter
in the direction of maximum antenna gain as compared to an isotropic
radiator.
• Path loss for the free space model with antenna gains
• When antenna gains are excluded
• The Friis free space model is only a valid predictor for for values of
d which is in the far-field (Fraunhofer region) of the transmission
antenna.
tt
GPEIRP
22
2
)4(
log10log10)(
d
GG
P
P
dBPL rt
r
t
22
2
)4(
log10log10)(
dP
P
dBPL
r
t
r
P

• The far-field region of a transmitting antenna is defined as the region
beyond the far-field distance
where D is the largest physical linear dimension of the antenna.
• To be in the far-filed region the following equations must be satisfied
and
• Furthermore the following equation does not hold for d=0.
• Use close-in distance and a known received power at that
point
or
2
2 D
d f
Dd f f
d
Ld
GGP
dP rtt
r 22
2
)4(
)(
0
d )( 0
dPr
2
0
0
)()(
d
d
dPdP rr
f
ddd 0
d
ddP
dP r
r
00
log20
W001.0
)(
log10dBm)( f
ddd 0

TheThree Basic Propagation Mechanisms
• Basic propagation mechanisms
– reflection
– diffraction
– scattering
• Reflection occurs when a propagating electromagnetic wave
impinges upon an object which has very large dimensions when
compared to the wavelength, e.g., buildings, walls.
• Diffraction occurs when the radio path between the transmitter
and receiver is obstructed by a surface that has sharp edges.
• Scattering occurs when the medium through which the wave
travels consists of objects with dimensions that are small
compared to the wavelength.

• Reflection from dielectrics
• Reflection from perfect conductors
– E-field in the plane of incidence
– E-field normal to the plane of incidence
riri
EEand
riri
EEand
Reflection

Considering orthogonal polarization
=
Where,
Now velocity (EMW) =

Now, bondry conditions at the surface of incidence, acc to Snells law,
Using boundary conditions from maxwell eq. (by laws of reflection)
&,

If 1st medium is free space &
The reflection coeefficients for vertical and horizontal
polarization can be reduced as:-

Brewster Angle
The angle,at which no reflection occurs in the medium of
origin .It is given by , as:-
If 1st medium is free space and relative permittivity of 2nd is
Than,

16
IV. Ground Reflection (2-Ray) Model
 Good for systems that use tall towers (over 50 m tall)
 Good for line-of-sight microcell systems in urban environments

17
 ETOT is the electric field that results from a combination of a
direct line-of-sight path and a ground reflected path
 is the amplitude of the electric field at distance d
 ωc = 2πfc where fc is the carrier frequency of the signal
 Notice at different distances d the wave is at a different phase
because of the form similar to

18
 For the direct path let d = d’; for the reflected path
d = d”then
 for largeT−R separation : θi goes to 0 (angle of incidence to the
ground of the reflected wave) and
Γ = −1
 Phase difference can occur depending on the phase difference
between direct and reflected E fields
 The phase difference is θ∆ due to Path difference , ∆ =
d”− d’, between

19
Using method of images (fig below) , the path difference can be
expressed as:-
 From two triangles with sides d and (ht + hr) or (ht – hr)

Using taylor series the expression can be simplyfied as:-
Now as P.D is known , Phase difference and time delay can be
evaluated as:-
If d is large than path difference become negligible and amplitude ELOS
& Eg are virtually identical and differ only in phase,.i.e
&

If than ETOT can be expresed as:-

Referring to the phasor diagram below:-

or
As E-field is function of “sin” it decays in oscillatory fashion with
local maxima being 6dB greater than free space and local minima
reaching to-∞ dB.

24
For d0=100meter, E0=1, fc=1 GHz, ht=50
meters, hr=1.5 meters, at t=0

25
 note that the magnitude is with respect to a reference of
E0=1 at d0=100 meters, so near 100 meters the signal can be
stronger than E0=1
 the second ray adds in energy that would have been lost
otherwise
 for large distances it can be shown that

Q.1
Q.2 calculate the free space path loss for a signal transmitted at afrequency
Of 900MHz forT-R seperation 1Km.

Diffraction
 Diffraction occurs when waves hit the edge of an obstacle
 “Secondary” waves propagated into the shadowed region
 Water wave example
 Diffraction is caused by the propagation of secondary wavelets into a
shadowed region.
 Excess path length results in a phase shift
 The field strength of a diffracted wave in the shadowed region is the
vector sum of the electric field components of all the secondary
wavelets in the space around the obstacle.
 Huygen’s principle: all points on a wavefront can be considered as
point sources for the production of secondary wavelets, and that
these wavelets combine to produce a new wavefront in the direction
of propagation.

Illustration of diffraction II

Diffraction occurs when waves hit the edge of an obstacle
“Secondary” waves propagated into the shadowed regionExcess
path length results in a phase shift

consider that there's an impenetrable obstruction
of height h at a distance of d1 from the
transmitter and d2 from the receiver. ,
α
h
d1 d2
T
R
β
γ

The path difference between direct path and the diffracted path is
∆ =
Thus the phase difference,
∆
If,
Then,

Thus , is It is clear that,

35
Fresnel zone
 The excess total path length traversed by a ray passing
through each circle is nλ/2
,

The radius of nth fresnel zone circle is denoted by rn
Where,

Knife-edge diffraction
 Fresnel integral, 4.59

Knife edge diffraction loss

Multiple knife edge diffraction
For multiple knife edges, replace them by single knife
edge, as below

41
Log-distance Path Loss Models
 We wish to predict large scale coverage using analytical and
empirical (field data) methods
 It has been repeatedly measured and found that Pr @ Rx
decreases logarithmically with distance
∴ PL (d) = (d / do )n where n : path loss exponent or
PL (dB) = PL (do ) + 10 n log (d / do )

42
 “bar” means the average of many PL values at a given value
of d (T-R sep.)
 n depends on the propagation environment
 “typical” values based on measured data

43
 At any specific d the measured values vary drastically because
of variations in the surrounding environment (obstructed vs.
line-of-sight, scattering, reflections, etc.)
 Some models can be used to describe a situation
generally, but specific circumstances may need to be
considered with detailed analysis and measurements.

44
 Log-Normal Shadowing
PL (d) = PL (do ) + 10 n log (d / do ) + Xσ
 describes how the path loss at any specific location may vary from the average
value
 has a the large-scale path loss component we have already seen plus a
random amount Xσ.

45
 Xσ : zero mean Gaussian random variable, a “bell curve”
 σ is the standard deviation that provides the second parameter for
the distribution
 takes into account received signal strength variations due to
shadowing
 measurements verify this distribution
 n & σ are computed from measured data for different area types

Assingment – determination of % coverage area.

Large scale path loss 1

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Large scale path loss 1