Path Loss
Prof. Murat Torlak
EE4367 Telecom. Switching & Transmission

Radio Wave Propagation
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The wireless radio channel puts fundamental limitations to
the performance of wireless communications systems
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Radio channels are extremely random, and are not easily
analyzed
Prof. Murat Torlak
EE4367 Telecom. Switching & Transmission
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Modeling the radio channel is typically done in statistical
fashion

Linear Path Loss
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Suppose s(t) of power P
t
is transmitted through a given
channel
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The received signal r(t) of power P
r
is averaged over any
random variations due to shadowing.
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We define the linear path loss of the channel as the ratio of
transmit power to receiver power
Prof. Murat Torlak
EE4367 Telecom. Switching & Transmission
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We define the path loss of the channel also in dB

Experimental results
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The measurements and predictions for the receiving van driven
along 19th St./Nash St.
Prof. Murat Torlak
EE4367 Telecom. Switching & Transmission
Prediction with distance
And transmission frequency

Line
-of
of
-Sight Propagation
Sight Propagation
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Attenuation
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The strength of a signal falls off with distance
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Free Space Propagation
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The transmitter and receiver have a clear line of sight path
between them. No other sources of impairment!
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Satellite systems and microwave systems undergo free space
propagation
Prof. Murat Torlak
EE4367 Telecom. Switching & Transmission
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The free space power received by an antenna which is
separated from a radiating antenna by a distance is given by
Friis free space equation

Friis Free Space Equation
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The relation between the transmit and receive power is given by
Friis free space equations:
2
2
(4
)
r
t
t
r
P
PG G
d
λ
π
=
d
G
G
t
P
t
P
r
Prof. Murat Torlak
EE4367 Telecom. Switching & Transmission
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G
t
and G
r
are the transmit and receive antenna gains
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λ
is the wavelength
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d is the T-R separation
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P
t
is the transmitted power
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P
r
is the received power
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P
t
and P
r
are in same units
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G
t
and G
r
are dimensionless quantities.
r

Free Space Propagation Example
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The Friis free space equation shows that the received power falls
off as the square of the T-R separation distances
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The received power decays with distance by 20 dB/decade
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EX:
Determine the isotropic free space loss at 4 GHz for the
shortest path to a geosynchronous satellite from earth (35,863
km).
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P
L
=20log
10
(4x10
9
)+20log
10
(35.863x10
6
)-147.56dB
Prof. Murat Torlak
EE4367 Telecom. Switching & Transmission
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P
L
=195.6 dB
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Suppose that the antenna gain of both the satellite and ground-
based antennas are 44 dB and 48 dB, respectively
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P
L
=195.6-44-48=103.6 dB
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Now, assume a transmit power of 250 W at the earth station.

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- Summer '19
- Cellular network, Prof. Murat Torlak, EE4367 Telecom