Page 73 - Integrated Wireless Propagation Models

C H A P T E R 2

Macrocell Prediction

Models Part 1:

Area-to-Area Models

2.1 Free Space Loss
Free space path loss occurs when a transmitted signal propagates over a line-of-sight
path through a free space with no obstacles nearby to cause reflection or diffraction. The
signal strength of the signal decreases with increasing distance. It excludes factors such
as the gain of the antennas used at the transmitter and receiver and any loss associated
with imperfections in hardware.
Free space loss can be calculated, as the signal strength decreases at a rate inversely
proportional to the distance traveled and proportional to the wavelength of the signal,
as shown from the Friis transmission formula:

p ( A ) 2 (2.1.1)
P, = gbg m 4nd
where gb and g"' are gains of the terminal antennas, i s the distance between the anten­
d
nas, and A is the wavelength. This can be visualized as arising from the spherical spread­
ing of power over the surface of a sphere of radius d centered at the transmitting antenna.
2
Since power is spread over the surface area of the sphere, which increases as d , the
2
available power at a receiver antenna of fixed aperture decreases in proportion to d •
1
Equation (2. . 1 ) can be rearranged to express it as a propagation loss in free space:
G
= ( d ( fr
L = �� ��� 4� r = 4n: (2 1 .2)
.
F
r
This expression defines L , the free space loss in which the square law depends on both
F
frequency and distance.
Expressing the free space loss in decibels, with frequency in megahertz and distance
d in kilometers or in miles, we obtain
L (in dB) = 32.4 + 20logd + 20logJ MHz d i n kilometers (2 1 .3)
.
F
f
= 36.57 + 20 log d + 20 log MHz d in miles
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