Page 74 - Integrated Wireless Propagation Models

52 C h a p t e r T w o

Thus, the free space loss increases by 6 dB for each doubling in either frequency or dis­
tance (or 20 dB per decade of either).
The free space value of the loss is used as a basic reference, and the loss experienced
in excess of this free space loss (in decibels) is referred to as the excess loss, Lex· Thus,

(2.1.4)
The free space loss is usually considered a practical minimum to the path loss for a
given distance.

2.2 Plane Earth Model
The ground plays a key role in the propagation of a radio wave. It acts as a partial reflec­
tor and a partial absorber, and it affects the radio energy along the radio distance. The
)
principal effect of plane earth propagation is shown in Eq. (2.2.1 .
E = E0[1 +Rei"' + (1 -R)Aei"' + . . ]
.
(2.2.1)
?) b) "C) d)
where a) is the direct wave, b) is the reflected wave, c) is the surface wave, and d) is
the induction field and secondary effects of the ground. R is the reflection coefficient
of the ground and is approximately equal to -1 when the incident angle and reflected
angle 8 is less than 1 radian. The symbol t. is the phase difference between the trans­
mitted wave and the reflected wave. A is a constant loss due to the reception of
surface wave.
The sum of three principal waves composes the ground wave. The direct wave and
the reflected wave are easy to understands, as they correspond to our common experi­
ence with visible light. The surface wave is the principal component of the total ground
wave at frequencies less than 3 MHz but usually can be neglected at frequencies above
300 MHz.
The ratio of the received power to the radiated power for transmission over plane
earth was derived in Chap. 1, Eq. (1.9.3.1.8), as follows:

(2.2.2)

where hb and h"' are the antenna heights of base and mobile and Gb and G"' are the antenna
gains of base and mobile.
The plane earth model has been derived theoretically based on the mobile radio
environment. Both the base station antenna and the mobile antenna are much smaller
compared to the distance between the two antennas. The model is oversimplified, as it
does not include terrain profile, vegetation, and buildings.
The plane earth model is a fundamental model used to explain the path loss expo­
nent in the mobile radio environment. The plane earth loss increases far more rapidly
than the free space loss and is independent of carrier frequency. The loss increases by
12 dB per octal, or by 40 dB per decade. The plane earth model is not an accurate tool to
be used to predict the path loss in real-world propagation.