Page 50 - Integrated Wireless Propagation Models

28 C h a p t e r O n e

at least one of the paths is dominant and can be treated as a nonfading signal component
under an LOS propagation condition. At the reception, the envelope of the signal is
affected by adding a de component to the random multipath.
The Rician distribution's pdf can be given by

l r _(r'+A'J (Ar)
-e 2cr' I -
p(r) = 0' 2 o 0' 2 for (A ;:o: 0, r ;:o: 0) (1.8.4.1)
0 for (r < 0)

The parameter A denotes the de amplitude of the dominant signal, and l0 (*) is the
modified Bessel function of the first kind and zero order. The Rician distribution is often
described in terms of a parameter a:
2
A
a( dB) = 10 log 2 dB (1.8.4.2)
20'
a is the ratio of the deterministic signal power and the average power of the multipath
signal.
When the dominant signal A becomes weak, as seen from Eq. (1.8.4.1), the composite
signal starts to resemble a noise signal. When the dominant signal fades away, the
Rician distribution degenerates to a Rayleigh distribution, as shown in Eq. (1.8.1.2).

1.9 Three Basic Propagation Mechanisms3 2
Three basic mechanisms affect radio signal propagation. They are reflection, diffraction,
and scattering. When a signal encounters an obstacle, which mechanism occur, depends
on the size of obstacle. If the obstacle is very large compared to the wavelength, reflec­
tion will occur, such as a radio wave impinging on something, such as the earth's sur­
face or walls. At the place where the obstruction has occurred, the radio wave could
bend or propagate around the obstacle; this is diffraction. But if the obstacle is small
compared to the wavelength, scattering will occur.

1 . 9 . 1 Reflection

1.9. 1 . 1 Introduction and Principles
The specular reflections from a smooth surface conform to Snell's law, which states that
the product of the refraction index N 1 and the cosine of the grazing angle (cos 8 1 )
is constant along the path of a given ray of energy. This relationship is illustrated in
Fig. . 9 1 . 1 . 1 , 32 Since N 1 is always the same for both incident and reflected waves, it
.
1
follows that the incident and reflected wave angles are also the same.
1.9. 1 . 1 . 1 Reflection Coefficient The ratio of the incident wave to its associated
reflected wave is called the reflection coefficient. The generalized Fresnel formulas for
horizontally and vertically polarized radio waves can be used to determine the power
and boundary relationships of transmitted, incident, and reflected radio waves con­
2
1
forming to Snell's law. These relationships are shown in Fig. . 9.1.1.2. 9 By disregarding
that part of the transmitted wave that is transmitted into the ground, the formulas can