MULTIPATH FADING AND THE DISTANCE–POWER RELATIONSHIP

 
MULTIPATH FADING AND THE DISTANCE–POWER RELATIONSHIP
In most radio channels the transmitted signal arrives at the receiver from various directions
over a multiplicity of paths. Figure 3.1 provides several examples of multipath
fading radio channels. Figure 3.1a represents a troposcatter radio communication link
used in military applications for communication at long distances. The transmitted
signal is directed toward the troposphere layer of the atmosphere, the incident wave
is scattered, and some of the scattered signal energy reaches the receiver. Communication
between the transmitter and the receiver can be modeled with several paths.
Figure 3.1b represents a line-of-sight (LOS) microwave radio link, as is widely used
in nationwide networks for terrestrial communications. At installation, the antennas  are aligned to provide LOS communication. However, for occasional short periods of
time, atmospheric conditions can affect radio propagation in such a way that signal
components reflected from the ground and the atmosphere become comparable to the
LOS component, creating a multipath condition. Figure 3.1c represents a mobile radio
scenario where the received signal arrives by several paths: bounced from large objects
such as buildings and local paths scattered from objects close to the receiver, such as
ground or trees. Figure 3.1d represents a simple multipath condition for an indoor area.
The phase and amplitude of the signal arriving on each path are related to path length
and conditions; this results in considerable amplitude fluctuation of the composite
received signal. An exact analysis of multipath propagation can be done by solving
Maxwell’s equations with boundary conditions representing the physical properties and
architecture of the environment. This method is computationally burdensome; even with
today’s most sophisticated computers, only the simplest structures can be treated. A
simpler analytical approach is to approximate the radio-wave propagation with opticalwave
propagation and to determine the directions of the arriving paths through the rules
of geometric optics. This method is commonly referred to as the ray-tracing method.
The transmitting and receiving antennas are assumed to be radiating points, and each
path is modeled as a ray. A ray is the path of an ideal bullet traveling in a straight line
and reflecting from the objects according to the rules of geometric optics. Figure 3.2 represents a mobile radio environment where the received signal arrives from two
paths: (1) the direct LOS connection between the transmitter and the receiver, and
(2) the path arriving after reflection from the ground. A more complete ray-tracing
algorithm includes the mechanism of transmission through walls, reflection from the
walls, and diffraction at the edges of buildings. Further details of the direct solution
to Maxwell’s equations and the ray-tracing algorithm are provided in Chapter 6. In
this chapter we use a simple ray-tracing technique to familiarize the reader with the
principles of radio propagation modeling for communication systems applications.