Figure 2.2: Ray Tracing Model
on the wavefront are approximated using simple geometric equations instead of Maxwell's more complex
wave equations.
The error of the ray tracing approximation is smallest when the receiver is many
wavelengths from the nearest scatterer, and all the scatterers are large relative to a wavelength and fairly
smooth. Comparison of the ray tracing method with empirical data shows it to accurately model received
signal power in rural areas [8], along city streets where both the transmitter and receiver are close to
the ground [6, 5, 8], or in indoor environments with appropriately adjusted diffraction coefficients [7].
Propagation effects besides received power variations, such as the delay spread of the multipath, are not
always well-captured with ray tracing techniques [9].
If the transmitter, receiver, and reflectors are all immobile then the impact of the multiple received
signal paths, and their delays relative to the LOS path, are fixed. However, if the source or receiver are
moving, then the characteristics of the multiple paths vary with time. These time variations are deter-
ministic when the number, location, and characteristics of the reflectors are known over time, otherwise,
statistical models must be used. Similarly, if the number of reflectors is very large or the reflector surfaces
are not smooth then we must use statistical approximations to characterize the received signal. We will
discuss statistical fading models for propagation effects in Chapter 3. Hybrid models, which combine ray
tracing and statistical fading, can also be found in the literature [11, 12], however we will not describe
them here.
The most general ray tracing model includes all attenuated, diffracted, and scattered multipath
components. This model uses all of the geometrical and dielectric properties of the objects surrounding
the transmitter and receiver. Computer programs based on ray tracing such as Lucent's Wireless Systems
Engineering software (WiSE), Wireless Valley's SitePlanner
R
, and Marconi's Planet
R
EV are widely used
for system planning in both indoor and outdoor environments. In these programs computer graphics are
combined with aerial photographs (outdoor channels) or architectural drawings (indoor channels) to
obtain a 3D geometric picture of the environment [5].
The following sections describe several ray tracing models of increasing complexity. We start with a
simple two-path model, which predicts signal variation resulting from a ground reflection interfering with
the LOS path. This model characterizes signal propagation in isolated areas with few reflectors, such
as rural roads or highways. It is not typically a good model for indoor environments. We then present
a ten-ray reflection model, which predicts the variation of a signal propagating along a straight street
or hallway. Finally, we describe a general model which predicts signal propagation for any propagation
environment. The two-ray model only requires information about the antenna heights, while the ten-ray
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