Wireless Network Design: Optimization Models and Solution ...

3 Channel Models for Wireless Communication Systems 49
of the delays introduced by the scattering environment which can cause significant
distortion in the signal. The relative velocity of the scattering environment between
the transmitter and receiver determines the extent of shift in the frequency of the
received signal, due to Doppler effect. This causes a change in the frequency spread
of the signal [50].
A channel has coherence if it does not show changes in its characteristics along
the space, time and frequency dimensions. The different types of coherence are explained
below. Consider a narrow band signal and fixed in space. Then the temporal
coherence of a channel can be expressed as |h(t)| ≈ constant, for |t − t0| ≤ Tc/2
where Tc is the temporal coherence time. It means that the temporal characteristics
of the channel do not change within the temporal coherence time. The frequency
coherence of a channel is defined when the magnitude of the channel does not
change over a certain frequency band of interest. The form of the expression is
similar to the previous case and is given by |h( f )| ≈ constant for | f − fc| ≤ Bc/2.
As in the previous cases, spatial coherence can be defined as h(r) ≈ constant for
|r − r0| ≤ DDc/2 with r0 is an arbitrary position in space, Dc is the spatial coherence.
All the above coherence parameters are very important for system design. For
example, the knowledge of the value of spatial coherence will help mitigate fading.
To explain further, if two antennas of the receiver are separated by a distance more
than the spatial coherence distance, it is likely that one of the antennas could receive
a stronger signal compared to the other antenna. Thus, one can combine the signals
from both antennas in an effective manner to increase the signal strength. In other
words, the principle of ‘diversity’ is employed. Similar techniques can be used in
the context of temporal and frequency coherence to improve signal quality.
3.4 Mathematical Modeling of Wireless Channels
For the design of wireless systems, where the signal is distorted due to physical
phenomena, it is necessary to characterize the channel, using mathematical models.
It is clear that the scattering environment would be different for different locations
of the transmitter and receiver. The best framework is to model the channel as a random
quantity and characterize it appropriately. In order to characterize the channel,
covering most of the possible cases, two approaches are used.
• Statistical model using experimental data : This model is based on measurements
which are carried out using transmitters and receivers in different terrain locations,
using different antennas, and other relevant experimental parameters. It is
clear that an exhaustive measurement campaign to cover all possibilities, is not
possible. Representative sets of experiments are carried out and the variations are
modeled in terms of a stochastic framework. Mathematical models are developed
based on the analysis of data. This is also called the classical modeling approach.
• Models using principle of geometry: In this technique, the scattering environment
is characterized by geometrical models where the signal paths are assumed to be
rays traveling between the transmitter and receiver [32, 36, 46]. The level of