Regardless of the model chosen the simulation methodology is shown in Fig. 3.53. The assumption
in the figure is that the channel is frequency flat. The frequency selective fading models can be
built using the flat fading model.
WIRELESS MULTIPATH CHANNEL 159
Transmitter
Channel
Simulator
Receiver
h(t)
N(t)
S(t)
R(t)
R(t) = S(t) . h(t) + N(t)
R(t) = S(t) . r(t) . ejq(t) + N(t)
FIGURE 3.53 Simplified communication system.
3.8.1 Jakes Fading Model
The classical model used to generate multipath fading is the Jakes model [1]. This model assumes the
local scatterers are uniformly distributed on a circle of constant radius around the mobile (see Fig. 3.54).
The Jakes model includes the effects of each arriving ray as a sinusoid with a certain frequency
shift. This frequency shift is due to the Doppler principle. These shifts are due to the incoming rays
Base
Station
Mobile
Station
FIGURE 3.54 Classical Jakes multipath fading model.
having an angle of arrival with respect to the MS velocity vector. The circle of constant radius is an
approximation of the surrounding scatterers/reflectors the MS would indeed see in reality, but its simplicity
allows for robust and insightful channel models.
Mathematical Representation.
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