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Chapter: Wireless Channels
Section: Multipath fading

Rayleigh fading

Hear a discussion of the basic model behind Rayleigh fading.

Rayleigh fading is caused by multipath reception. The mobile antenna receives a large number, say N, reflected and scattered waves. Because of wave cancellation effects, the instantaneous received power seen by a moving antenna becomes a random variable, dependent on the location of the antenna.

In case of an unmodulated carrier, the transmitted signal has the form

.

Next we'll discuss the basic mechanisms of mobile reception.

Effect of Motion

Let the n-th reflected wave with amplitude c_n and phase arrive from an angle relative to the direction of the motion of the antenna.

The Doppler shift of this wave is

,

where v is the speed of the antenna.

Phasor representation


Animation and Figure: Phasor diagram of a set of scattered waves (in blue), resulting a Rayleigh-fading envelope (in black). Check out the Java animated version for details.

The received unmodulated signal r(t) can be expressed as

An inphase-quadrature representation of the form

can be found with in-phase component

and quadrature phase component

.

This propagation model allows us, for instance,

If the set of reflected waves are dominated by one strong component, Rician fading is a more appropriate model.



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