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Rician fading
The model behind Rician fading is similar to that for Rayleigh fading,
except that in Rician fading a strong dominant component is present. This
dominant component can for instance be the line-of-sight wave. Refined Rician
models also consider that
- that the dominant wave can be a phasor sum of two or more dominant
signals, e.g. the line-of-sight, plus
a ground
reflection. This combined signal is then mostly treated as a deterministic
(fully predictable) process, and that
- the dominant wave can also be subject to shadow
attenuation. This is a popular assumption in the modelling of satellite
channels.
Besides the dominant component, the mobile antenna receives
a large number of reflected and scattered waves.
PDF of signal amplitude
The derivation is similar to the derivation for
Rayleigh fading. In order to obtain the probability density of the signal
amplitude 
we observe the random
processes I(t) and Q(t) at one particular instant t_0. If
the number of scattered waves is sufficiently large, and are i.i.d., the central
limit theorem says that I(t_0) and Q(t_0) are Gaussian, but, due
to the deterministic dominant term, no longer zero mean. Transformation of
variables shows that the amplitude and the phase have the joint pdf
Here, 
is the local-mean
scattered power and 
is the
power of the dominant component. The pdf of the amplitude is found from the
integral
,
where 
is the modified Bessel
function of the first kind and zero order, defined as
Exercise:
show that the total local-mean power is
Rician factor
The Rician K-factor is defined as the ratio of
signal power in dominant component over the (local-mean) scattered power. Thus
Expressed in terms of the local-mean power 
and the Rician K-factor, the
pdf of the signal amplitude becomes
Exercise
Show
that for a large local-mean signal-to-noise ratio 
, the probability that the
instantaneous power p drops below a noise threshold 
tends to
Exercise
Describe how you would measure the Rician K-factor. Answer
Rician Channels
Examples of Rician fading are found in
