Fading in wireless communication has been a cause of severe degradation in the strength of the
signal. When the transmitted signal undergoes reflection or diffraction such that it follows two
or more than two paths to reach the destination antenna, it is said that a multipath fading has
occurred. This multipath fading results in an ambiguous signal reception at the receiver as the
same transmitted signal arrives at different times and phases to the receiver end. It is how the
environment plays with the signal that defines the degree of fading. So, it is difficult to predict
in a concrete manner, the rules of fading. But then, there have been several statistical models
that could help realize and analyze the fading of the received signal.
For a small geographical region, a Rayleigh or Rician model can be helpful in determining the
fading envelop of the received signal whereas a log-normal fading channel can be used for large
geographical regions. The Nakagami-m fading channel which includes Rayleigh as well as closely
approximates the Rician fading channel, is a probability distribution related to a gamma
distribution. In case of urban cities, where the infrastructures are closely spaced, the fading
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observed can be modeled better with Nakagami-m fading channel. The Nakagami-m fading
channel is thus more preferable as it enables to model a wider class of fading channel
conditions and to fit well with empirical data [19]. The Nakagami-m distribution is given by
(2.1)
where is the channel amplitude, m is the fading severity parameter which varies from 0.5 to
, = E[] which controls the spread. For m = 1, (2.1) gives Rayleigh distribution and for
m = 0.5, we obtain a one sided Gaussian distribution [20]. Different values of m determine the
changing severity of the fading compared to Rayleigh fading.
