The Model
Rayleigh fading is a reasonable model when there are many objects in the environment that scatter the radio signal before it arrives at the receiver. The central limit theorem holds that, if there is sufficiently much scatter, the channel impulse response will be well-modelled as a Gaussian process irrespective of the distribution of the individual components. If there is no dominant component to the scatter, then such a process will have zero mean and phase evenly distributed between 0 and 2π radians. The envelope of the channel response will therefore be Rayleigh distributed.
Calling this random variable, it will have a probability density function:
where .
Often, the gain and phase elements of a channel's distortion are conveniently represented as a complex number. In this case, Rayleigh fading is exhibited by the assumption that the real and imaginary parts of the response are modelled by independent and identically distributed zero-mean Gaussian processes so that the amplitude of the response is the sum of two such processes.
Read more about this topic: Rayleigh Fading
Famous quotes containing the word model:
“When Titian was mixing brown madder,
His model was posed up a ladder.
Said Titian, That position
Calls for coition,
So he lept up the ladder and had her.”
—Anonymous.
“One of the most important things we adults can do for young children is to model the kind of person we would like them to be.”
—Carol B. Hillman (20th century)