What is the reason to model a wireless channel as a Rayleigh channel?
Modeling a wireless channel as a Rayleigh fading channel serves the purpose of modeling a non line of sight transmission.
In this case, the transmission occurs only by reflections, since a direct path between two devices does not exist. Obviously, since only reflections are accounted for, the behavior encompasses time variant fading, which are modeled as a Rayleigh distribution.
This is done in contrast to the Rician fading, which is more suitable to model a line-of-sight communication.
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Rayleigh fading is described by less parameters than Rician fading. When planning real networks, accurate models of specific situations are desirable, while in science, simplified, idealized and generic models with few parameters, for example the Rayleigh channel, are often preferable. Such models shows more explanatory power and can easily be reused as reference model by other scientists.
The choice of model also depends on what performance measure we want to analyze. If we do not know the typical scenario, worst-case and/or best-case scenarios are useful. Rician fading may be seen as a typical case, while Rayleigh fading to my understanding reflects worst-case line-of-sight wave-propagation (as Frederico described), for example near the cell-boarder, which is interesting if we want to analyze for example the outage probability. In other studies, where we want to analyze diversity gain, Rayleigh fading may be seen as a best-case scenario.
It is used to represent multipath scenario. In this case, receiver receives multiple copies of transmitted signal due to reflections, diffractions and scattering. As per central limit theorem, the impulse response of such channel is gaussian with zero mean. And the distribution of amplitude of channel coefficient is Rayleigh because phase of channel is uniformly distributed in (0, 2*pi).
Moreover, it is used for non line -of -sight communication.
Whereas, Racian is used for LOS and mean value represents LOS component between transmitter and receiver.
Experimental results published by many researcher have shown that attenuation of electromagnetic signal propagation in tropospheric and ionospheric regions can be model with Rayleigh fading model with good level of accuracy. However this model is good when no dominant propagation along LoS.
Rayleigh model is statistical model that is developed based on some observation
Mathematically speaking, fading coefficients are assumed to be complex Gaussian variables, where the real and imaginary parts are assumed to be zero-mean and independent, thus the magnitude (envelope) of such a complex Gaussian is Rayleigh distributed, i.e., square root of the sum of squares of two independent and identically distributed zero-mean Gaussian random variables is Rayleigh distributed.
If they're not zero-mean, the square root of the sum of squares of two such Gaussian variables leads to the Rician random variable.
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