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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.
In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables. Up to rescaling, it coincides with the chi distribution with two degrees of freedom .
Where the magnitudes of the signals arriving by the various paths have a distribution known as the Rayleigh distribution, this is known as Rayleigh fading. Where one component (often, but not necessarily, a line of sight component) dominates, a Rician distribution provides a more accurate model, and this is known as Rician fading.
Rician fading or Ricean fading is a stochastic model for radio propagation anomaly caused by partial cancellation of a radio signal by itself — the signal arrives at the receiver by several different paths (hence exhibiting multipath interference), and at least one of the paths is changing (lengthening or shortening).
This model is reasonable when the main scattering appears close to the antenna arrays and has been validated by both outdoor and indoor measurements. [2] [3] With Rayleigh fading, the Kronecker model means that the channel matrix can be factorized as
This results in frequency selective fading and inter-symbol interference. The gains may be Rayleigh or Rician distributed. The echoes may also be exposed to Doppler shift, resulting in a time varying channel model. Nakagami fading; Log-normal shadow fading; Rayleigh fading; Rician fading; Two-wave with diffuse power (TWDP) fading; Weibull fading
In case of only fast fading due to multipath propagation, its amplitude may have Rayleigh distribution or Ricean distribution. This can be convenient, because power is proportional to the square of amplitude. Squaring a Rayleigh-distributed random variable produces an exponentially distributed random variable. In many cases, exponential ...
The Nakagami distribution is relatively new, being first proposed in 1960 by Minoru Nakagami as a mathematical model for small-scale fading in long-distance high-frequency radio wave propagation. [4] It has been used to model attenuation of wireless signals traversing multiple paths [ 5 ] and to study the impact of fading channels on wireless ...