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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 .
In wireless communications, channel state information (CSI) is the known channel properties of a communication link.This information describes how a signal propagates from the transmitter to the receiver and represents the combined effect of, for example, scattering, fading, and power decay with distance.
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
Some components of the scattered energy travel in the direction of the receiver antennas and form the receive signal. Since there are very many particles to cause scattering in this region, the Rayleigh fading statistical model may usefully predict behaviour and performance in this kind of system.
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.
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This corresponds to the following non-logarithmic gain model: =, where = / is the average multiplicative gain at the reference distance from the transmitter. This gain depends on factors such as carrier frequency, antenna heights and antenna gain, for example due to directional antennas; and = / is a stochastic process that reflects flat fading.