Rician fading or Ricean fading is a

stochastic Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; i ...

model for

radio Radio is the technology of communicating using radio waves. Radio waves are electromagnetic waves of frequency between 3 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmitter connec ...

propagation anomaly caused by partial cancellation of a

radio signal Radio waves (formerly called Hertzian waves) are a type of electromagnetic radiation with the lowest frequencies and the longest wavelengths in the electromagnetic spectrum, typically with frequencies below 300 gigahertz (GHz) and wavelengths g ...

by itself — the signal arrives at the receiver by several different paths (hence exhibiting

multipath interference In radio communication, multipath is the radio propagation, propagation phenomenon that results in radio signals reaching the receiving antenna (electronics), antenna by two or more paths. Causes of multipath include atmospheric ducting, ionosph ...

), and at least one of the paths is changing (lengthening or shortening). Rician fading occurs when one of the paths, typically a line of sight signal or some strong reflection signals, is much stronger than the others. In Rician fading, the amplitude gain is characterized by a

Rician distribution In probability theory, the Rice distribution or Rician distribution (or, less commonly, Ricean distribution) is the probability distribution of the magnitude of a circularly-symmetric bivariate normal distribution, bivariate normal random variab ...

Rayleigh fading Rayleigh fading is a statistical model for the effect of a propagation environment on a radio signal, such as that used by wireless devices. Rayleigh fading models assume that the magnitude of a signal that has passed through such a transmission ...

is sometimes considered a special case of Rician fading for when there is no line of sight signal. In such a case, the Rician distribution, which describes the amplitude gain in Rician fading, reduces to a

Rayleigh distribution 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. The distributi ...

. Rician fading itself is a special case of two-wave with diffuse power (TWDP) fading.

Channel characterization

A Rician fading channel can be described by two parameters. The first one,

K

, is the ratio between the power in the direct path and the power in the other, scattered, paths: :

K = \frac

The second one,

\Omega

, is the total power from both paths, and acts as a scaling factor to the distribution: :

\Omega=\nu^2+2\sigma^2

The received signal amplitude (''not'' the received signal power)

R

is then Rice distributed with the following parameters:Richards, M.A.
Rice Distribution for RCS
Georgia Institute of Technology (Sep 2006) :

\nu^2 = \frac\Omega

\sigma^2 = \frac

The resulting

Probability density function In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a Function (mathematics), function whose value at any given sample (or point) in the sample space (the s ...

is: :

f(x) = \frac \exp\left(-K-\frac\right) I_0\left(2\sqrtx\right)
,

where

I_0(\cdot)

is the 0th order

modified Bessel function Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex ...

of the first kind.

References

* Lindsey, W.
Error probabilities for Rician fading multichannel reception of binary and N-ary signals
, ''IEEE Transactions on Information Theory'', Volume 10, Number 4, October 1964, Pages 339–350.

explained o
wirelesscommunication.nl
{{DEFAULTSORT:Rician Fading Radio frequency propagation fading

Channel characterization

See also

References