Rician fading or Ricean fading is a

stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...

model for

radio Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmit ...

propagation Propagation can refer to: * Chain propagation in a chemical reaction mechanism *Crack propagation, the growth of a crack during the fracture of materials * Propaganda, non-objective information used to further an agenda * Reproduction, and other fo ...

anomaly caused by partial cancellation of a radio

signal In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...

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

multipath interference In radio communication, multipath is the propagation phenomenon that results in radio signals reaching the receiving antenna by two or more paths. Causes of multipath include atmospheric ducting, ionospheric reflection and refraction, and refle ...

), 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.

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 m ...

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 distribut ...

. 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), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can ...

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, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary ...

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