Rician

Rician, in the context of probability and signal processing, refers to the Rician distribution (also known as the Rice distribution). It is the probability distribution that describes the magnitude of a complex Gaussian random variable with a nonzero mean. In practical terms, it models the envelope of a signal that contains a dominant line-of-sight component plus a random, isotropic scattering component. The term is widely used in wireless communications to describe fading when a strong direct path coexists with multipath reflections, and it is also referred to as Rice fading in that setting.

Mathematically, if X and Y are independent Gaussian random variables with equal variance σ^2 and nonzero means forming a two-dimensional vector with a nonzero average, then R = sqrt(X^2 + Y^2) has a Rician distribution. The noncentrality parameter ν is the magnitude of the mean vector (ν = sqrt(mu_x^2 + mu_y^2)). The probability density function for R ≥ 0 is

f_R(r) = (r/σ^2) exp(-(r^2 + ν^2)/(2σ^2)) I0(rν/σ^2),

where I0 is the modified Bessel function of the first kind of order zero. A common channel metric, the K-factor, is defined as K = ν^2/(2σ^2), representing the ratio of the power in the line-of-sight component to the power in the scattered components. The distribution reduces to the Rayleigh distribution when ν = 0 (no line-of-sight component).

In applications, the Rician distribution is used to model wireless radio channels with LOS paths, radar and sonar signal amplitudes, and other physical scenarios where a dominant signal component coexists with scattering. The complementary distribution function can be expressed using the Marcum Q-function of order one. The term is sometimes distinguished as Rice distribution in radar literature, while in many communications contexts it is referred to as the Rician distribution or fading.