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). Rician fading occurs when one of the paths, typically a line of sight signal, is much stronger than the others. In Rician fading, the amplitude gain is characterized by a Rician distribution.

Rayleigh fading is the specialised model for stochastic fading when there is no line of sight signal, and is sometimes considered as a special case of the more generalised concept of Rician fading. In Rayleigh fading, the amplitude gain is characterized by a Rayleigh distribution. Rician fading itself is a special case of two-wave with diffuse power (TWDP) fading.

A Rician fading channel can be described by two parameters:





K




{\displaystyle K}


and





Ω





{\displaystyle \Omega }


.





K




{\displaystyle K}


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





Ω





{\displaystyle \Omega }






Ω



=



ν




2




+


2



σ




2






{\displaystyle \Omega =\nu ^{2}+2\sigma ^{2}}


), and acts as a scaling factor to the distribution.

The received signal amplitude (not the received signal power)





R




{\displaystyle R}







ν




2




=




K



1


+


K





Ω





{\displaystyle \nu ^{2}={\frac {K}{1+K}}\Omega }







σ




2




=




Ω




2


(


1


+


K


)







{\displaystyle \sigma ^{2}={\frac {\Omega }{2(1+K)}}}


. The resulting PDF then is:

where






I



0




(






)




{\displaystyle I_{0}(\cdot )}


is the 0th order modified Bessel function of the first kind.