Rician fading

Bit error ratio performance of the PSK and QAM transmission over Rician flat fading channel (${\displaystyle K}$ = 0.6, ${\displaystyle \Omega }$ = 1).

A Rician fading channel can be described by two parameters.[1] The first one, ${\displaystyle K}$, is the ratio between the power in the direct path and the power in the other, scattered, paths:[2]

${\displaystyle K={\frac {\nu ^{2}}{2\sigma ^{2}}}}$

The second one, ${\displaystyle \Omega }$, is the total power from both paths, and acts as a scaling factor to the distribution:

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

The received signal amplitude (not the received signal power) ${\displaystyle R}$ is then Rice distributed with the following parameters:[3]

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

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

The resulting Probability density function is:

${\displaystyle f(x)={\frac {2(K+1)x}{\Omega }}\exp \left(-K-{\frac {(K+1)x^{2}}{\Omega }}\right)I_{0}\left(2{\sqrt {\frac {K(K+1)}{\Omega }}}x\right),}$

where ${\displaystyle I_{0}(\cdot )}$ is the 0th order modified Bessel function of the first kind.

• Fading
• Multipath propagation
• Diversity schemes
• Rayleigh fading
• Rice distribution
• Stochastics
• Statistics
• Stephen O. Rice
• Two-wave with diffuse power (TWDP) fading

• 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.
• Rician Fading explained on wirelesscommunication.nl.