## Channel characterization

A Rician fading channel can be described by two parameters: ${\displaystyle K}$ and ${\displaystyle \Omega }$.[1] ${\displaystyle K}$ is the ratio between the power in the direct path and the power in the other, scattered, paths.[2] ${\displaystyle \Omega }$ is the total power from both paths (${\displaystyle \Omega =\nu ^{2}+2\sigma ^{2}}$), and acts as a scaling factor to the distribution.

The received signal amplitude (not the received signal power) ${\displaystyle R}$ is then Rice distributed with parameters ${\displaystyle \nu ^{2}={\frac {K}{1+K}}\Omega }$ and ${\displaystyle \sigma ^{2}={\frac {\Omega }{2(1+K)}}}$.[3] The resulting PDF then 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.