# rician fading model

Fading model for narrowband fading channel gain.

Here, there is a dominant line of sight path.

Recall that the channel being studied is of the form

\begin{equation}
\beta(t) = \alpha_0(t)e^{j\phi_0(t)} + \sum_{n = 1}^{N} \alpha_n(t)e^{j\phi_n(t)}
\end{equation}

The first part is complex gaussian, but the sum follows the rayleigh fading model.

We know the variance (power) of the rayleigh part is \(2\sigma^2\), this is the expected power of the sum of all the NLOS parts of the channel.

The variance (power) of the line of sight channel component is \(s^2\)

The **Rician K-factor** is \(s^2/(2\sigma^2)\).

- When K-factor is high, the distribution behaves like a gaussian

(mostly LOS)

- When K-factor is low, the distribution behaves like the rayleigh distribution