# MT Rician Fading Profile (Gans) (G Dataflow)

Generates a Rician flat-fading profile for the multipath channel. The envelope for the first path statistically obeys the Rician distribution, while the envelope for the remaining path obeys the Rayleigh distribution implemented using the Gans model.

## rician parameter k

The desired ratio, in dB, of the dominant line-of-sight (LOS) path to the scattering component. A large positive value of k represents a strongly additive white Gaussian noise channel, while a large negative value of k represents a Rayleigh fading (predominantly scattering) channel.

Mathematical definition of Rician parameter k

Mathematically, the Rician parameter k is defined as:

$K\left(dB\right)\text{\hspace{0.17em}}=\text{\hspace{0.17em}}10×\mathrm{log}\left(\frac{Power\left[LOS\text{\hspace{0.17em}}component\right]}{Power\left[scattering\text{\hspace{0.17em}}component\right]}\right)$

The Rician fading profile is generated by adding a DC specular component to a Rayleigh distributed scattering component. var denotes the requested fading variance, which is the variance of the underlying Rayleigh fading profile. The amplitude (A) of the specular DC component is given by the following formula:

$A=\sqrt{\mathrm{var}×K}$

By varying K, you can parameterize the extent of the scattering component relative to the LOS component of fading. For a strongly Gaussian channel, K approaches infinity, while K < 0 indicates a strongly scattering (Rayleigh fading) channel.

Default: 0

## profile length

The number of complex-valued fading profile samples (having Rician-distributed envelopes) to generate.

Default: 1000

## sampling frequency

The system sample rate, in hertz (Hz). This rate is the product of the symbol rate × samples per symbol.

Default: 1

The desired input Doppler spread f m of the channel, in hertz (Hz).

This parameter denotes the measure of the spectral broadening caused by the time rate of change of the channel. Doppler spread is defined as the range of frequencies over which the received Doppler spectrum is essentially nonzero. When a pure sine tone at frequency f c is transmitted, the received signal spectrum, called the Doppler spectrum, has components in the range (f c - f m ) to (f c + f m ). The Doppler spread is related to the mobile velocity v, carrier frequency f c , and the speed of light c by the relation f m = v f c /c.

Note

The inverse of the Doppler spread T c = 1 / 16 $\pi$f m (known as the coherence time) is the time duration over which the channel impulse response is essentially invariant.

Default: 0.01

## seed in

The initial state for generating the fading profile. If seed in is set to -1, the generated fading profile is randomly chosen during every call when reset? is set to TRUE. Otherwise, the generated fading profile returns the same set of fading coefficients when reset? is set to TRUE.

Default: -1

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: no error

The desired variance of the complex-valued Rician distributed fading profile.

Default: 1

## reset?

A Boolean that determines whether the fading profile generation is reset on subsequent calls to this node.

 TRUE Resets the fading profile generation on every call to this node. FALSE Continues generating the fading profile from the previous iteration on subsequent calls.

Default: TRUE

Complex-valued coefficients of the generated fading profile size that equals profile length. Wire this parameter to MT Apply Fading Profile to apply this fading profile to a baseband I/Q signal.

## seed out

The internal state of the node at the end of generation of the fading profile for the current iteration. When reset? is set to FALSE, this state is used to continue the fading profile generation at the beginning of the next iteration.

## error out

Error information. The node produces this output according to standard error behavior.

## Rician Distribution Equation

The Rician fading profile describes a time-varying channel with an envelope that follows a Rician distribution. The channel can be characterized by a single-tap impulse response comprising a dominant line-of-sight (LOS) path superimposed on a random multipath. The limiting case of a Rician fading channel (when the LOS path is much weaker than the random multipath) is the Rayleigh fading channel. The Rician distribution is given by:

$p\left(r\right)=\frac{r}{{\sigma }^{2}}\mathrm{exp}\left(-\frac{{r}^{2}+{A}^{2}}{2{\sigma }^{2}}\right){I}_{0}\left(\frac{Ar}{{\sigma }^{2}}\right)u\left(r\right)$

where A denotes the peak amplitude of the dominant signal, I0() denotes the modified Bessel function of the first kind and zero-order, and r is the specified fading variance.

## Gans Model Equation

The Gans model generates the Rayleigh fading profile by passing quadrature Gaussian I/Q components through a Doppler filter with a U-shaped power spectral density profile. For the selective fading model, the implementation ensures that the generated fading profile for all paths is uncorrelated.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported