Last Modified: January 9, 2017

Generates a Rician flat-fading profile with an envelope that statistically obeys the Rician distribution, using the Jakes fading model.

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:

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

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:

$A=\sqrt{\mathrm{var}\times K}$

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

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

**Default: **1000

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*.

**Default: **0.01

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. The **seed in** value is used only for the first call or when **reset?** is set to TRUE.

**Default: **-1

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

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.

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:

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

where *A* denotes the peak amplitude of the dominant signal, *I*_{0}() denotes the modified Bessel function of the first kind and zero-order, and *r* is the specified **fading variance**.

The Jakes model is a deterministic method that simulates time-correlated Rayleigh fading waveforms. The model assumes that *N* equal-strength rays arrive at a moving receiver with uniformly distributed arrival angles, such that ray *n* experiences a Doppler shift defined by the following equation:

${\omega}_{n}={\omega}_{m}\mathrm{cos}\left({\alpha}_{n}\right)$

where

${\omega}_{n}={2\pi f}_{m}$

and

${\alpha}_{m}=2\pi \frac{(n-0.5)}{N}$ represents the arrival angle of the ray *n*.

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported