Last Modified: January 9, 2017

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

The number of complex-valued fading profile samples (having Rayleigh-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 Rayleigh 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 Rayleigh distribution describes a flat-fading channel characterized by a single-tap impulse response with a time-varying envelope that is Rayleigh-distributed. This model describes the statistical time-varying nature of the received envelope of a flat fading channel or the envelope of an individual multipath component. The Rayleigh distribution has a probability density function (PDF) given by the following equation:

$p\left(r\right)=\frac{r}{{\sigma}^{2}}\mathrm{exp}(-\frac{{r}^{2}}{{2\sigma}^{2}})u\left(r\right)$

where *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