MT Rayleigh Selective Fading profile (Jakes) (G Dataflow)

Generates a Rayleigh selective-fading profile for the multipath channel. The envelope for each path statistically obeys the Rayleigh distribution implemented using the Jakes fading model.

number of paths

The number of paths in the simulated multipath channel. A fading profile is generated for each of these paths.

Default: 1

profile length

The number of complex-valued fading profile samples (having Rayleigh-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. The seed in value is used only for the first call or 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 Rayleigh 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

A two-dimensional array of complex-valued coefficients. The number of rows corresponds to the number of paths in the channel, and the number of columns is equal to the 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.

error out

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

Rayleigh Distribution Equation

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:

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

where r is the specified fading variance.

Jakes Model Equation

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

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

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported