MT Rayleigh Selective Fading profile (Jakes)
- Updated2023-02-17
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MT Rayleigh Selective Fading profile (Jakes)
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.
Inputs/Outputs
profile length
The number of complex-valued fading profile samples (having Rayleigh-distributed envelopes) to generate.
Default value: 1000
sampling frequency
The system sample rate, in hertz (Hz). This rate is the product of the symbol rate × samples per symbol.
Default value: 1
doppler spread
The desired input Doppler spread fm 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 fc is transmitted, the received signal spectrum, called the Doppler spectrum, has components in the range (fc - fm) to (fc + fm). The Doppler spread is related to the mobile velocity v, carrier frequency fc, and the speed of light c by the relation fm = vfc/c.
Default value: 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 value: -1
error in
Error conditions that occur before this node runs.
The node responds to this input according to standard error behavior.
Default value: No error
number of paths
The number of paths in the simulated multipath channel. A fading profile is generated for each of these paths.
Default value: 1
fading variance
The desired variance of the complex-valued Rayleigh distributed fading profile.
Default value: 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 value: TRUE
fading profile
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:
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:
where
and