MT Rician Selective Fading profile (Jakes)
- Updated2023-02-17
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MT Rician Selective Fading profile (Jakes)
Generates a Rician selective-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 Jakes model.
Inputs/Outputs
profile length
The number of complex-valued fading profile samples (having Rician-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
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.
Default value: 0
Mathematical definition of Rician parameter k
Mathematically, the Rician parameter k is defined as:
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:
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.
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 Rician 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.
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:
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.
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