MT Apply Flat Fading Profile

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Updated2023-02-17
5 minute(s) read

Applies a flat fading profile to the input complex waveform. The faded waveform can be used to test receiver immunity to fading channels.

Note This node normalizes the fading profile to ensure that the power in the input complex waveform is equal to the fading variance. The Modulation Toolkit 4.0 version of MT Apply Flat Fading does not apply this normalization algorithm.

Inputs/Outputs

input complex waveform

The modulated complex baseband waveform data.

t0

Trigger (start) time of the Y array.

Default value: 0.0

dt

Time interval between data points in the Y array.

Default value: 1.0

Y

The complex-valued signal-only baseband modulated waveform. The real and imaginary parts of this complex data array correspond to the in-phase (I) and quadrature-phase (Q) data, respectively.

fading profile

The sample-by-sample profile to be applied to the input complex waveform. At each call, this node begins applying this fading profile from the index point where it left off on the previous iteration unless reset? is set to TRUE. Wire the fading profile parameter of MT Generate Fading Profile to this parameter.

Setting the right fading profile length

fading profileinput complex waveformfading profileinput complex waveformfading profileinput complex waveformfading profilereset?input complex waveform

error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Default value: No error

reset?

A Boolean that determines whether this node begins applying the fading profile at the index point where it left off on the last iteration.

TRUE	Applies the fading profile at index point 0.
FALSE	Does not apply the fading profile at index point 0.

Default value: TRUE

output complex waveform

The faded modulated complex baseband waveform data returned by this node. This parameter is always the same size as the input complex waveform, regardless of the size of the fading profile.

t0

Time of the first value in the Y array.

dt

Time interval between data values in the Y array.

Default value: 1.0

Y

The complex-valued signal-only baseband modulated waveform. The real and imaginary parts of this complex data array correspond to the in-phase (I) and quadrature-phase (Q) data, respectively.

error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Normalizing the Rician Fading Profile

To match the output complex waveform power to the specified fading variance, this VI first normalizes the power array of the power delay profile, and the amplitude corresponding to power element is then multiplied by the corresponding fading profile, f_kl, where l = 1, 2 …, L, and L is the profile length.

For the selective Rayleigh profile, the power coefficients,

C_{k}^{2}

, corresponding to each path are shown in the following equation:

C_{k}^{2} = 10^{\frac{P_{k}}{10}}

The normalized power coefficients can then be represented by:

{\bar{C}}_{k}^{2} = \frac{C_{k}^{2}}{\sum_{k = 1}^{N} C_{k}^{2}}

for k = 1,...,N.

For the selective Rician profile, the power in the line-of-sight (LOS) path is given by:

P_{L O S} = (k + 1) \times P_{1}

The normalized power coefficients can then be represented by the following equation:

{\bar{C}}_{k}^{2} = \frac{C_{k}^{2}}{(k_{L O S} + 1) \times C_{1}^{2} + \sum_{k = 2}^{N} C_{k}^{2}}

By multiplying these power coefficients with the generated fading profile, f_kl, for each path, we can obtain the amplitude, a_kl, to apply to the Rician profile as shown in the following equation:

a_{k l} = {\bar{C}}_{k} \times f_{k l}

for k = 1,...,N and l = 1,...,L, where L is the profile length.

The time array,

τ_{k}

, is approximated to an integer multiple of the sampling duration, dt, to obtain the integer delay, n_k. The integer delay is applied to the input complex waveform as shown by the following equation:

n_{k} = \frac{τ_{k}}{d t}

The input complex waveform is then delayed for each path by y_k[n] = x[n - n_k], where n = 1,...,M and M is the input complex waveform size.

Finally, y_k[n] is point-by-point multiplied with amplitude coefficients to obtain the output complex waveform as shown by the following equation:

y [n] = \sum_{k = 1}^{N} a_{k l} \times x [n - n_{k}]

In MT Apply Selective Fading Profile, the power from the power delay profile, set for each path, is applied to the corresponding fading profile generated by MT Generate Fading Profile. The power delay profile is specified in terms of power, P_k, and time,

τ_{k}

, for each path, where k = 1, 2…,N. The delay in the power delay profile is approximated to an integer multiple of the sampling duration,

\frac{τ_{k}}{d t}

for each path, for k = 1,…N, where N is the total number of paths. The input complex waveform is delayed by this amount and then multiplied by the corresponding attenuated fading profile. All these paths are summed to calculate the received signal, y(t), as illustrated by the following figure.

LabVIEW Modulation Toolkit

Table of Contents

MT Apply Flat Fading Profile

Inputs/Outputs

input complex waveform

t0

dt

Y

fading profile

Setting the right fading profile length

error in

reset?

output complex waveform

t0

dt

Y

error out

Normalizing the Rician Fading Profile

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