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

The modulated complex baseband waveform data.

Trigger (start) time of the **Y** array.

**Default: **0.0

Time interval between data points in the **Y** array.

**Default: **1.0

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.

A two-dimensional array of sample-by-sample profiles to be applied to the **input complex waveform** for each path in the multipath channel. 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.

The arrival time, in seconds, of the different ray paths versus their received power, in dB. The times are relative to the arrival of the first ray path. The first column of the power delay profile array must be the relative power loss, in dB, and the second column represents the relative time of arrival, in seconds.

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

**Default: **no error

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**.

Time of the first value in the **Y** array.

Time interval between data values in the **Y** array.

**Default: **1.0

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

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:

${\stackrel{\xaf}{C}}_{k}^{2}=\frac{{C}_{k}^{2}}{{\displaystyle \underset{k=1}{\overset{N}{\sum}}{C}_{k}^{2}}}$

for *k* = 1,...,*N*.

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

${P}_{LOS}=(k+1)\times {P}_{1}$

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

${\stackrel{\xaf}{C}}_{k}^{2}=\frac{{C}_{k}^{2}}{({k}_{LOS}+1)\times {C}_{1}^{2}+{\displaystyle \underset{k=2}{\overset{N}{\sum}}{C}_{k}^{2}}}$

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:

${a}_{kl}={\stackrel{\xaf}{C}}_{k}\times {f}_{kl}$

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

The time array,
${\tau}_{k}$, 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:

${n}_{k}=\frac{{\tau}_{k}}{dt}$

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:

$y\left[n\right]={\displaystyle \underset{k=1}{\overset{N}{\sum}}{a}_{kl}}\times x[n-{n}_{k}]$

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,
${\tau}_{k}$, 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,
$\frac{{\tau}_{k}}{dt}$ 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.

**Installed By: **LabVIEW Communications System Design Suite (introduced in 1.0)

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported