# MT Apply IQ Impairments (G Dataflow)

Applies various I/Q impairments to the complex baseband modulated waveform.

## impairment definition

A value that indicates which set of equations is used to represent impairments.

In the equations in the following table, $I$ is the real component and $Q$ is the imaginary component of each sample in the input complex waveform. ${I}^{\prime }$ and ${Q}^{\prime }$ are the real and imaginary components of the corresponding sample in the output complex waveform. ${I}_{\circ }$ is I DC Offset (%) / 100, and ${Q}_{\circ }$ is Q DC Offset (%) / 100.

Name Description
Vertical Shear

The definition uses the following equations for I/Q impairments:

${I}^{\prime }=a*\text{\hspace{0.17em}}I+\text{\hspace{0.17em}}{I}_{\circ }$

${Q}^{\prime }=a*\mathrm{sin}\left(\phi \right)\text{\hspace{0.17em}}*\text{\hspace{0.17em}}I+\text{\hspace{0.17em}}b*\text{\hspace{0.17em}}\mathrm{cos}\left(\phi \right)\text{\hspace{0.17em}}*\text{\hspace{0.17em}}Q+\text{\hspace{0.17em}}{Q}_{\circ }$

where

$\gamma$ = 10(IQ gain imbalance/20)

$a=\gamma *\text{\hspace{0.17em}}b$

$b=\sqrt{\frac{2}{1+{\gamma }^{2}}}$

In matrix form, these equations are represented by

$\left[\begin{array}{c}{I}^{\prime }\\ {Q}^{\prime }\end{array}\right]=S\left[\begin{array}{c}I\\ Q\end{array}\right]+\left[\begin{array}{c}{I}_{\circ }\\ {Q}_{\circ }\end{array}\right]$

where

$S=\left[\begin{array}{cc}a& 0\\ a*\mathrm{sin}\phi & b*\mathrm{cos}\phi \end{array}\right]$

Axis Shear

With this option selected, this node uses an impairment definition that simplifies the conversion between measured impairments and their inverse impairments. For example, you may want to measure the I/Q impairments of a system and compensate for those impairments by applying the inverse impairments to the generated or received waveform. Using the Axis Shear definition, given a measured skew and imbalance (in dB), the inverse impairments are -1.0 * skew and -1.0 * imbalance. This definition uses the following equations for IQ impairments:

${I}^{\prime }=I*\text{\hspace{0.17em}}\sqrt{\gamma }-Q*\left(\frac{\phi }{2}\right)+{I}_{\circ }$

${Q}^{\prime }=-I*\left(\frac{\phi }{2}\right)+Q*\left(\frac{1}{\sqrt{\gamma }}\right)+{Q}_{\circ }$

where

$\gamma$ = 10(IQ gain imbalance/20)

In matrix form, these equations are represented by

$\left[\begin{array}{c}{I}^{\prime }\\ {Q}^{\prime }\end{array}\right]=S\left[\begin{array}{c}I\\ Q\end{array}\right]+\left[\begin{array}{c}{I}_{\circ }\\ {Q}_{\circ }\end{array}\right]$

where

$S=\left[\begin{array}{cc}\sqrt{\gamma }& -\phi /2\\ -\phi /2& \frac{1}{\sqrt{\gamma }}\end{array}\right]$

Default: Vertical Shear

## i dc offset

The desired DC offset of the I waveform as a percentage of full scale of the input complex waveform. Valid values are between -100 and +100.

Default: 0.0

## input complex waveform

The modulated complex baseband waveform data.

### t0

Trigger (start) time of the Y array.

Default: 0.0

### dt

Time interval between data points in the Y array.

Default: 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.

## q dc offset

The desired DC offset of the Q waveform as a percentage of the input complex waveform. Valid values are -100 to +100, inclusive.

Default: 0

## iq gain imbalance

The desired ratio of I gain to Q gain, in dB. Valid values are between -6.0 and +6.0.

Default: 0

The desired quadrature skew of the complex waveform in degrees. Valid values are between -30.0 and +30.0 degrees.

Default: 0

## error in

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

Default: no error

## frequency offset

The desired frequency offset, in Hertz (Hz), to apply to the output complex waveform.

Default: 0

## reset?

A Boolean that determines whether this node continues applying the impairments using the previous iteration states.

 TRUE Restarts the impairment generation process. FALSE Continues applying the impairments using the previous iteration states.

Default: TRUE

## output complex waveform

The impaired complex baseband modulated waveform data returned by this node.

### t0

Trigger (start) time of the Y array.

Default: 0

### dt

Time interval between data values in the Y array.

Default: 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.

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported