# MT Measure PSK Quadrature Impairments (G Dataflow)

Last Modified: January 9, 2017

Calculates and reports PSK quadrature impairments on a symbol-by-symbol basis at the symbol timing.

## recovered complex waveform

The time-aligned and oversampled complex waveform data after matched filtering, frequency offset correction, and phase offset correction. Wire the recovered complex waveform parameter of MT Demodulate PSK to this parameter.

### 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.

## input bit stream

The demodulated bit stream from the output bit stream parameter of MT Demodulate PSK.

## impairment measurement window

The window over which impairments are measured.

### start index

Index of the first sample of the measurement window.

Default: 0

### width

Number of symbols over which to measure impairments. A value of -1 (default) measures impairments over all symbols. Positive values must be two or greater.

Default: -1

## error in

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

Default: no error

## 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

φ is the specified quadrature skew, in radians

$\gamma$ = 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)

φ is the specified quadrature skew, in radians

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

## reset?

A Boolean that determines how the node handles bits from partial symbols in the input bit stream.

 TRUE Discards bits making up incomplete symbols. FALSE Saves the leftover bits and starts with them on the next iteration.

Default: TRUE

## quadrature skew

The measured quadrature skew of the complex waveform in degrees.

## PSK system parameters

Parameter values defining the PSK system. Wire the PSK system parameters cluster of MT Generate PSK System Parameters (M) or MT Generate PSK System Parameters (map) to this cluster. Do not alter the values.

### samples per symbol

An even number of samples dedicated to each symbol. Multiply this value by the symbol rate to determine the sample rate.

Note

The demodulation and detector nodes use timing recovery, which is optimized for four or more samples per symbol.

Default: 16

### symbol map

An ordered array that maps each Boolean symbol to its desired coordinates in the complex plane. The number of states in the array must be 2 N , where N is the number of bits per symbol.

### differential PSK

A value that indicates how the PSK modulation represents symbols.

Differential operation is used to implement PSK formats such as differential quadrature PSK (DQPSK) and $\pi$/4-DQPSK.

Name Description
disable

Symbols are represented as constellation points.

enable

Symbols are represented as the transitions between constellation points.

Default: disable

### PSK type

Type of PSK modulation.

Name Description
normal

Sets the modulation type to regular PSK.

shifted

Rotates the constellation by $\pi$/M each symbol.

offset

Sets the modulation type to offset quadrature phase-shift keying (OQPSK). This modulation scheme is a form of phase-shift keying in which four different phase angles are used. This scheme is sometimes referred to as staggered quadrature phase-shift keying (SQPSK). For offset PSK, the ideal symbol timing for Q is offset by 1/2 of a symbol period from the ideal symbol timing for I. offset is currently only supported for M= 4.

Default: normal

## magnitude error

The measured magnitude error as a percentage. Magnitude error is the magnitude difference between the ideal and the actual measured symbol locations.

### RMS measurement

The RMS impairment value calculated over the impairment measurement window.

### peak measurement

The peak impairment value measured over the impairment measurement window.

### peak symbol index

Index of the symbol having the peak magnitude of impairment.

### individual symbol measurements

The impairment value for each individual symbol.

## DC offset measurements

The measured DC offset of the I or Q waveforms as a percentage of the largest I and Q value in the symbol map of the recovered complex waveform.

### I

The DC offset of the I waveform, expressed as a percentage of the largest I or Q value in the symbol map.

### Q

The DC offset of the Q waveform, expressed as a percentage of the largest I or Q value in the symbol map.

### origin offset

The offset, in dB, of the constellation origin from its ideal location.

## IQ gain imbalance

The measured ratio of I gain to Q gain, in dB.

Tip

For shifted BPSK (also called $\pi$/2 BPSK with or without differential encoding), certain measurements, including IQ gain imbalance, quadrature skew, and DC offset measurements, are not performed by the current version of the node. The current version of the node returns NaN in these cases. Other measurements, specifically modulation error ratio, error vector magnitude, magnitude error, and phase error, are valid and returned for shifted ( $\pi$/2) BPSK.

## phase error

The measured phase error in degrees. Notice that the phase offset is removed by the demodulator and is excluded from this measurement.

### RMS measurement

The RMS impairment value calculated over the impairment measurement window.

### peak measurement

The peak impairment value measured over the impairment measurement window.

### peak symbol index

Index of the symbol having the peak magnitude of impairment.

### individual symbol measurements

The impairment value for each individual symbol.

## EVM

The measured error vector magnitude (EVM) expressed as a percentage.

### RMS measurement

The RMS impairment value calculated over the impairment measurement window.

### peak measurement

The peak impairment value measured over the impairment measurement window.

### peak symbol index

Index of the symbol having the peak magnitude of impairment.

### individual symbol measurements

The impairment value for each individual symbol.

## modulation error ratio

The measured modulation error ratio in dB.

## 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