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Create complex baseband model of signal impairments caused by imbalances between in-phase and quadrature receiver components

RF Impairments

The I/Q Imbalance block creates a complex baseband model of the signal impairments caused by imbalances between in-phase and quadrature receiver components. Typically, these are caused by differences in the physical channels for the two components of the signal.

The I/Q Imbalance block applies amplitude and phase imbalances to the in-phase and quadrature components of the input signal, and then combines the results into a complex signal. The block

Separates the signal into its in-phase and quadrature components.

Applies amplitude and phase imbalances, specified by the

**I/Q amplitude imbalance (dB)**and**I/Q phase imbalance (deg)**parameters, respectively, to both components.Combines the in-phase and quadrature components into a complex signal.

Applies an in-phase dc offset, specified by the

**I dc offset**parameter, and a quadrature offset, specified by the**Q dc offset**parameter, to the signal.

The block performs these operations in the subsystem shown in
the following diagram, which you can view by right-clicking the block
and selecting **Mask** > **Look
under mask**:

Let

*I _{a}* = I/Q amplitude
imbalance

*I _{p}* = I/Q phase imbalance

*I _{DC}* = in-phase DC
offset

*Q _{DC}* = quadrature DC
offset

Also let *x* = *x _{r}* +

Then, for an I/Q amplitude imbalance, *I _{a}*

*y _{AmplitudeImbalance}* = $$[{10}^{(0.5*\frac{{I}_{a}}{20})}*{x}_{r}]+j[{10}^{(-0.5*\frac{{I}_{a}}{20})}*{x}_{i}]$$

$$\triangleq $$

For an I/Q phase imbalance *I _{p}*

*y _{PhaseImbalance}* = $$[\mathrm{exp}(-0.5*j*\pi *{\scriptscriptstyle \frac{{I}_{p}}{180}})*{y}_{{r}_{Amplitude\mathrm{Im}balance}}]+\{\mathrm{exp}[j({\scriptscriptstyle \frac{\pi}{2}}+0.5*\pi *{\scriptscriptstyle \frac{{I}_{p}}{180}})]*{y}_{{i}_{Amplitude\mathrm{Im}balance}}\}$$

$$\triangleq $$

For DC offsets *I _{DC}* and

y = (y_{r PhaseImbalance} + *I _{DC}*)
+ j * (

The value of the **I/Q amplitude imbalance
(dB)** parameter is divided between the in-phase and quadrature
components such that the block applies a gain of *+X/2* dB
to the in-phase component and a gain of *-X/2* dB
to the quadrature component where *X* can be positive
or negative.

The effects of changing the block's parameters are illustrated
by the following scatter plots of a signal modulated by 16-ary quadrature
amplitude modulation (QAM) with an average power of `0.01`

watts.
The usual 16-ary QAM constellation without distortion is shown in
the first scatter plot:

The following figure shows a scatter plot of an output signal,
modulated by 16-ary QAM, from the I/Q block with **I/Q amplitude
imbalance (dB)** set to `8`

and all other
parameters set to `0`

:

Observe that the scatter plot is stretched horizontally and compressed vertically compared to the undistorted constellation.

If you set **IQ phase imbalance (deg)** to `30`

and
all other parameters to `0`

, the scatter plot is
skewed clockwise by 30 degrees, as shown below:

Setting the **I dc offset** to `0.02`

and
the **Q dc offset** to `0.04`

shifts
the constellation 0.02 to the right and 0.04 up, as shown below:

See Illustrate RF Impairments That Distort a Signal for a description of the model that generates this plot.

**I/Q amplitude imbalance (dB)**Scalar specifying the I/Q amplitude imbalance in decibels.

**I/Q phase imbalance (deg)**Scalar specifying the I/Q phase imbalance in degrees.

**I dc offset**Scalar specifying the in-phase dc offset.

**Q dc offset**Scalar specifying the amplitude dc offset.

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