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# I/Q Imbalance

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

RF Impairments

## Description

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

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

2. Applies amplitude and phase imbalances, specified by the I/Q amplitude imbalance (dB) and I/Q phase imbalance (deg) parameters, respectively, to both components.

3. Combines the in-phase and quadrature components into a complex signal.

4. 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

Ia = I/Q amplitude imbalance

Ip = I/Q phase imbalance

IDC = in-phase DC offset

Also let x = xr + j *xi be the complex input to the block, with xr and xi being the real and imaginary parts, respectively, of x. Let y be the complex output of the block.

Then, for an I/Q amplitude imbalance, Ia

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

For an I/Q phase imbalance Ip

yPhaseImbalance = $\left[\mathrm{exp}\left(-0.5*j*\pi *\frac{{I}_{p}}{180}\right)*{y}_{{r}_{Amplitude\mathrm{Im}balance}}\right]+\left\{\mathrm{exp}\left[j\left(\frac{\pi }{2}+0.5*\pi *\frac{{I}_{p}}{180}\right)\right]*{y}_{{i}_{Amplitude\mathrm{Im}balance}}\right\}$
$\triangleq$ yrPhaseImbalance+ j * yiPhaseImbalance

For DC offsets IDC and QDC

y = (yr PhaseImbalance + IDC) + j * (yiPhaseImbalance + QDC )

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.

## Parameters

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.