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Create complex baseband model of signal impairments caused by imbalances between in-phase and quadrature receiver components
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} + j *x_{i} be the complex input to the block, with x_{r} and x_{i} 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, I_{a}
y _{AmplitudeImbalance} = $$[{10}^{(0.5*\frac{{I}_{a}}{20})}*{x}_{r}]+j[{10}^{(-0.5*\frac{{I}_{a}}{20})}*{x}_{i}]$$
$$\triangleq $$ y _{rAmplitudeImbalance} +
j*y_{iAmplitudeImbalance}
For an I/Q phase imbalance I_{p}
y_{PhaseImbalance} = $$[\mathrm{exp}(-0.5*j*\pi *{\scriptscriptstyle \frac{{I}_{p}}{180}})*{y}_{{r}_{Amplitude\mathrm{Im}balance}}]+\{\mathrm{exp}[j({\scriptscriptstyle \frac{\pi}{2}}+0.5*\pi *{\scriptscriptstyle \frac{{I}_{p}}{180}})]*{y}_{{i}_{Amplitude\mathrm{Im}balance}}\}$$
$$\triangleq $$ y_{rPhaseImbalance}+ j * y_{iPhaseImbalance}
For DC offsets I_{DC} and Q_{DC}
y = (y_{r PhaseImbalance} + I_{DC}) + j * (y_{iPhaseImbalance} + Q_{DC} )
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.