I/Q Imbalance

Apply I/Q imbalances to complex signal

• 

Libraries:
Communications Toolbox / RF Impairments and Components

Description

The I/Q Imbalance block applies in-phase and quadrature imbalances to a complex signal. This block applies an amplitude imbalance, a phase imbalance, and a DC offset to the in-phase and quadrature signal components. For more information, see I/Q Imbalance Implementation and Algorithms.

Examples

Apply I/Q Imbalance to 16-QAM Signal in Simulink

The cm_iq_imbalance_16qam model applies I/Q imbalance and DC offset impairments to a set of 16-QAM symbols, and then plots the signal constellation.

Display the signal constellation with zero values applied for all impairments. The signal samples and the reference constellation points align and overlay with each other in the constellation diagram.

Display the signal constellation with amplitude imbalance impairment only. The 16-QAM constellation elongates to a rectangular shape.

The amplitude imbalance is: 3.00 dB.

Display the signal constellation with phase imbalance impairment only. The 16-QAM constellation shifts to a rhombus shape.

The phase imbalance is: 30.00 degrees.

Display the signal constellation with in-phase DC offset impairment only. The 16-QAM constellation translates in the direction of the in-phase DC offset.

The in-phase DC offset is: 1.50.

Display the signal constellation with quadrature DC offset impairment only. The 16-QAM constellation translates in the direction of the quadrature DC offset.

The quadrature DC offset is: 1.50.

Impairments can be applied as negative values. Display the signal constellation with all imbalance impairments set to nonzero negative values.

The amplitude imbalance is: -3.00 dB.
The phase imbalance is: -30.00 degrees.
The in-phase DC offset is: -1.50.
The quadrature DC offset is: -1.50.

Compensate I/Q Imbalance

This example shows how to use the I/Q Imbalance Compensator block to remove the effects of an amplitude and phase imbalance on a modulated signal.

Explore Model

The model adds I/Q amplitude and phase imbalance to an 8-PSK signal, and then applies I/Q imbalance compensation to correct the impairments. Impairment addition and compensation performed on the signal by using the I/Q Imbalance and I/Q Imbalance to Compensator Coefficient blocks, respectively. The I/Q Imbalance block sets the amplitude imbalance to 5 dB, the phase imbalance to 7 degrees, and DC offset to 0.

The Constellation Diagram block displays the 8-PSK reference constellation, and the signal constellation before and after impairment correction.

Run Model and Display Measurements

Run the model for 20 seconds, which is not long enough for the impairment compensation to converge. The reference constellation is plotted with red plus signs (+). The impaired signal plots the effects of the amplitude and phase imbalance on the 8-PSK signal. The compensated signal shows that the signal is not well aligned with the reference constellation.

The compensation algorithm is adaptive and requires time to accurately estimate the I/Q imbalance. Increase the simulation time to 100 seconds and rerun the model. You can see that the constellation is now well aligned with the reference constellation.

Further Exploration

You can try changing other simulation parameters, such the step size in the I/Q Imbalance Compensator block, the amplitude and phase imbalance in the I/Q Imbalance block, the modulation type. Then, observe the effects on the Compensated Signal constellation diagram.

Ports

Input

In1 — Complex signal

scalar | vector

Complex signal, specified as a scalar or vector.

Data Types: double | single
Complex Number Support: Yes

Output

Out1 — Output signal

scalar | vector

Output signal, returned as a scalar or vector. This output is the same dimension and data type as the input signal.

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

I/Q amplitude imbalance (dB) — I/Q amplitude imbalance

0 (default) | scalar

I/Q amplitude imbalance in decibels of signal power, specified as a scalar. For more information, see Algorithms.

I/Q phase imbalance (deg) — I/Q phase imbalance

0 (default) | scalar

I/Q amplitude imbalance in degrees, specified as a scalar.

I dc offset — In-phase component DC offset

0 (default) | scalar

In-phase component DC offset, specified as a scalar.

Q dc offset — Quadrature component DC offset

0 (default) | scalar

Quadrature component DC offset, specified as a scalar.

Block Characteristics

Data Types	double | single
Multidimensional Signals	no
Variable-Size Signals	no

More About

I/Q Imbalance Implementation

The I/Q Imbalance block applies amplitude imbalance, phase imbalance, and DC offsets to the in-phase and quadrature components of the complex input signal.

The block performs these operations consecutively, as shown by the subsystem in this model diagram. You can view the subsystem by right-clicking the block and selecting Mask > Look under mask.

To apply the impairments, the block follows this workflow.

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

2. Apply amplitude imbalance, specified by the I/Q amplitude imbalance (dB) parameter.

3. Apply phase imbalance, specified by the I/Q phase imbalance (deg) parameter.

4. Recombine the in-phase and quadrature components into a complex signal.

5. Apply an in-phase DC offset, specified by the I dc offset parameter, and a quadrature DC offset, specified by the Q dc offset parameter, to the signal.

For more information, see Algorithms.

Algorithms

The I/Q amplitude imbalance, I/Q phase imbalance, and DC offset impairments are described sequentially in the section.

1. For an I/Q amplitude imbalance, I_a, the impairment is applied to the input signal, x_r+ jx_i and y _{AmplitudeImbalance} is an intermediate output.

   y _{AmplitudeImbalance} $$\triangleq$$ y _{rAmplitudeImbalance} + jy_{iAmplitudeImbalance}

   y _{AmplitudeImbalance} = $$\left({10}^{(0.5I_{\text{a}}/20)}{x}_{\text{r}}\right)+j\left({10}^{(-0.5I_{\text{a}}/20)}{x}_{\text{i}}\right)$$

2. For an I/Q phase imbalance, I_p, the impairment is applied to y _{AmplitudeImbalance} and y_{PhaseImbalance} is an intermediate output.

   y_{PhaseImbalance} $$\triangleq$$ y_{rPhaseImbalance} + jy_{iPhaseImbalance}

   y_{PhaseImbalance} =$$\left(e^{\left(j\left(-0.5\pi \frac{I_p}{180}\right)\right)}{y}_{{\text{r}}_{\text{AmplitudeImbalance}}}\right)+\left(e^{\left(j\left(\frac{\pi }{2}+0.5\pi \frac{I_{\text{p}}}{180}\right)\right)}{y}_{{\text{r}}_{\text{AmplitudeImbalance}}}\right)$$

3. For DC offsets, I_DC and Q_DC, the impairment is applied to y _{PhaseImbalance} and y is the final output.

   y = (y_{rPhaseImbalance} + I_DC) + j(y_{iPhaseImbalance} + Q_DC)

Variables for these calculations are defined in this list.

• I _a is the I/Q amplitude imbalance.

• I_p is the I/Q phase imbalance.

• I_DC is the in-phase DC offset.

• Q_DC is the quadrature DC offset.

• x is the complex input signal and is given by x_r + jx_i.

  • x_r and x_i are the real and imaginary parts, respectively, of x.

• y is the complex output signal and is given by y_r + jy_i.

  • y_r and y_i are the real and imaginary parts, respectively, of y.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a