# comm.IQImbalanceCompensator

Compensate for IQ imbalance

## Description

The `comm.IQImbalanceCompensator`

System object™ compensates for the imbalance between the in-phase and quadrature (IQ)
components of a modulated signal. The adaptive algorithm inherent to the IQ imbalance
compensator is compatible with *M*-PSK, *M*-QAM, and OFDM
modulation schemes, where *M*>2. For more information, see Algorithms.

**Note**

The output of the compensator might be scaled and rotated, that is, multiplied by a complex number, relative to the reference constellation. In practice, this transformation is not an issue because, before demodulation, receivers correct for it by using channel estimation.

To compensate for IQ imbalance:

Create the

`comm.IQImbalanceCompensator`

object and set its properties.Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

## Creation

### Description

creates
a compensator System object that compensates for the imbalance between the in-phase and quadrature
components of the input signal.`iqcomp`

= comm.IQImbalanceCompensator

creates an IQ imbalance compensator object and sets properties using one or more
name-value arguments. For example,
`iqcomp`

= comm.IQImbalanceCompensator(Name=Value)`comm.IQImbalanceCompensator(CoefficientSource="Input port")`

specifies
that the compensator coefficients must be provided when you call the object. For this
configuration, all other properties are disabled.

## Properties

## Usage

### Syntax

### Description

accepts input compensation coefficients, `y`

= iqcomp(`x`

,`c`

)`c`

, instead of generating
them internally. This syntax applies when the `CoefficientSource`

property
is set to `Input port`

. When using this syntax, adaptive estimation of
the compensator coefficient is disabled.

accepts input step size, `y`

= iqcomp(`x`

,`s`

)`s`

. This syntax applies when the `StepSizeSource`

property is set
to `Input port`

.

accepts the adaptation control signal, `y`

= iqcomp(`x`

,`a`

)`a`

, to enable or disable
coefficient updates. This syntax applies when the `AdaptInputPort`

property is set
to `true`

.

accepts the step size, `y`

= iqcomp(`x`

,`s`

,`a`

)`s`

, and the adaptation control signal,
`a`

, to enable and disable coefficient updates. This syntax applies
when the `StepSizeSource`

property is set
to `Input port`

and the `AdaptInputPort`

property is set
to `true`

.

`[`

also returns estimated compensation coefficients with input arguments from any of the
previous syntaxes. This syntax applies when the `y`

,`coef`

] = iqcomp(`x`

,___)`CoefficientOutputPort`

property is set to `Input port`

.

### Input Arguments

### Output Arguments

## Object Functions

To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named `obj`

, use
this syntax:

release(obj)

## Examples

## Algorithms

Imbalance between the in-phase and quadrature components of signal output from RF receivers can be cost-effectively compensated rather than improving the analog front-end RF hardware. Direct conversion receivers, in particular, introduce IQ imbalance. A circularity-based blind compensation algorithm is used as the basis for the IQ imbalance compensator.

A generalized IQ imbalance model is shown, where *g* is the amplitude
imbalance and *ϕ* is the phase imbalance. For no impairment, *g* = 1 and *ϕ* = 0. In the figure, *H*(*f*) is the nominal
frequency response of the branches due to, for example, low-pass filters.
*H*_{I}(*f*) and
*H*_{Q}(*f*) represent the portions of
the in-phase and quadrature amplitude and phase responses that differ from the nominal
response. With perfect matching, *H*_{I}(*f*) =
*H*_{Q}(*f*) = 1.

Let *z(t)* be the ideal baseband equivalent signal of the received
signal, *r(t)*, where its Fourier transform is denoted as
*Z(f)*. Given the generalized IQ imbalance model, the Fourier transform of
the imbalanced signal, *x(t)* =
*x*_{I}(*t*) +
*x*_{Q}(*t*), is

$$X(f)={G}_{1}(f)Z(f)+{G}_{2}(f){Z}^{*}(-f)$$

where *G*_{1}(*f*) and *G*_{2}(*f*) are the direct and conjugate components of the IQ imbalance. These
components are defined as

$$\begin{array}{l}{G}_{1}(f)=\left[{H}_{I}(f)+{H}_{Q}(f)g\mathrm{exp}(-j\varphi )\right]/2\\ {G}_{2}(f)=\left[{H}_{I}(f)+{H}_{Q}(f)g\mathrm{exp}(j\varphi )\right]/2\end{array}$$

Applying the inverse Fourier transform to *X(f)*, the signal model
becomes *x(t)* =
*g*_{1}(*t*) ×
*z(t)* +
*g*_{2}(*t*) ×
*z ^{*}(t)*.

This transformation suggests the compensator structure as shown in which discrete-time
notation expresses the variables. The compensated signal is expressed as *y(n)* = *x(n)* +
*wx ^{*}(n)*.

An algorithm of the form

$$\{\begin{array}{l}y(n)=x(n)+w(n){x}^{*}(n)\\ w(n+1)=w(n)-M{y}^{2}(n)\end{array}$$

is used to determine the weights because it ensures that the output is
*proper*, that is, the condition, *E*[*y*^{2}(*n*)]
= 0 is satisfied. For further details, see [1]. The initial value
of *w* is determined by the initial compensator coefficient, which has a
default value of `0 + 0i`

. *M* is the adaptation step size
as described in `StepSize`

.

## References

[1] Anttila, L., M. Valkama, and M. Renfors. "Blind compensation of
frequency-selective I/Q imbalances in quadrature radio receivers: Circularity-based approach.",
*Proc. IEEE ^{®} ICASSP* (2007): III-245–48.

[2] Kiayani, A., L. Anttila, Y. Zou, and M. Valkama, "Advanced
Receiver Design for Mitigating Multiple RF Impairments in OFDM Systems: Algorithms and RF
Measurements." *Journal of Electrical and Computer Engineering*
2012.

## Extended Capabilities

## Version History

**Introduced in R2014b**