iqimbal2coef

Convert I/Q imbalance to compensator coefficient

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Syntax

C = iqimbal2coef(A,P)

Description

C = iqimbal2coef(A,P) converts an I/Q amplitude and phase imbalance to its equivalent compensator coefficient.

example

Examples

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Generate Coefficients for I/Q Imbalance Compensation

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Generate coefficients for the I/Q imbalance compensator System object™ using iqimbal2coef. The compensator corrects for an I/Q imbalance using the generated coefficients.

Create a raised cosine transmit filter System object.

txRCosFilt = comm.RaisedCosineTransmitFilter;

Modulate and filter random 64-ary symbols.

M= 64;
data = randi([0 M-1],100000,1);
dataMod = qammod(data,M);
txSig = txRCosFilt(dataMod);

Specify amplitude and phase imbalance.

ampImb = 2; % dB
phImb = 15; % degrees

Apply the specified I/Q imbalance.

gainI = 10.^(0.5*ampImb/20);
gainQ = 10.^(-0.5*ampImb/20);
imbI = real(txSig)*gainI*exp(-0.5i*phImb*pi/180);
imbQ = imag(txSig)*gainQ*exp(1i*(pi/2 + 0.5*phImb*pi/180));
rxSig = imbI + imbQ;

Normalize the power of the received signal.

rxSig = rxSig/std(rxSig);

Remove the I/Q imbalance by creating and applying a comm.IQImbalanceCompensator object. Set the compensator such that the complex coefficients are made available as an output argument.

iqComp = comm.IQImbalanceCompensator('CoefficientOutputPort',true);
[compSig,coef] = iqComp(rxSig);

Compare the final compensator coefficient to the coefficient generated by the iqimbal2coef function. Observe that there is good agreement.

idealcoef = iqimbal2coef(ampImb,phImb);
[coef(end); idealcoef]

ans = 2×1 complex

  -0.1137 + 0.1296i
  -0.1126 + 0.1334i

Input Arguments

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`A` — Amplitude imbalance
real-valued scalar or vector

Amplitude imbalance in dB, specified as a real-valued row or column vector.

Example: 3

Example: [0; 5]

Data Types: double

`P` — Phase imbalance
real-valued scalar or vector

Phase imbalance in degrees, specified as a real-valued row or column vector.

Example: 10

Example: [15; 45]

Data Types: double

Output Arguments

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`C` — Compensator coefficient
complex-valued vector

Coefficient that perfectly compensates for the I/Q imbalance, returned as a complex-valued vector having the same dimensions as A and P.

More About

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I/Q Imbalance Compensation

The function iqimbal2coef is a supporting function for the comm.IQImbalanceCompensator System object™.

Define S and X as 2-by-1 vectors representing the I and Q components of the ideal and I/Q imbalanced signals, respectively.

$X = K \cdot S$

where K is a 2-by-2 matrix whose values are determined by the amplitude imbalance, A, and phase imbalance, P. A is expressed in dB and P is expressed in degrees.

The imbalance can be expressed as:

$\begin{array}{l} I_{g a i n} = 10^{0.5 A / 20} \\ Q_{g a i n} = 10^{- 0.5 A / 20} \\ θ_{i} = - (\frac{P}{2}) (\frac{π}{180}) \\ θ_{q} = \frac{π}{2} + (\frac{P}{2}) (\frac{π}{180}) \end{array}$

Then K has the form:

$K = [\begin{matrix} I_{g a i n} \cos (θ_{i}) & Q_{g a i n} \cos (θ_{q}) \\ I_{g a i n} \sin (θ_{i}) & Q_{g a i n} \sin (θ_{q}) \end{matrix}]$

The vector Y is defined as the I/Q imbalance compensator output.

$Y = R \cdot X$

For the compensator to perfectly remove the I/Q imbalance, R must be the matrix inversion of K, namely:

$R = K^{- 1}$

Using complex notation, the vector Y can be rewritten as:

$\begin{matrix} y = w_{1} x + w_{2} conj (x) \\ = w_{1} (x + (\frac{w_{2}}{w_{1}}) conj (x)) \end{matrix}$

where,

$\begin{array}{l} Re {w_{1}} = (R_{11} + R_{22}) / 2 \\ Im {w_{1}} = (R_{21} - R_{12}) / 2 \\ Re {w_{2}} = (R_{11} - R_{22}) / 2 \\ Im {w_{2}} = (R_{21} + R_{12}) / 2 \end{array}$

The output of the function is w₂/w₁. To exactly obtain the original signal, the compensator output needs to be scaled and rotated by the complex number w₁.

Note

There are cases for which the output of iqimbal2coef is unreliable.

If the phase imbalance is ±90°, the in-phase and quadrature components will become co-linear; consequently, the I/Q imbalance cannot be compensated.
If the amplitude imbalance is 0 dB and the phase imbalance is 180°, w₁ = 0 and w₂ = 1i; therefore, the compensator takes the form of y = 1i*conj(x).

iqimbal2coef

Syntax

Description

Examples

Generate Coefficients for I/Q Imbalance Compensation

Input Arguments

`A` — Amplitude imbalance
real-valued scalar or vector

`P` — Phase imbalance
real-valued scalar or vector

Output Arguments

`C` — Compensator coefficient
complex-valued vector

More About

I/Q Imbalance Compensation

Extended Capabilities

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

Version History

See Also

Functions

Objects

iqimbal2coef

Syntax

Description

Examples

Generate Coefficients for I/Q Imbalance Compensation

Input Arguments

A — Amplitude imbalance real-valued scalar or vector

P — Phase imbalance real-valued scalar or vector

Output Arguments

C — Compensator coefficient complex-valued vector

More About

I/Q Imbalance Compensation

Extended Capabilities

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

Version History

See Also

Functions

Objects

`A` — Amplitude imbalance
real-valued scalar or vector

`P` — Phase imbalance
real-valued scalar or vector

`C` — Compensator coefficient
complex-valued vector

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