iqimbal2coef

Convert I/Q imbalance to compensator coefficient

Syntax

C = iqimbal2coef(A,P)

Description

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

Examples

Generate Coefficients for I/Q Imbalance Compensation

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

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

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

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:

$$\begin{array}{l}{I}_{gain}={10}^{0.5A/20}\\ Q_{gain}={10}^{-0.5A/20}\\ {\theta }_i=-\left(\frac{P}{2}\right)\left(\frac{\pi }{180}\right)\\ {\theta }_q=\frac{\pi }{2}+\left(\frac{P}{2}\right)\left(\frac{\pi }{180}\right)\end{array}$$

Then K has the form:

$$K=\left[\begin{array}{cc}{I}_{gain}\cos ({\theta }_i)& Q_{gain}\cos ({\theta }_q)\\ I_{gain}\sin ({\theta }_i)& Q_{gain}\sin ({\theta }_q)\end{array}\right]$$

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:

$$\begin{array}{c}y=w_{1}x+w_2\mathrm{conj}(x)\\ =w_1\left(x+\left(\raisebox{1ex}{$w_2$}\!\left/ \!\raisebox{-1ex}{$w_1$}\right.\right)\mathrm{conj}(x)\right)\end{array}$$

where,

$$\begin{array}{l}\mathrm{Re}\left\{w_1\right\}=(R_{11}+R_{22})/2\\ \mathrm{Im}\left\{w_1\right\}=(R_{21}-R_{12})/2\\ \mathrm{Re}\left\{w_2\right\}=(R_{11}-R_{22})/2\\ \mathrm{Im}\left\{w_2\right\}=(R_{21}+R_{12})/2\end{array}$$

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).

Extended Capabilities

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

Version History

Introduced in R2014b