iqimbal

Apply I/Q imbalance to input signal

Syntax

y = iqimbal(x,A)

y = iqimbal(x,A,P)

Description

y = iqimbal(x,A) applies I/Q amplitude imbalance A to input signal x.

y = iqimbal(x,A,P) applies I/Q amplitude imbalance A and phase imbalance P to input signal x.

Examples

Apply Amplitude Imbalance to 16-QAM

Generate a 16-QAM signal. Display the scatter plot.

x = qammod(randi([0 15],1000,1),16);
h = scatterplot(x);
hold on

Apply a 10 dB amplitude imbalance. A positive amplitude imbalance causes horizontal stretching of the constellation.

y = iqimbal(x,10);
scatterplot(y,1,0,'ro',h)

Apply a -10 dB amplitude imbalance. A negative amplitude imbalance causes vertical stretching of the constellation.

z = iqimbal(x,-10);
scatterplot(z,1,0,'k*',h)
hold off

Apply Phase and Amplitude Imbalance to 16-QAM Signal

Generate a 16-QAM signal having two channels.

x = qammod(randi([0 15],1000,2),16);

Apply a 3 dB amplitude imbalance and a 10 degree phase imbalance to the first channel. Apply a –5 dB amplitude imbalance and a –15 degree phase imbalance to the second channel.

y = iqimbal(x,[3 -5],[10 -15]);

Plot the constellation diagram of both channels of the impaired signal.

h = scatterplot(y(:,1),1,0,'b*');
hold on
scatterplot(y(:,2),1,0,'ro',h)
hold off

The first channel is stretched horizontally, and the second channel is stretched vertically.

Apply I/Q Imbalance and DC Offset to QPSK

Apply a 1 dB, 5 degree I/Q imbalance to a QPSK signal. Then apply a DC offset. Visualize the offset using a spectrum analyzer.

Generate a QPSK sequence.

x = pskmod(randi([0 3],1e4,1),4,pi/4);

Apply a 1 dB amplitude imbalance and 5 degree phase imbalance to a QPSK signal. Apply a 0.5 + 0.3i DC offset.

y = iqimbal(x,1,5);
z = y + complex(0.5,0.3);

Plot the spectrum of the impaired signal.

sa = dsp.SpectrumAnalyzer('SampleRate',1000,'YLimits',[-50 30]);
sa(z)

Display the corresponding scatter plot.

scatterplot(z)
grid

The effect of the I/Q imbalance and the DC offset is observable.

Correct I/Q Imbalance on Noisy 8-PSK Signal

Generate random data and apply 8-PSK modulation.

data = randi([0 7],2000,1);
txSig = pskmod(data,8,pi/8);

Pass the transmitted signal through an AWGN channel. Apply an I/Q imbalance.

noisySig = awgn(txSig,20);
rxSig = iqimbal(noisySig,2,20);

Create a constellation diagram object that displays only the last 1000 symbols. Plot the constellation diagram of the impaired signal.

cd = comm.ConstellationDiagram('ReferenceConstellation',pskmod(0:7,8,pi/8), ...
    'SymbolsToDisplaySource','Property','SymbolsToDisplay',1000);
cd(rxSig)

Correct for the I/Q imbalance by using a comm.IQImbalanceCompensator object. Plot the constellation diagram of the signal after compensation.

iqComp = comm.IQImbalanceCompensator('StepSize',1e-3);
compSig = iqComp(rxSig);

cd(compSig)

The compensator removes the I/Q imbalance.

Input Arguments

x — Input signal

column vector | matrix

Input signal, specified as a column vector or matrix. The function supports multichannel operations, where the number of columns corresponds to the number of channels.

Example: pskmod(randi([0 3],100,1),4,pi/4)

Data Types: single | double
Complex Number Support: Yes

A — Amplitude imbalance

real scalar | row vector

Amplitude imbalance in dB, specified as a real scalar or row vector.

• If A is a scalar, the function applies the same amplitude imbalance to each channel.

• If A is a vector, then each element specifies the amplitude imbalance that is applied to the corresponding column (channel) of the input signal. The number of elements in A must equal the number of columns in x.

Example: 3

Example: [0 5]

Data Types: single | double

P — Phase imbalance

0 (default) | real scalar | row vector

Phase imbalance in degrees, specified as a real scalar or row vector.

• If P is omitted, a phase imbalance of zero degrees is used.

• If P is a scalar, the function applies the same phase imbalance to each channel.

• If P is a vector, then each element specifies the phase imbalance that is applied to the corresponding column (channel) of the input signal. The number of elements in P must equal the number of columns in x.

Example: 10

Example: [2.5 7]

Data Types: single | double

Output Arguments

y — Output signal

vector | matrix

Output signal, returned as a vector or matrix having the same dimensions as x. The number of columns in y corresponds to the number of channels.

Data Types: single | double
Complex Number Support: Yes

Algorithms

The iqimbal function applies an I/Q amplitude and phase imbalance to an input signal.

Given amplitude imbalance I_a in dB, the gain, g, resulting from the imbalance is defined as

$$g\triangleq g_r+i{g}_i=\left[{10}^{0.5\frac{I_a}{20}}\right]+i\left[{10}^{-0.5\frac{I_a}{20}}\right].$$

Applying the I/Q imbalance to input signal x results in output signal y such that

$$y=\mathrm{Re}(x)\cdot g_r{e}^{-i0.5I_p\left(\pi /180\right)}+i\mathrm{Im}(x)\cdot g_i{e}^{i0.5I_p\left(\pi /180\right)},$$

where g is the imbalance gain and I_p is the phase imbalance in degrees.

Extended Capabilities

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