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iqimbal

Apply I/Q imbalance to input signal

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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.

example

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

example

Examples

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Open Live Script

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

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

Figure Scatter Plot contains an axes object. The axes object with title Scatter plot, xlabel In-Phase, ylabel Quadrature contains a line object which displays its values using only markers. This object represents Channel 1.

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)

Figure Scatter Plot contains an axes object. The axes object with title Scatter plot, xlabel In-Phase, ylabel Quadrature contains 2 objects of type line. One or more of the lines displays its values using only markers This object represents Channel 1.

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

Figure Scatter Plot contains an axes object. The axes object with title Scatter plot, xlabel In-Phase, ylabel Quadrature contains 3 objects of type line. One or more of the lines displays its values using only markers This object represents Channel 1.

Open Live Script

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

Figure Scatter Plot contains an axes object. The axes object with title Scatter plot, xlabel In-Phase, ylabel Quadrature contains 2 objects of type line. One or more of the lines displays its values using only markers This object represents Channel 1.

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

Open Live Script

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 nonimpaired and impaired signals.

sa = spectrumAnalyzer( ...
    SampleRate=1000, ...
    ChannelNames=["Nonimpaired","Impaired"], ...
    YLimits=[-50 30]);
sa(x,z)

Display the corresponding scatter plot to see the effect of the I/Q imbalance and the DC offset.

cd = comm.ConstellationDiagram( ...
    NumInputPorts=2, ...
    ChannelNames=["Nonimpaired","Impaired"]);
cd(x,z)

Open Script

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

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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

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

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

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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 Ia in dB, the gain, g, resulting from the imbalance is defined as

g≜gr+igi=[100.5Ia20]+i[10−0.5Ia20].

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

y=Re(x)⋅gre−i0.5Ip(π/180)+iIm(x)⋅giei0.5Ip(π/180) ,

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

Extended Capabilities

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

Version History

Introduced in R2016b

See Also

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