The purpose of this project is to estimate and correct the IQ imbalance in a QPSK modulation using Simulink and Matlab. Both amplitude and phase imbalance can occur as shown in the figure below.
The Simulink model to view the saved signals was taken from the example QPSK Transmitter and Receiver in Simulink and is illustrated in figure below. The files are previously saved as 801 frames consisting of 12500 samples.
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Simulink model NO_USRP.slx allows to view the saved signals with imbalance
- signal_1: unbalanced signal
- signal_2: unbalanced signal with higher power than signal_1
- signal_IQ10: signal with 10% imbalance in transmission
- signal_IQ20: signal with 20% imbalance in transmission
- signal_IQ30: signal with 30% imbalance in transmission.
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The function delete_first_zeroes.m deletes the first zeroes from a signal
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The function apply_IQ_imbal.m applies an IQ imbalance to a signal
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The function imbalance_algorithm_estimation.m estimates the imbalance from a signal
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The function imbalance_correction.m corrects the imbalance of a signal
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The function imbalance_estimation.m estimates the amplitude and phase imbalance from a signal using comm.IQImbalanceCompensator
For more information type in Matlab:
help delete_first_zeroeshelp apply_IQ_imbalhelp imbalance_algorithm_estimationhelp imbalance_correctionhelp imbalance_estimation
Open Matlab and run main.m.
The input signals are not available due to the large dimensions. The input signals signal_1, signal_2, signal_IQ10, signal_IQ20, signal_IQ30 are 801x12500 matrices (801 frames x 12500 samples).
signal_IQ30 after raised cosine
signal_IQ30 after symbol synchronizer
signal_IQ30 after carrier synchronizer
Comparison of the real part of the signal with imbalance and the original signal
Comparison of the imaginary part of the signal with imbalance and the original signal
Comparison of the real part of the corrected signal and the original signal
Comparison of the imaginary part of the corrected signal and the original signal
The output of imbalance_estimation.m is very similar to the expected values, in fact for the signal modified by apply_IQ_imbal.m, an amplitude imbalance of 2.4623 dB is estimated, while the expected one is 20 log_10 (1.3) = 2.2789 dB.
The results of imbalance_algorithm_estimation.m are listed in the following table.
| Signal | Imbalance [dB] | Estimated imbalance [dB] |
|---|---|---|
| Signal_IQ10 | 0.82785 | 0.81093 |
| Signal_IQ20 | 1.5836 | 1.2474 |
| Signal_IQ30 | 2.2789 | 1.6251 |
This project showed, through the Matlab script, how it is possible to apply and correct the IQ imbalance and how to estimate the imbalance from a signal unknown. This estimate is best for a software unbalanced signal compared to an imbalanced signal acquired by a transmitter. This error is due to the recovery of the receiving carrier and ambiguity phase.
The errors that arise due to a phase and frequency error are shown respectively in the figures below.
Example of QPSK carrier recovery frequency error causing rotation of the received symbol constellation. Wikipedia
Example of QPSK carrier recovery phase error causing a fixed rotational offset of the received symbol constellation. Wikipedia
For more information please see Relazione.pdf in Italian language.