Korolev has a good blog about IQ imbalance and compensation at this site
The approach is to send a test tone and measure image rejection ratio at RF mixer or PA output to figure out IQ AM/AM mismatch and AM/PM mismatch. However the blog doesn’t mention how to measure IRR. Here one way to do so is to use TSSI.
TSSI stands for TX Signal Strength Indicator. Its counterpart in RX chain is called RSSI, Received Signal Strength Indicator, which is used to measure received signal power and then adjust receive chain gain accordingly. TSSI many times is to do TX chain auto-calibration. The gains of components in tx chain such as PA , pre-PA amplifier, mixer, etc., are PVT (process, voltage, and temperature) dependant. So you need to calibrate gains per chip to achieve desired or optimal output power.
There are several ways to implement TSSI or envelope detector. The most mentioned way is to use a diode based circuit as below.
Mathworks has a good page about envelope detector which is implemented using two methodologies, squaring and lowpass filtering, and Hilbert transform. http://www.mathworks.com/help/dsp/examples/envelope-detection.html
Among above envelope detectors (ED), squaring and LPF is relatively easy to do some derivation. Below let me show you how this ED (aka TSSI) can be used for IQ imbalance compensation.
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