I get an IF signal from microwave circuit which looks like this:
As we can see there is a distinct unwanted Amplitude Modulation which is believed to be due to coupling between antennae. This signal will also have a FM modulation.
I want to remove this AM modulation so that only FM modulation remains. I want the carrier signal NOT the AM modulation. Something like how a Automated Gain Control (AGC) would work.
Well, then you need to adjust your filter. Every kind of AGC is but a high pass filter in effect.
Seriously, don't do that. FM demodulation doesn't need constant envelope. As a FM demodulator doesn't care the least about amplitude, it will not care about what you consider to be AM.
EDIT I though you'd probably already tried, but what about the AGC, AGC2 and AGC3 block in GNU Radio?