Yes it would be possible. Just use a CW microwave source and an antenna with a detector. A drop in the detector voltage would occur from something blocking the signal.
If you just want to see if something is in front of the transmitter, you might try to find a surplus automatic door opener (like the ones on grocery store automatic sliding doors).
Is there any reason you want to use RF? If you just need a simple setup that will tell when something passes, why not use an IR LED and a simple receiver? This would be easier than going to a 10GHz microwave frequency setup. This would work for people and animals just as well as metal.
The best to detect moving humans and animals are the passive PIR detectors. They are low-cost and very reliable. Some are sold even cheaper as triggers for spot-lights. I have used such devices for years without problems.
Being passive, they cannot be detected like RF or IR or microwave active sensors.
Yes, I remember making an improvised mouse trap using a short IR LED + photodiode link.
Once the beam was broken it released the current to a homemade electromagnet and a metal biscuit tin was then released on top of the mouse trapping it inside.
I ate all the biscuits first :smile: and just left the crumbs in a trail leading through the light beam for the mouse...
It worked the first night I tried it after all other types of trap had failed.
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Modern human motion detectors use conventional EM radar and can detect a human breathing on the other side of a concrete wall. They detect subtle Doppler shifts and can build up a 3D image of what is on the other side of the wall as long as it is moving 'a bit'