This all sounds very much like there is some reaaally simple solution and nothing fancy going on.
Expecially the "always circular" part threw me off. It looks like the blend effects you get when you make photos against the sun. There might be something similar with radio waves as well.
There are plenty of funny optical artifacts that can happen, and I guess they may have their radio equivalents.
Just today, when shooting our traditional New Year's Eve photo with my wife and kid - us with sparklers in hand - first few images were ruined by ghastly green circles appearing out of nowhere. After quick investigation with a flashlight, I realized that they're artifacts of a bright point light (like a sparkler) hitting the camera - I'm guessing an undesired reflection inside camera's optics. I wonder if something similar may be going on here?
Expecially the "always circular" part threw me off. It looks like the blend effects you get when you make photos against the sun. There might be something similar with radio waves as well.