sub playing by itself

You hearing just low bass or high frequencies as well?

If you are hearing highs and lows, then the RF is getting into the sub electronics after its low pass filters. A sub should not reproduce anything higher than a couple hundred Hz because there are filters on the input to remove them.

Which rules out induction into the interconnects.

If its just low bass you hear, then try running the sub from the high level outputs of your power amp. The impedances of the power amp are much lower, which makes RF induction into those more difficult. You can also try double shielded interconnects, or balanced line interconnects (if your sub takes them, my HSU does) using twisted/shielded pair wiring.

If using better shielded interconnects does not work, then perhaps the RF is being induced within the sub itself, and only a in depth look at the internal construction will yield a solution (read can of worms).

OK,trying that next

1. Change your cable orientation; just a little bit can do it. One of my active speakers was picking up 94.9FM (with a nearby 50 KW transmitter and wavelength 4X the vertical speaker wire length) until I made minor adjustments to where the excess was in the cabinet.

2. Change interconnects to ones with better shielding. They can act like FM antennas and better shielding can reduce this.

I used to have a similar problem, which I was able to fix by changing interconnects. I won't claim to understand radio frequency interference or shielding or much about electricity, even, but I'd look to the interconnects first. If you can't swap in others because of length, etc., perhaps changing where they run might help.
-- Howard

Radio not on ...guy

Turn off the radio ? :>