It happens even with the unit disconnected from power. After cousulting with a stereo shop and a Porsche dealership, I dismantled the whole thing. The stock stereo, hooked up as from the factory still does the same thing. Has anyone else noticed this? The stereo guy said this is probably normal for cars that don't shut all systems off as soon as you turn off the key. The guy from the dealership had no idea but said I might have damaged my radio (which I can't imagine given that I just unplugged the antenna). I reinstalled the modulator and am going to try it out for a while.

I should point out that the radio makes a clicking sound and the hissing stops exactly 5 minutes after the key is turned to the off position and removed.