I know this is an old thread, but I also had this high pitched white noise in my 2012 135i even with the radio off. Since I have no warranty, I put in an aftermarket stereo and the noise is now gone.
http://www.1addicts.com/forums/showthread.php?t=1510420
I thought I would get used to the noise or it would blend in to the road noise or air vent/fan noise, but now that it is gone the car is noticeably quieter and more enjoyable to drive.