OP here's a quick and cheap mod you can do, replace the OE antenna with a short version, which is not at all hard to find. Costs maybe 30 bucks shipped, and "installation" is a sub 60 second type deal. IMO the OE unit is ridiculously long, it makes the car look much better from behind.
E88 N54 Alpinweiss/Coral Red/Motiv HTA 3586r Tial .82AR/Other stuff...652WHP
F30 N55 XDrive EBII