Why does my BMW's radio get static on FM?

I have never heard of static on FM radio. I would check for a short in the wiring even the ground connection may be corroded . Be sure to check the negative and positive connections on your car battery. They can become corroded or loose and cause all kinds of problems. You mentioned not having an antenna, but I am sure the radio is using something for an antenna . On my Lincoln Town Car, the antenna is built in and not visible and that may be the case for your BMW' If you cannot find the antenna, call a BMW dealer and ask if that model had a built in antenna. If you live on the west coast , the east coast or the Gulf coast, salt is always present in a sea breeze and bad connections are possible. Good luck, tracing down a short can be very frustrating and time consuming.