Radio turns itself on

My friends 3 series has a problem and it is this .
The radio keeps turning itself on.
as in he got home from work the other day he turned his car off locked up went in his house his son came home went in to the house to tell his dad that the cars radio is on.
so he went out turned it off and after a minute or so it had turned itself back on.
we have had to push start him this morning so that he could go to work and he had to have a push start then he had to get a push start to get home.
Ok now the only thing I could think is to take the fuse for the radio out.
has any one else had there radio automatically turn itself on and if so what do you do to fix it .
Thanks for any help that you give.