It's been the dream of a few SF writers, too...

Looks to me like, maybe, you're working up something that wouldn't have to be manned (or installed by a human crew and then left in place). That's not a bad idea, though of course I'd rather see a manned facility.

I just want to make sure I've visualized correctly: do you mean, a basic spherical "balloon", with one hemisphere reflective to radio? The "horn" would then be on a telescoping (pun allowed) arm deployed into the center? Could work, I think... You mean this to be steerable, right? The structure still needs sufficient rigidity to keep down the inevitable oscillation set up during repositioning, and the immobile base will still need to be fairly massive and/or well anchored.

Big problem: punctures.