The location of this transmitter is a shortwave transmission facility within a US military base in Böblingen, 15 km southwest of Stuttgart, Germany. The coordinates:

48°41'26"N 9°05'12"E

https://www.google.com/maps/place/48%C2%B041'26.0%22N+9%C2%B...

Interesting. I have no reason to disbelieve you.

So...

If its being broadcast by the US military or the CIA, why Persian?

Because they're issueing activation orders to their network of ani-regime operatives inside Iran? Who, mysteriously for spies, only know that language?

Or because they want the Iranian government to think that? And a numbers station broadcasting in - unusually - Persian, is an easy way to get the attention of the Iranians?

I'm thinking the latter.