iphone no service but 3g works good

Hi everybody,

that's my strange problem:

last week my iPhone 4 suddenly stopped to receive gsm signal, i can't do calls,send messages but 3g works good (iMessage,whatsapp,safari etc).

I tried to restore "ex novo" without restoring with my old backup but it still doesn't work. Sometimes when i turn it on it starts again to work but after one,two or three hours it become again with "no service 3g". The strange fact is that it recognize my operator but it seems that the gsm part doesn't work!

At the first time if i put another sim on it works perfectly (works with sim of my same carrer and also of others carrers). But now if i put in also another sim the situation remain the same. Does anybody have the same problem? How do you resolve it?

Thank's in advance.

P.S. The problem was at first with iOs 6.1.2 and also now with iOs 6.1.3, the iPhone is italian factory unlocked.