Low/bad signal on iPhone 4 after upgrading to IOS 6

I recently upgraded my iPhone 4 to IOS 6 (from 5.1.1 it had before), and since then I'm having lots of signal troubles: the signal is always low and unreliable, and the iPhone continuously switches between 3G and GPRS (also draining the battery in the process). Internet access is almost unusable, and sometimes I can't even make or receive calls. I'm in Italy, my carrier is TIM; however, this is not a carrier problem, and is unrelated to the actual place I'm in: I'm having these signal troubles in the very same places where I had full signal strength before the IOS upgrade. I've been searching around for a while, and looks like this is quite a common problem; various solutions have been proposed (including downgrading to IOS 5 on the assumption that this is caused by some bug in IOS 6), but no agreement has been reached about how to actually solve it. How to fix this?