iPhone 5 Low Wifi Range with iOS 6.0.2

Hello,

Since I got my new iPhone 5 yesterday, the last one had a problem so I changed it, I have big problems with the Wifi-Range. With the last one it was possible to go to the Internet via Wifi, even if I went upstairs. But when I got the new one, it wasn't even possible to walk int the next room, I must stay next to the router. I tried everything, I restored the Networksettings, I rebooted my router and I restored my iPhone (not from Backup). I even have iOS 6.0.2, which should have solved all Wifi-Problems. I hope that there's an Update or a solution, which solves this problem, because it's really annoying and Idon't want to change my iPhone again, but when it is still there with the next Update, I see no other solution.

Greetings

Jonas