Importing Wifi Problems After Restoring from A Defective Phone

Is it possible to import wifi problems to my iPhone 5 when restoring from a backup of an iPhone 4? My iPhone 4 was smashed against concrete and since then my wifi signal has been weak where it shouldn't be. So I bought an iPhone 5 and restore it to a backup of the older iPhone 4. Unfortunately now my iPhone 5 seems to have the same wifi problems. Is this a coincidence or wifi issues really got passed on from the restore??? I'm puzzled.