Are you using a case with metallic back that stretches from top of phone to bottom?
Those could block degrade signal. Those cases that have a metallic part on the back but leave the top and bottom part non-metallic are ok. Those which are metallic on the entire back can cause decrease in reception.
If you are seeing this kind of signal degradation (ie 4G, LTE, wifi) everywhere you go, I would suggest you go into Apple and get a replacement phone, since you are only 1 week into this phone.
If you have good reception else where but not your primary place of residence, the you should call at&t support and report it.
The iphone has a field test mode, dial *3001#12345#* and you will see your antenna's reception in a numeric value, which would be more precise when reporting trouble tickets.osxdaily.com/2012/08/20/fie...