I have that issue on my JB 7+, went to the apple store and I have to wait up to a week to get a replacement.
Also I updated my phone to iOS 10.1 Beta, no difference. I have AT&T, i get full bars on 4G or "No Service", LTE doesn't show anymore even though my 6S shows full LTE bars, but the phone is not able to receive or make any calls, text or use data nor GPS with bars or no bars. The only way to make it operational is by using WiFi. Initially I thought it was a software/firmware issue but this is looking like faulty hardware now.