Since I have upgraded to IOS 9.3.1 I am getting "no service" intermittently
and when service is available calls are dropping after 30 seconds or so.
I am wondering if it is just co-incidental that the problem started occurring just after the update
or if its another problem with the phone.(iPhone5S)
I don't think its a problem with the provider for other phones in the house (non-iPhones)
are working.
I have tried If you can't connect to a cellular network or cellular data - Apple Support
to no avail.