Q: My iphone 5 uses data at 1:xx am every day even though I am connected to wifi and have cellular data service turned off for all apps.  Does anyone know why this happens?

My iphone 5 uses data at 1:xx am every day even though my phone is connected to wifi.  I have cellular data turned on but turned off for each app that uses it.  Does anyone know what is occurring at this time each night to make my phone use data?  I am not receiving push notifications, photos, messages, etc. at this time.  Over the last two weeks the data used at 1:xx am each morning totals ~ 29000 kb.  Doesn't seem like much but I have only 200MB on my data plan so this is significant.  I talked with AT&T support and they were not able to help me.  They suggested I talk with Apple support but my phone is out of warranty so I don't want to pay the $19 fee for one-time support.