Mysterious early morning cellular data usage
It could be something like this secret (well, not so secret any more) program as detailed in the Wall Street Journal:


  Updated Nov. 13, 2014 8:22 p.m. ET
  
  WASHINGTON—The Justice Department is scooping up data from thousands
  of mobile phones through devices deployed on airplanes that mimic
  cellphone towers, a high-tech hunt for criminal suspects that is
  snagging a large number of innocent Americans, according to people
  familiar with the operations.
  
  The U.S. Marshals Service program, which became fully functional
  around 2007, operates Cessna aircraft from at least five
  metropolitan-area airports, with a flying range covering most of the
  U.S. population, according to people familiar with the program.


I've noticed the same thing myself, and I hear light planes flying over my greater NYC area home in the early morning several times a week. Because I'm a bit paranoid, I turn off my phone at night.