4am is too early he would have to have a permit to work 24 hours (me thinks)..

we are also living next to a construction site, whereby most the noise commences at 5-5:30am and eases from 9am and stays quiet until the rest of the day (wish it was the other way around).

when i probed and asked about the early start, i was advised that the contractor has a 24 construction hour permit - and if that's the case with your noise pollution unfortunately as ghazalz said, you'll need to try to live with it.