My side of town is relatively quiet when compared to the rest of Abu Dhabi. We're on the side of town without major traffic or a lot of road construction. There are some buildings being put up around me, but I don't really hear the noise from that in my apartment. Occasionally, there will be some sort of event like an outdoor concert on the beach a block or two away. Usually those sorts of things are scheduled on the weekends, but they also spill over until late Saturday night, the night before most people start their workweek.
With all that in mind, the worst of the noise comes from various celebrations, usually due to some soccer victory. On these occasions, it's impossible to sleep with all of the horns honking, engines revving until they backfire and just general shouting. Here is a link to a video to give you a short idea of what it's like. This video is actually from UAE National Day which went on for three days but it's very similar to what happens around my apartment when there's any sort of major sporting victory. Or holiday. Or when a group of young guys just feel like being noisy at 2:00 in the morning.