Not only has the area we call Iraq been trampled over by many empires, it has also been the trampler over empires. The various iterations of Assyria and Babylonia were quite aggressive, vis-a-vis Egypt, the Levant, what is now Eastern Turkey and what is now Armenia. Whether these empires consisted of the same genetic stock of modern Iraq is a question for the scientists, but unlike Egyptian mummies, I'm not sure there are a lot of 4000 year old Mesopotamian human remains available for checking.