At the height that it flies, the E-3 is nearly always in controlled airspace and has to receive a mandatory radar service from a recognised Air Traffic Control. However, the mission crew routinely dedicates one console to "AWACS Monitor" where the operator ensures that other aircraft in the vicinity do not infringe the radar "safety zone" (or gets close enough to impinge upon JTIDS radiation rules) - this is necessary to fulfil the aircraft's safety case so we do not "fry" any civvies going on their holibobs. Also, the radar has an "underfoot" as well as an overhead, and ground radar fills in the hole for ATC purposes.
Any more detail and I would have to shoot you.