Radar doesn't matter.
Sorry, that's facetious. Radar isn't enough. You can't just put up a Radar set and call it good. You've got to... Well, pull a Dowding. You've got to develop a system that's able to receive radar data; then discriminate, interpret, and analyse it; then communicate that information to airfields and aircraft such that your pilots are able to make timely interceptions.
The mere presence of Radar does not an Integrated Air Defence System make. I've seen it asserted that the German lack of an IADS is what caused the Luftwaffe to not prioritise the British Radar Network as much as they should have during the BoB. They had Radar, but they had failed to develop an IADS, so Radar didn't actually do very much for them. Their failure to conceptualise of an IADS meant that they couldn't conceive of the British having one; and so did not understand how much impact Radar had on British effectiveness.
As GarethC put it, Carrier Raids are easy, from a C3I perspective. You've got one Radar location and one 'Airfield'. This immediately takes away much of the complexity in the processing and analysing your Radar data.
Even more conviently (this does make things a lot easier) the two are co-located, and they're the big shiny lure the bogies are gunning for. Which means that if you've got an incoming contact at 5,000 feet along bearing 207, then all you (nominally) need to do to ensure an intercept is to send fighters to 5,000 feet and along bearing 207. And your communication process should be reasonably fast, given that the Radar operators and the Pilots may literally be within shouting distance of each other.
The moment your Airfield and Radar aren't co-located, every potential interception becomes a trigonometry problem.