Even the mighty USN's Aegis system cannot block all the missiles. I remember an expert mentioned it in an academic article, forgot what it was about, he briefly touched on this topic. He said even the latest Patriot system can't block more than 30% of the missiles in real combat. The stat from Gulf war was extremely exaggerated. On top of that, Iraq was one of the least capable in terms of missile capability. For a country like Russia or China, the latest missiles are much harder to intercept, especially if it cruises at extremely low altitude and switch to supersonic speed at terminal attack stage. With all the Standards, Sparrows and gatlin guns combined, they'll be lucky if they can get 50% of the incoming missiles. When there are more than a 100 missiles flying towards you, it's almost impossible to intercept them all.
In wartime, the US is not going to send any carrier anywhere that they might be "swarmed" by 20-30 Type 022 FACs. Count on it.
They will use subs, aircraft, and numerous other assets to sllwly work their way in, sanitizing an area they seek to deny access to by agressor vessels. And they will stand a long way off when they begin that process.
If a force get an attack in on a carrier far out to sea, it is most apt to come from sub launched missiles and aircraft launched missiles as the aircraft of the carrier will be aboe to most probably find and detect any large surface group approaching for those purposes (ie. a missile attack), unless that force has its own adequate carrier defense coverage, in which case you are into a strike at sea, carier group vs carrier group battle, which at this time there is no country with enough carriers or the right carrier wing to really challenge the US Navy. That may change over the next coupld ofdecades.
So, you will have basically a Socviet doctrine of tryoing to overwhelm the US defenses with enough missiles (from aircraft and or subs) and what the AEGIS system has been designed specifically to defend against.
Aircraft will take out some missiles or the aircraft carrying them. Picket vessels will take out some, far from the carrier on the various threat axis.
Then closer in, there will be a defense zone where the main escoryts use cooperatve engagement to use all of their defenses to take out the incoming missile streams from which ever threat axis they are located on. With extended range standard missiles, to medium range standard missiles, to Evolved Sea Sparrow missiles, to RAM missile.
At the same time very powerful EQ will be in play reacking havoc on many of the missiles themselves.
Any that get through all of that will then have to deal with the gaol tender group right with the carrier with their own standard missiles, evolved sea sparrow missiles, RAM missiles and finally CIWS gatlin guns, and more EW.
In wartime it is likely that there will be two AEGIS cruisers and 2-4 AIEGIS DDGs with each carrier. That will be upwards of 600 defensive missile ready to go from those vessels, not counting the 58 missiles and gatling guns each carrier carriers itself, or any missiles (AMRAAM, etc) that the fleet defense fighters engage with.
The Soviets felt they would have to use several multi-regimiental sized attacks on each carrier to get through back in the 80s. It will take more now.
One thought was to incrementally come in closer and closer to the carrier by massively attacking the various rings of defense. This takes longer and requires more aircraft overall. Another tactic was to drive direct in towards the carrier inner ring with as many aircraft and missiles as possible so the outer rings cannot possible get them all, and keep hammering at the inner ring until you break it down and begin scoring hits on the carrier.
Either way, it takes a masive investment in aircraft, subs, and recon technology to make those things happen. I do not believe the PLAN is ready for that yet...let's hope it never comes to that.
