The DF-21D is using a active radar guidance system that existed on the US Pershing II back in 1983.
The DF-21D does not have a convetional payload that guarantys a 100% kill on a US carrier. That is why it also has the option to carry a nuclear weapons payload. This is the only way to get a 100% kill on a US carrier.
F -15's or any aircraft from a US carrier battle group would not even figure in a defense against a MRBM *(Medium Range Ballistic Missle) which is what a DF-21D is.
The Ageis Cruiser
coupled with other vessels in the CVBG would use SM-3 and medium range missle defense systems.
"...Standard Missile SM-3 now deployed on Ticonderoga class cruisers and Improved Arleigh Burke class destroyers was designed specifically to engage theater ballistic missiles in their midcourse (free-fall) phase; they have proven very effective in tests. Each cruiser and destroyer will, presumably, carry a dozen or more of these missiles for the defense of the carrier-"...Electronic and infrared jamming; decoy deployment; maneuvering; and, of course, shooting back.
China May Turn Missiles into Carrier-KillersBy Noah Shachtman March 31, 2009
The technical challenges still seem daunting, including the fact that ballistic missles aren’t designed for tactical precision strikes of relatively small (in oceanic terms) targets speeding at 30
knots. But the really troubling issue is this: ballistic missiles are strategic weapons (the DF-21 has roughly the same range as a Pershing 2). They’re designed to carry nuclear weapons. Everyone knows they’re designed to carry nukes, and to hurl them long distances. So if the U.S. detects missiles hurtling over the
Pacific, and NORAD has 15 minutes to decide whether it’s a tactical strike on the Nimitz, or if some city is going to be vaporized… Of course, in the rational world of deterrence theory and defense planning, U.S.
decision-makers would know these were tactical weapons and wouldn’t overreact.
Or maybe not.
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China May Turn Missiles into Carrier-Killers (Corrected) | Danger Room | Wired.com