The easiest way, by far, to nail a CVBG isn't through SIGINT or ELINT methods... it's to hit it while it's in port or steaming along known shipping lines; i.e., good old-fashioned HUMINT.
What you don't realize is that first, a CVBG can run completely 'silent' (e.g. no radar or comms EM emissions) for its entire 6-month deployment cruise, simply listening to other sensors in the US global defense grid. USN CV doctrine and training ops have evolved to the point where a CVBG can steam up to an opposing coastline and run deep penetration strikes without making a single radio transmission for the last 1000 nm of the journey... between all those dozens of helos and planes and 6-10 combat and support vessels.
In that case, UAVs have to use visual methods to find the CVBG. This limits their scan range to about 6nm in either direction, assuming they're flying at sea level in normal sea states. Of course, if they were flying at a super high altitude, they would have a much larger search radius, but they would also be much easier to find by the ELINT suite on E-2D AWACS and/or the carrier's own CAP.
Now, even if the UAVs are sent out--e.g., China/Russia knows there's a CVBG in the area--then there are also a variety of ways to spoof 'em.
For example: the CVBG finds a large civilian radar signature, like an oil tanker or cargo ship or passenger liner, and when the air wing takes off, it first vectors out to that radar signature at wavetop height (below the minimum detection altitude of OTH radars) before climbing to standard cruising altitude, and when they're done bombing or performing air superiority missions, they fly back to that big ship and then vector at low altitude to the CVN. Sure, this cuts down on the range of the aircraft, but what it does is it makes that civilian ship look like an aircraft carrier to the opponent--it'll look like a big radar signature launching and landing aircraft. It's basically baiting the opponent into killing a bunch of civilians, or at the very least wasting a sub or UAV to go and check it out--a sub or UAV that can then be easily killed itself as it wades into a preplanned trap.
Another example: the CVBG baits the opponent into searching the wrong area of ocean based on the path of its incoming and outgoing flight vectors. Basically, you do aerial buddy-refueling of a few fighters, run them in and out along a triangular path that, by the listed range on their fuel tanks, implies the carrier is hundreds of nm away from its actual location.
Yet another example: say the CVBG has been found by a UAV, and the UAV gets detected and shot down. Now the Chinese/Russian side has a snapshot of the CVBG location--not a real-time track, so they'll need to sortie out a regiment of land-based strike aircraft (likely J-20s, Su-34s, or Tu-22M3s) to the last known location of the CVBG. This usually takes about two hours, assuming the CVBG is operating three or four hundred nm away from the coast and five or six hundred nm away from the nearest airbase. So then in those two hours, the CVBG can run a pair of DDGs 60nm down the threat axis (e.g. towards the airbase) as a picket, leave a CG and a DDG at its original location, set up a combat air patrol flanking the expected flight vector of the J-20 regiment, and sail another 60nm with a lone DDG escort in an off-axis direction. (e.g. diagonally away from the airbase) Then, when the J-20 regiment arrives and pops up 150nm away for a radar peek to launch their YJ-12 anti-ship missiles, the picketing DDGs can spam the area with SAMs from the front at the same time the air patrol swarms the J-20s from behind--as close to a turkey shoot as modern air combat allows--and the anti-ship missiles, set to go and sink a big ship in the target area, lock on to a CG boasting 128 VLS tubes loaded with anti-missile-missiles. In effect, the entire J-20 regiment is wasted and the CVN is never even threatened. And the best thing about it is that the USN trains to run this entire maneuver in radio silence--which means the opponent has no idea it's coming. And, yes, if US ELINT/SIGINT (satellites) or HUMINT (spies/cyber) detect that those planes aren't taking off for whatever reason, the CVBG can cancel its maneuver or reorient itself if the planes are vectoring out from an unexpected airbase.
Of course, these tactics themselves can all be counteracted by good training and coordination between the PLAAF, PLAN, and 2nd Artillery, and better ELINT/SIGINT capabilities. It's not a one-sided affair at all, and yes, the DF-21D and J-20 have made things harder for the USN in very uncomfortable ways--but those weapons are by no means the game-changers and magic bullets proponents would like to believe.
China needs to learn to use these weapons by upping the annual training regimen's quantity (flight hours, sim hours, deployment hours, total # of exercises), quality (real-time combat conditions with large doses of mindfuckery on both sides, and preferably involving large numbers of aircraft and ground assets to stress-test C4ISR systems), and internationalization (e.g. run these exercises with partners like Russia on a more than once-per-year basis). Combine that with 5th-gen fighters, ASBMs, transport/tanker/AWACS, and advanced sub/surface/naval air assets, and the PLA will be on track to challenge or even usurp military dominance in the Western Pacific. Until then, no dice.
