The good news is that all it takes for you to take down a stealth fighter jet is a regular fighter jet, ideally one with good kinematic performance (something like the Typhoon, F-15, early models on the T-10S platform), and lots of hardpoints under the wings for lots of missiles.
As for the sensors needed to detect an “invisible” aircraft: you’ll have to focus on good old-fashioned full spectrum infra-red. You see (heh), the F-22 might be jaw-droppingly good at being an air superiority fighter, but this does not exempt it from abiding by the laws of physics. It still generates heat by throwing plasma-stage kerosene to go forward and by friction with the air around it while doing so.
An integrated infrared search and track “radar” (like you find on the 4th gen Russian fighters or the Typhoon) would help, for both detection radius and situational awareness. If you’re too cheap to equip your fighter aircraft with an IRST (Infrared Search and Track), you could try integrating the seeker heads of your missiles with the aircraft’s avionics so they can feed an image to your cockpit displays -- like they do in the Rafale.
Your 4th or 4.5 gen fighter will need to be guided to the general direction where its target can be detected by its admittedly short ranged IR sensors. You could do that by using a long band ground control radar, since stealth fighters are only optimized to be “invisible” against short-wave tracking radars -- the type that can pinpoint a target and apply nano-second corrections to a missile heading towards it.
This is why all medium-range radar guided missile, either passive or semi-active (Fox 1 and Fox 3 respectively, in modern gamer parlance) are basically useless for our task. So feel confident to throw away all Sparrows, R-27s, R530s or whatever else you might have tucked away in a closet somewhere. (Semi-actives might be good for other applications. Do well to keep those.)
The answer to this is twofold: first, the R-27EM isn’t all that agile and would struggle to catch on to a fighter-sized target (it was developed to down AWACSs, after all). Second, if Westinghouse is to be believed the APG-77 can barely be perceived by radar warning receivers, let alone have a missile lock on to its radiation wave. I hope that settles it.
When it comes to what missiles we recommend… we can’t escape without looking like greasy salesmen, who came to your door on behalf of either Vympel or MBDA. But in good conscience; for your IR guided air-to-air, medium-range needs; we can recommend none other than the R-77T, and the good, the old, the well-proven and slender and fast: MICA! These are just the best; there’s no American competitor in sight, and recommending anything made by industries with a reputation for whisking away intellectual rights rather than designing their own tech would be a disservice to our readers.
This is the end of part one, follow us in part two, where we will discuss more about launch platforms and sensors. (And also underline the importance of having an IRST on board, if some of you are worried quality of the initial input of your missiles.)
*meaning they lock on to the radiation that comes off a radar scanning you. Like the AGM-88 Harm.