Lol go to sleep, I never wanted you to lose sleep over our F-14s.
(I joke)
Actually the F-16D's radar (APG 68) is pretty good, range of up to 300 km and digitized. So the AIM-120 is well within radar range. It's just that the US Navy's upgraded AWG-9 dubbed the APG 71 was bigger and had a longer range of about 350 km. That was 90s so upgraded Iranian AWG-9 should be around the same, if not more, and with better targeting because it's newer technology.
The reason I discount the F-16s range is because it's a light fighter and can't carry useful numbers (if at all, AIM-54 is HUGE) of long range missiles like the F-14 can (up to 6 AIM-54s with 2 sidewinders). There's not really any point in having a long range radar for a fighter jet unless you have the long range missiles to utilise it.
Lastly, the F-16 and F-14 radars use the same pulse doppler radar waves. They really don't really have much difference in terms of size of target identification. The reason they say F-14 is better for long range is simply because the plane has a long range, the radar is big, as are the AIM-54 missiles. This all adds up to a long range system that was designed to counter Soviet bombers carrying long range anti ship missiles but is no less effective against fighter sized targets, as was proved by the massive number of kills against Iraqi fighter jets in the imposed war (1980-1988).