BUT what you can get with some IR systems is that the aircraft radar has a link-through system which helps the IR seeker acquire the target before launch. In those cases, a radar warning receiver will detect the change in the radar operating mode from tracking to targetting and may sound an alarm to notify the pilot they are being actively targetted BUT it will not detect the missile launch.
That's basically how SARH missiles are detected too.
Actually, in Vietnam war, the S-75 / SA-2 crews used this technique (switching from scan to track)
without firing a missile to test whether an enemy plane was equipped with Shrike ARMs. If yes, an enemy pilot would asume it's being fired upon by an SA-2 and would fire a Shrike towards tracking radar in order either to destroy enemy radars or to force their operators to shut them down and thus loose the missile.
So if Shrike was fired back from an enemy plane, they'd simply switch the radars off (and keep all the missiles). If there was no Shrike, they knew they can fire an SA-2 with lower risk of being targetted by a Shrike in return.
Some modern AA missiles (short range at least) do not use smoke-less motors by accident - eyeball Mk.1 is still the primary detection instrument for these.