There are many different ways to communicate with a missile, but most ATGMs are either wire guided or use a laser “beam rider”.

The Kornet uses the beam rider method in which an operator “paints” the enemy vehicle with a laser designator which tells the missile via radio waves what target to lock onto and what course to maintain. As the missile nears is target the operator can move the laser point to further aim the missile. This can either be done by an operator manually or by an automatic firing system, which “talks” with a radar system in the missile that compares data from the receiver and missile to tell the missile how close it is to its target, when it needs to begin its terminal approach, and any other information that the missile needs to factor in.

So basically yes, there is a radar device in the launcher, and radar device in the missile that communicate. The missile is telling the receiver what it sees, and the receiver guides the missile in.

This is also what radar jamming focuses on stopping. The countermeasure detects the missile and receiver, and attempts to flood the radio waves the receivers on the missile and launch platform are using to communicate, to “confuse” the missile.