Thank you everybody for the eloborate answers about the history of the radar, why it was build that way in that particular time period, the theory of its working, etc. I learned a lot in this thread.
But really my question was more practical. How do you use it when you play DCS? Not how it was used in RL.
I guess I came to the same conclusion as the poster above. The aiming assist of the Radar for guns is awesome. (DG mode) I find it to be very accurate and I use it all the time. But for missile firing and target searching I find it useless. Correct me if you think I'm wrong.
So here is how I use the radar when playing.
1. Leave it in Standby mode, i guess this reduces your own radar signature as wel.
2. When engaging in a dogfight, leave it of when firing missiles. It not helping your missiles hit target anyway.
3. Turn it on before switching to guns to help with aiming.
4. Turn it off again when you are victorious.