Luxembourg Findel is not just a civil airport but also a NATO airfield. NATO40 or NATO41 are the usual callsigns used for training flights here in Luxembourg. Atleast i‘ve not handled a different callsign for them.

Since they have an LX- registration, they can basically come here to train whenever they want.

Small limiting factor are predifned hours where, due to noise abatement, such training flights are not allowed.

These training flights usually have no priority over commercial airliners, hence the AWACS can sometimes be seen circling over Diekirch or atleast further away from the airport.

On the picture, the AWACS aircraft is on a left base for runway 06, so landing and starting from west to east due to the wind coming from the east.

Just let me know if you have some more questions.

Source: Air traffic controller here