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Dont know how to avoid detection, but this is how I solved it.

Lunch two fighters as soon as the mission starts on military power N. Followed by one more as back up.
The fighters will be able to intercept the missiles. Remember to fire 3 missiles per incoming to ensure a kill.

Good luck
 
The problem is that the enemy sub is 5 to 7 nm away and its missile breaks the surface and smacks into your boat. I think we need to add minimum launch range to some weapons.