Are these sentences All OK?
I can't sleep with this noise.
I can't sleep in this noise.
I can't hear the TV with your noise.
I can't hear the TV because of your noise.

Question

Answer

I would say they are all "correct", but the second one sounds a bit off.  It would be more natural to say, "I can't sleep with this noise."  Instead of the second one, the following sound  more natural to me:

I can't sleep in this noisy room.
I can't sleep in this noisy hotel.
etc.