With correct encoding you can detect signals way below the noise floor. Thats how GPS work, you detect a satellite signal orbiting at 400 km with an antenna the size of a chip.
The Curiosity rover communicates with Earth from Mars with an antenna the size of a soda can.
But the receiver has to know the encoding to be able to detect it. Maybe the aliens are using a different type of spectrum spreading technique that makes a lot of sense to them but is unknown to us.
The Curiosity rover communicates with Earth from Mars with an antenna the size of a soda can.