Larger antennas help even though both signal and noise are amplified. The difference is that former is more amplified due to coherence: the antenna is shaped in

Larger antennas help even though both signal and noise are amplified. The difference is that former is more amplified due to coherence: the antenna is shaped in a way to add the signal parts in the same phase. On the other hand, the noise is added together in a non-coherent way, with different phases, which makes the result smaller. Think about it as the difference between summing two unit vectors in the same direction - with a resulting vector of magnitude 2 - and doing the same thing with two ortogonal unit vectors - the result will have a magnitude sqrt(2).