Dave wrote:
Aerials for weak areas have greater gain, this means that you get more
signal, but you also get more noise.

Not true.

Antenna gain is noiseless. You only get noise when you introduce
amplification using electronics.

I will be happy to be proved wrong though :-)

Dave

It depends on what you class as "noise". High gain antennae tend to
pick up signals from other sources than the intended transmitter - many
class these signals as noise (they are included in calculations for
SNR)