I saw a thing about the Voyager 1 probe, and how they communicate with it using two satelite dishes - one pointed at Voyager, and one pointed in the direction of but very slightly off of Voyager. Since both have the same background noise but only one dish has the transmissions from Voyager in it, you essentially subtract the non-Voyager dish's input from the other one and are left with the clean (or at least a lot cleaner) signal from Voyager.
Perhaps something similar could be done to reduce noise, using an empty patch of ground nearby the target.