I doesn't even need to be that big. A 60 meter dish would do nicely.

Problem is, you would want to have several Gigahertz of (radio) bandwidth. You are not going to down link that raw, but rather as a number of channels, integrated over a number of microseconds and digitized at something between 4 and 64 samples per bit, but we are still talking a down link data rate of gigabits per second.