Maybe multiple receiving antennas could be used, spaced widely apart (e.g. one on Earth, one on the moon, one in orbit somewhere); each would receive some signal affected by noise, but the noise would be different for each (such as the atmosphere affecting only the on-ground antenna). Also given that we know the precise location of the transmitter, we can work-out the exact phase difference between the antennas. Some digital post-processing would combine the raw signal+noise from the multiple receivers and extract the signal.

In fact, I assume that at this distance, even a very narrow signal would spread wide enough to illuminate more than just the Earth diameter.