[toomuchtodo]

https://www.google.com/search?q=virtual+antenna+array

Or, for those who want the production grade stuff:

http://www.vla.nrao.edu/

"The Very Large Array, one of the world's premier astronomical radio observatories, consists of 27 radio antennas in a Y-shaped configuration on the Plains of San Agustin fifty miles west of Socorro, New Mexico. Each antenna is 25 meters (82 feet) in diameter. The data from the antennas is combined electronically to give the resolution of an antenna 36km (22 miles) across, with the sensitivity of a dish 130 meters (422 feet) in diameter. For more information, see our overview of the VLA, and the configuration schedule."

So, yes, with multiple IP-connected software-defined radios, you could provide the required signal strength without a Deep Space Network antenna.

[ErsatzVerkehr]

At best, your signal will improve linearly with the number of antennas (N), while the noise will be completely incoherent and scale like sqrt(N). Thus your signal-to-noise ratio will improve like N/sqrt(N)=sqrt(N). You're going to need an awful lot of radios...