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 sig

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...