Uncoded transmission in MAC channels achieves arbitrarily small error probability

We consider an uplink with a large number of uncoded non cooperating transmitters and joint processing at the multi-antenna receiver. We investigate the minimum number of receiver antennas that are needed for perfect recovery of the transmitted signals with asymptotically high probability. We find that in the limit of a large number of users, and in a rich scattering environment, the per user number of receive antennas can be arbitrarily small. Comparison with the ergodic capacity of the resulting channel in the limit of a large number of users suggests that even with uncoded transmissions we can achieve optimal per user number of receiver antennas.