Reliable Uncoded Communication in the SIMO MAC

A single-input multiple-output multiple access channel, with a large number of uncoded noncooperating single-antenna transmitters and joint processing at a multiantenna receiver is considered. The minimum number of receiver antennas per transmitter that is needed for perfect recovery of the transmitted signals with overwhelming probability is investigated. It is shown that in the limit of a large number of transmitters, and in a rich scattering environment, the per-transmitter number of receiver antennas can be arbitrarily small, not only with the optimal maximum likelihood decoding rule, but also with much lower complexity decoders. Comparison with the ergodic capacity of the channel in the limit of a large number of transmitters suggests that uncoded transmissions achieve the Shannon-theoretic scaling behavior of the minimum per-transmitter number of receiver antennas. Thus, the diversity of a large system not only makes the performance metrics for some coded systems similar to that of uncoded systems, but also allows efficient decoders to realize close to the optimal performance of maximum likelihood decoding.