  A single input multiple output (SIMO) multiple access channel, with a large
number of transmitters sending symbols from a constellation to the receiver of
a multi-antenna base station, is considered. The fundamental limits of joint
decoding of the signals from all the users using a low complexity convex
relaxation of the maximum likelihood decoder (ML, constellation search) is
investigated. It has been shown that in a rich scattering environment, and in
the asymptotic limit of a large number of transmitters, reliable communication
is possible even without employing coding at the transmitters. This holds even
when the number of receiver antennas per transmitter is arbitrarily small, with
scaling behaviour arbitrarily close to what is achievable with coding. Thus,
the diversity of a large system not only makes the scaling law for coded
systems similar to that of uncoded systems, but, as we show, also allows
efficient decoders to realize close to the optimal performance of
maximum-likelihood decoding. However, while there is no performance loss
relative to the scaling laws of the optimal decoder, our proposed
low-complexity decoder exhibits a loss of the exponential or near-exponential
rates of decay of error probability relative to the optimal ML decoder.
