  A multiplicity of autonomous terminals simultaneously transmits data streams
to a compact array of antennas. The array uses imperfect channel-state
information derived from transmitted pilots to extract the individual data
streams. The power radiated by the terminals can be made inversely proportional
to the square-root of the number of base station antennas with no reduction in
performance. In contrast if perfect channel-state information were available
the power could be made inversely proportional to the number of antennas. Lower
capacity bounds for maximum-ratio combining (MRC), zero-forcing (ZF) and
minimum mean-square error (MMSE) detection are derived. A MRC receiver normally
performs worse than ZF and MMSE. However as power levels are reduced, the
cross-talk introduced by the inferior maximum-ratio receiver eventually falls
below the noise level and this simple receiver becomes a viable option. The
tradeoff between the energy efficiency (as measured in bits/J) and spectral
efficiency (as measured in bits/channel use/terminal) is quantified. It is
shown that the use of moderately large antenna arrays can improve the spectral
and energy efficiency with orders of magnitude compared to a single-antenna
system.
