A Basic Unified Context for Evaluating the Beam Forming and MIMO Options   in a Wireless Link
  For one isolated wireless link we take a unified look at simple beamforming (BF) as contrasted with MIMO to see how both emerge and under which conditions advantage goes to one or the other. Communication is from a high base array to a user in clutter. The channel propagation model is derived from fundamentals. The base knows the power angular spectrum, but not the channel instantiation. Eigenstates of the field spatial autocorrelation are the preferred apodizations (APODs) which are drivers of the natural modes for exciting lectric fields. Preference for MIMO or BF depends on APOD spectra which are surveyed pointing to various asymptotic effects, including the maximum BF gain. Performance is studied under varying eigenmode power settings at 10% outage. We focus on (1,4) driving the strongest mode for BF and (4,4) driving the 4 strongest for MIMO. Results are obtained under representative parameter settings, e.g. an angular spread of 8 deg, 2 GHz carrier, 0 dB SNR and an array aperture of 1.68m (4 field decorrelation lengths) with antenna elements spaced as close as lambda/2. We find MIMO excelling for array apertures much larger than the decorrelation length; BF does almost as well for smaller apertures. 
Dmitry Chizhik, Gerard J. Foschini and Reinaldo A. Valenzuela
cs.IT math.IT