  We propose Joint Spatial Division and Multiplexing (JSDM), an approach to
multiuser MIMO downlink that exploits the structure of the correlation of the
channel vectors in order to allow for a large number of antennas at the base
station while requiring reduced-dimensional Channel State Information at the
Transmitter (CSIT). This allows for significant savings both in the downlink
training and in the CSIT feedback from the user terminals to the base station,
thus making the use of a large number of base station antennas potentially
suitable also for Frequency Division Duplexing (FDD) systems, for which
uplink/downlink channel reciprocity cannot be exploited. JSDM forms the
multiuser MIMO downlink precoder by concatenating a pre-beamforming matrix,
which depends only on the channel second-order statistics, with a classical
multiuser precoder, based on the instantaneous knowledge of the resulting
reduced dimensional effective channels. We prove a simple condition under which
JSDM incurs no loss of optimality with respect to the full CSIT case. For
linear uniformly spaced arrays, we show that such condition is closely
approached when the number of antennas is large. For this case, we use Szego
asymptotic theory of large Toeplitz matrices to design a DFT-based
pre-beamforming scheme requiring only coarse information about the users angles
of arrival and angular spread. Finally, we extend these ideas to the case of a
two-dimensional base station antenna array, with 3-dimensional beamforming,
including multiple beams in the elevation angle direction. We provide
guidelines for the pre-beamforming optimization and calculate the system
spectral efficiency under proportional fairness and maxmin fairness criteria,
showing extremely attractive performance. Our numerical results are obtained
via an asymptotic random matrix theory tool known as deterministic equivalent
approximation.
