  This paper studies the sum rate performance of two low complexity
eigenmode-based transmission techniques for the MIMO broadcast channel,
employing greedy semi-orthogonal user selection (SUS). The first approach,
termed ZFDPC-SUS, is based on zero-forcing dirty paper coding; the second
approach, termed ZFBF-SUS, is based on zero-forcing beamforming. We first
employ new analytical methods to prove that as the number of users K grows
large, the ZFDPC-SUS approach can achieve the optimal sum rate scaling of the
MIMO broadcast channel. We also prove that the average sum rates of both
techniques converge to the average sum capacity of the MIMO broadcast channel
for large K. In addition to the asymptotic analysis, we investigate the sum
rates achieved by ZFDPC-SUS and ZFBF-SUS for finite K, and show that ZFDPC-SUS
has significant performance advantages. Our results also provide key insights
into the benefit of multiple receive antennas, and the effect of the SUS
algorithm. In particular, we show that whilst multiple receive antennas only
improves the asymptotic sum rate scaling via the second-order behavior of the
multi-user diversity gain; for finite K, the benefit can be very significant.
We also show the interesting result that the semi-orthogonality constraint
imposed by SUS, whilst facilitating a very low complexity user selection
procedure, asymptotically does not reduce the multi-user diversity gain in
either first (log K) or second-order (loglog K) terms.
