  We study the MIMO broadcast channel and compare the achievable throughput for
the optimal strategy of dirty paper coding to that achieved with sub-optimal
and lower complexity linear precoding (e.g., zero-forcing and block
diagonalization) transmission. Both strategies utilize all available spatial
dimensions and therefore have the same multiplexing gain, but an absolute
difference in terms of throughput does exist. The sum rate difference between
the two strategies is analytically computed at asymptotically high SNR, and it
is seen that this asymptotic statistic provides an accurate characterization at
even moderate SNR levels. Furthermore, the difference is not affected by
asymmetric channel behavior when each user a has different average SNR.
Weighted sum rate maximization is also considered, and a similar quantification
of the throughput difference between the two strategies is performed. In the
process, it is shown that allocating user powers in direct proportion to user
weights asymptotically maximizes weighted sum rate. For multiple antenna users,
uniform power allocation across the receive antennas is applied after
distributing power proportional to the user weight.
