  The downlink of a multiple-input multiple output (MIMO) broadcast channel
(BC) is considered, where each receiver is equipped with a single antenna and
the transmitter performs nonlinear Dirty-Paper Coding (DPC). We present an
efficient algorithm that finds the optimum transmit filters and power
allocation as well as the optimum precoding order(s) possibly affording
time-sharing between individual DPC orders. Subsequently necessary and
sufficient conditions for the optimality of an arbitrary precoding order are
derived. Based on these we propose a suboptimal algorithm showing excellent
performance and having low complexity.
