Nonlinear Downlink Beamforming Under QOS Constraints: Optimum Precoding Order and the Need for Time-Sharing

We consider the downlink of a multi-antenna system where the transmitter performs nonlinear dirty-paper coding (DPC) and each receiver is equipped with a single antenna. Assuming that the base station must support a certain quality of service (QoS) for each user, we analyze the minimum power transmit strategy consisting of filters, power allocation and precoding order. We derive necessary and sufficient conditions for the optimality of pure strategies, i.e. strategies achieving the QoS without time-sharing. Based on these conditions, we present a very simple algorithm yielding a suboptimal pure strategy showing excellent performance. This is of considerable interest especially for real systems, where time-sharing is hard to implement.