Transmitter design with interference pre-subtraction for Uncertain broadcast channels

We consider the design of Tomlinson-Harashima (TH) precoders for broadcast channels in the presence of channel uncertainty. For systems in which uplink-downlink reciprocity is used to obtain a channel estimate at the transmitter, we present a robust design based on a statistical model for the channel uncertainty. We provide a convex formulation of the design problem subject to two types of power constraints: A set of constraints on the power transmitted from each antenna and a total power constraint. For the case of the total power constraint, we obtain a closed-form solution for the robust TH precoder that has essentially the same computational cost as the corresponding designs that assume perfect channel knowledge. For systems in which the receivers feed back quantized channel state information to the transmitter, we present a robust design based on a bounded model for the channel uncertainty. We provide a convex formulation for the TH precoder that maximizes the performance under the worst-case channel uncertainty subject to both types of power constraints. An interesting feature of the proposed robust TH precoders is that they do not necessarily use all the allowable power. Simulation studies verify our analytical results and show that the robust TH precoders can significantly reduce the high sensitivity of broadcast transmissions to errors in the channel state information.