Robust Linear Precoding for Uncertain MISO Broadcast Channels

We consider linear precoding for the downlink of a multiuser communication system in the presence of uncertain channel state information (CSI) at the base station. We consider systems in which the base station has multiple antennas and each user has a single antenna; i.e. multiple-input single-output (MISO) systems. For systems with uplink-downlink reciprocity we propose a statistical model for the channel uncertainty and provide a convex optimization formulation for the precoder that maximizes an average mean square performance measure. For systems in which the channel measurements are quantized and fed back to the base station we propose a deterministically bounded model for the channel uncertainty and a convex formulation for the precoder that maximizes the worst-case performance. Both formulations allow the incorporation of power constraints on individual antennas in addition to the overall power constraint. Our simulations indicate that the proposed approach can significantly reduce the sensitivity of the linearly precoded downlink to uncertainty in the CSI.