Minimax Linear Precoding for MISO Broadcast Channels with Bounded Uncertainty

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 and the channel estimate at the receivers is quantized and fed back to the base station. For these systems we propose a deterministically bounded model for the channel uncertainty and a convex optimization formulation for the precoder that maximizes the worst-case performance under constraints on the power transmitted from each antenna. We also derive a closed-form expression for the precoder that maximizes the worst-case performance under a constraint on total transmitted power. The cost of computing this closed-form solution is the same as that of computing the solution to the corresponding method that assumes perfect channel knowledge. An interesting property of the proposed robust precoders is that they do not necessarily use all the allowable transmission power. Our simulations indicate that the proposed approach can significantly reduce the sensitivity of the linearly precoded downlink to uncertainty in the CSI.