Linear Matrix Inequality Formulations of Robust QoS Precoding for Broadcast Channels

We consider the design of linear precoders for broadcast channels with Quality of Service (QoS) constraints for each user, in scenarios with uncertain channel state information at the transmitter. Our goal is to design a robust precoder that minimizes the total transmitted power required to satisfy the users' QoS constraints for all channels within a specified uncertainty region around the estimate of each user's channel. Unfortunately, this design problem is computationally intractable, but we will make progress by deriving three conservative design approaches that yield convex and computationally-efficient restrictions of the original design problem. The three approaches yield semidefinite program (SDP) formulations that offer different trade-offs between the degree of conservatism and the size of the SDP. Our simulations indicate that the proposed approaches can significantly reduce the additional power required to satisfy users' QoS requirements when the CSI that is available at the transmitter is imperfect.