Tractable approaches to fair QoS broadcast precoding under channel uncertainty

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. Given a total power constraint on the transmission power, our goal is to design a robust fair precoder that maximizes the minimum QoS over all users that can be guaranteed for every channel within a specified uncertainty region around the estimate of each user´s channel. Since this problem is not known to be computationally tractable, we will derive three conservative design approaches that yield quasi-convex and computationally-efficient restrictions of the original design problem. The three approaches yield formulations that offer different trade-offs between the degree of conservatism and the size of the design problem. Our simulations indicate that the proposed approaches can significantly increase the minimum QoS of all users when the available channel knowledge at the transmitter is imperfect.