Rate balancing in the vector BC with erroneous CSI at the receivers

For the vector broadcast channel (BC), the case of erroneous channel state information (CSI) at the receiver is considered. Employing a well established lower bound for the mutual information with Gaussian signaling, a rate balancing problem is formulated where the rates of the different users are maximized under a transmit power constraint, but the rates of the different users have fixed ratios. A duality w.r.t. the signal-to-interference-and-noise ratio (SINR) between the vector BC with erroneous receiver CSI and an appropriately constructed vector multiple access channel (MAC) is established. Based on the observation that an interference function can be defined in the dual vector MAC that is standard, an iterative algorithm can be found for an appropriately formulated quality-of-service (QoS) optimization that is used for solving the balancing problem.