Gradient-based rate balancing for MIMO broadcast channels with linear precoding

The rate balancing problem is considered in the multiple-input single-output (MIMO) broadcast channel with linear transceivers. After introducing relative per-stream rate targets as auxiliary variables, the optimization is performed by a gradient projection algorithm. In addition, the transmit and receive filters are updated and the mean square error matrices are diagonalized in each iteration. Although the algorithm can only find local optima of the considered non-convex optimization problem, numerical simulations show that it achieves good performance while it has a lower complexity than a comparable existing algorithm.