Weighted sum rate maximization with multiple linear conic constraints

In the downlink (DL) of a multi-user multiple-input and multiple-output (MU-MIMO) system, the maximization of the weighted sum rate with dirty paper precoding (DPC) is treated under multiple linear and linear conic constraints. By network duality, the problem is transformed to a minimax uplink (UL) problem. In the UL, the minimization of the utility with respect to the noise covariance and the maximization of the utility with respect to the transmit covariances is solved either jointly or alternately with the gradient-projection algorithm. The proposed algorithms do not only allow to find the maximum weighted sum rate with respect to conic constraints, they are also efficient implementations with respect to multiple linear constraints.