Sum Rate maximization in the noisy MIMO interfering broadcast channel with partial CSIT via the expected weighted MSE

We consider the maximization of Weighted Sum Rate (WSR) for a Noisy Multiple-Input-Multiple-Output (MIMO) K cell Interfering Broadcast Channel (IBC) when only partial channel state information is available at the transmit side (CSIT) while assuming perfect CSI at the receiver (CSIR). In this work, CSIT is modeled by means of a Gaussian prior representing the mean and the covariance of the channel. The expected WSR is then maximized exploiting the relationship between WSR and the Weighted Mean Square Error (WMSE). This leads to an approximate solution but allows to capitalize on a convenient iterative algorithm for the optimization of the transmit beamforming (BF) matrices. The algorithm uses alternating minimization between BF, receiver (RX) filters and WMSE weights by exploiting convexity properties of each sub problem.