Robust sum rate maximization in the multi-cell MU-MIMO downlink

This paper studies linear precoding designed for the multi-cell multi-user multiple-input-multiple-output (MU-MIMO) downlink. The objective is to maximize the weighted sum rate (WSR) under imperfect channel state information (CSI) conditions and per base station (BS) transmit power constraints. The expectation of the WSR over the CSI error can be lower bounded by minimizing the expected weighted sum mean square error (MSE) assuming minimum MSE (MMSE) receive filters. The problem can be solved by an iterative algorithm which alternately calculates the MMSE receive filters given a fixed precoding matrix and vice versa. The algorithm converges to a local optimum. For the optimization of the precoding matrix under per BS power constraints, we present two robust solutions. The first one is based on the transmit Wiener filter solution under a sum power constraint combined with a consistent scaling to satisfy each per BS power constraint. In the second solution the problem is transformed into a second order cone program (SOCP) where per BS power constraints can be directly included. Simulation results show performance gains compared to robust and non-robust state of the art schemes.