On the MIMO interference channel

We propose an iterative algorithm to design optimal linear transmitters and receivers in a K-user frequency-flat MIMO Interference Channel (MIMO IFC) with full channel state information (CSI). The transmitters and receivers are optimized to maximize the Weighted Sum Rate (WSR) of the MIMO IFC. Maximization of WSR is desirable since it allows the system to cover all the rate tuples on the Pareto-optimal rate region boundary for a given MIMO IFC. The proposed algorithm is rooted in a recent result [S.S. Christensen et al., 2008] showing a correspondence between local optima of the Minimum Weighted Sum Mean Squared Error (MWSMSE) and Maximum Weighted Sum Rate (MWSR) objective functions for the MIMO Broadcast Channel (BC). This connection between the MWSR and MWSMSE is shown to hold true also in the MIMO IFC and is exploited to design an alternating minimization algorithm for MIMO IFC that maximizes the WSR. The MWSMSE-MWSR connection also allows to solve the transmit filter design subproblem in the alternating algorithm by invoking a heuristic solution first proposed in [M. Joham et al,m 2002]. Another contribution of this paper is to propose an extension of [M. Stojnic et al., 2006] to MIMO problems, following the philosophy of [S.S. Christensen et al., 2008] in part. This path is shown to lead in fact to the same iterative algorithm, showing the optimality of the heuristic of [M. Joham et al,m 2002] when applied in the context of the alternating transmitter-receiver optimization approach of [S.S. Christensen et al., 2008].