An efficient parameterization for Pareto-optimal beamformers for k-user MIMO interference channels

In this paper, Pareto-optimal beamforming in the K-pair Gaussian multiple-input multiple-output (MIMO) interference channel is considered. Under the assumption of Gaussian signaling at transmitters and single-user decoding at receivers, a necessary condition for any transmit signal covariance matrix to achieve a Pareto boundary point of the achievable rate region is derived. Based on the necessary condition for Pareto-optimality, an efficient parameterization for Pareto-optimal transmit signal covariance matrices is obtained. The obtained parameter space is given by the product manifold of a Stiefel manifold and a subset of a hyperplane, which is a low dimensional embedded submanifold of the original high dimensional beam search space. The new parameterization enables us to devise very efficient beam design algorithms for the K-pair MIMO interference channel.