Outage balancing in multiuser MISO networks: Network duality and algorithms

This paper studies joint beamforming and power control in a multiuser MISO interference network with statistical channel information. Such information consists of the slow-varying covariance matrices in the beamforming network, and can be employed to reduce instantaneous feedback needs. With the outage event induced by the utilization of statistical channel information, we optimize signal transmission strategies to minimize the maximum outage probability under weighted sum power constraint to achieve outage balancing in the interference network. Under the condition of fixed beamformer, we use nonlinear Perron-Frobenius theory to present a decentralized algorithm with provable geometrically fast convergence rate to compute the optimal power. Since the joint beamformer and power optimization problem is non-convex, we examine its certainty-equivalent margin counterpart. By leveraging nonlinear Perron-Frobenius theory and the established network duality, we present a near-optimal decentralized algorithm to jointly optimize the beamformer and power. The algorithm converges quickly and the convergence rate of the algorithm is proven to be geometrical.