Max-min weighted SINR in coordinated multicell MIMO downlink

This paper studies the optimization of a multicell multiple-input-single-output (MISO) downlink system in which each base station serves multiple users, and each user is served by only one base station. First, we consider the problem of maximizing the minimum weighted signal-to-interference-plus-noise ratio (SINR) of all users subject to a single weighted-sum power constraint, where the weights can represent relative power costs of serving different users in each cell. We apply concave Perron-Frobenius theory to propose a joint power control and linear beamforming algorithm which converges geometrically fast to the optimal solution. As a by-product, we resolve an open problem of convergence of a previously proposed algorithm by Wiesel, Eldar, and Shamai in 2006. Next, we study the max-min weighted SINR problem subject to multiple weighted-sum power constraints and we show that it can be decoupled into its associated single-constrained subproblems.