Abstract
This paper considers the max-min weighted signal-to-interference-plus-noise ratio (SINR) problem subject to multiple weighted-sum power constraints, where the weights can represent relative power costs of serving different users. First, we study the power control problem. We apply nonlinear Perron-Frobenius theory to derive closed-form expressions for the optimal value and solution and an iterative algorithm which converges geometrically fast to the optimal solution. Then, we use the structure of the closed-form solution to show that the problem can be decoupled into subproblems each involving only one power constraint. Next, we study the multiple-input-single-output (MISO) transmit beamforming and power control problem. We use uplink-downlink duality to show that this problem can be decoupled into subproblems each involving only one power constraint. We apply this decoupling result to derive an iterative subgradient projection algorithm for the problem.