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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, the authors study the power control problem. They 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, they use the structure of the closed-form solution to show that the problem can be decoupled into sub-problems each involving only one power constraint. Next, they study the Multiple-Input-Single-Output (MISO) transmit beamforming and power control problem.
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