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On the Convergence of Max-Min Fairness Power Allocation in Massive MIMO Systems

Power allocation techniques, among which the max-min fairness power allocation (MMFPA) is one of the most widely used, are essential to guarantee good data throughput for all users in a cell. Recently, an efficient MMFPA algorithm for massive multiple-input multiple-output (MIMO) systems has been proposed. However, this algorithm is susceptible to the initial search interval employed by the underlying bisection search. Even if the optimal point belongs to the initial search interval, this algorithm may fail to converge to such a point. In this letter, we use the Perron-Frobenius theory to explain this issue and provide search intervals that guarantee convergence to the optimal point. Furthermore, we propose the bound test procedure as an efficient way of initializing the search interval. Simulation results corroborate our findings.