Fairness based admission control and beamforming design for the MISO downlink

This paper studies fairness problem concerning admission control and beamforming design in the multiple-input-and-single-output (MISO) downlink channel with various users: guaranteed users (GUs) who have the requirements on individual signal-to-interface-noise ratios (SINR) and best-effort users (BUs) who have no such requirements. The problem is modeled as maximizing the worst SINR of BUs while meeting SINR requirements of GUs and limiting total power of base station (BS). We figure out feasibility of the problem with solving the max-min-weighted-fairness (MMWF) problem. If it is feasible, we propose a heuristic removal algorithm to turn the infeasible problem into a feasible one; otherwise, we study the relation between the feasible problem and the MMWF problem by introducing auxiliary variables. Based on that relation, a fixed-point iterative algorithm converging to the optimal solution is proposed to solve the feasible problem. Besides, the algorithm can be implemented distributively. Simulation results reveal the effectiveness of the heuristic removal algorithm, and the optimality and fast convergence of the fixed-point iterative algorithm.