Globally optimal joint uplink base station association and power control for max-min fairness

In a heterogeneous network (HetNet) with a large number of low power base stations (BSs), proper user-BS association and power control is crucial to achieving desirable system performance. In this paper, we consider the joint BS association and power allocation problem for an uplink cellular network under the max-min fairness criterion. We first present a binary search method whereby a QoS (Quality of Service) constrained subproblem is solved at each step. Then, we propose a normalized fixed point iterative algorithm to directly solve the original problem and prove its geometric convergence to the global optimal solution, which implies the pseudo-polynomial time solvability of the considered problem. Simulation results show that the proposed normalized fixed point iterative algorithm converges much faster than the binary search method.