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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 systematically study the joint BS association and power allocation problem for a downlink cellular network under the max-min fairness criterion. First, we show that this problem is NP-hard. Second, we show that the upper bound of the optimal value can be easily computed, and propose a two-stage algorithm to find a high-quality suboptimal solution. Simulation results show that the proposed algorithm is near-optimal in the high-SNR regime. Third, we show that the problem under some additional mild assumptions can be solved to global optima in polynomial time by a semi-distributed algorithm. This result is based on a transformation of the original problem to an assignment problem with gains log(g<sub>ij</sub>), where {g<sub>ij</sub>} are the channel gains.

Joint Downlink Base Station Association and Power Control for Max-Min Fairness: Computation and Complexity