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

TL;DR

This paper investigates the joint user association and power control problem in HetNets, demonstrating its NP-hardness, proposing near-optimal algorithms, and identifying conditions for polynomial-time solutions.

Contribution

It provides a comprehensive analysis of the problem's complexity, introduces a two-stage near-optimal algorithm, and offers a polynomial-time solution under mild assumptions.

Findings

The joint BS association and power control problem is NP-hard.

A two-stage algorithm achieves near-optimal performance in high-SNR regimes.

Under certain conditions, the problem can be solved optimally in polynomial time.

Abstract

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 $\log(g_{ij})$, where $\{g_{ij}\}$ are the channel gains.