Energy-Efficient Base Station Operation and Association in HetNets: Complexity and Algorithms

Abstract

This paper studies the base station operation and association (BOA) problem for energy-efficient heterogeneous cellular networks. The objective is to find the set of base stations (BSs) to activate and to associate users to BSs under minimum rate requirements. BOA is formulated as a nonconvex programming problem. In order to solve it, we distinguish between two cases: 1) BOA with high-rate requirements (BOAH) and 2) BOA with low-rate requirements (BOAL). First, we show that finding feasible solutions for BOAH is NP-hard, and second, we reduce it to a BS operation problem (i.e., user association becomes straightforward). Based on this reduction, we develop a brute force algorithm and show that its complexity can be extremely reduced though it is still exponential. Hence, we propose a polynomial-time heuristic algorithm. As for BOAL, since BOA is extremely coupled, we relax the problem. Consequently, BOAL can be formulated as an integer linear program. Finding feasible solutions to it is shown to be NP-hard. To efficiently solve it, we propose a greedy-based algorithm. The proposed greedy algorithm is shown to admit a logarithmic approximation factor when it finds feasible solutions and a constant approximation factor otherwise. Finally, simulation results illustrate the performance of the proposed algorithms.