User-Base Station Association in HetSNets: Complexity and Efficient Algorithms

TL;DR

This paper investigates user association problems in HetSNets, proves their NP-hardness, and proposes efficient heuristic algorithms that perform close to optimal, balancing user load and fairness.

Contribution

It proves the NP-hardness of unweighted user association in HetSNets and develops two efficient heuristics with near-optimal performance.

Findings

Proposed algorithms are computationally more efficient than brute-force and branch-and-bound methods.

Algorithms achieve close-to-optimal solutions in numerical simulations.

Weighted association solutions can balance load and improve fairness.

Abstract

This work considers the problem of user association to small-cell base stations (SBSs) in a heterogeneous and small-cell network (HetSNet). Two optimization problems are investigated, which are maximizing the set of associated users to the SBSs (the unweighted problem) and maximizing the set of weighted associated users to the SBSs (the weighted problem), under signal-to-interference-plus-noise ratio (SINR) constraints. Both problems are formulated as linear integer programs. The weighted problem is known to be NP-hard and, in this paper, the unweighted problem is proved to be NP-hard as well. Therefore, this paper develops two heuristic polynomial-time algorithms to solve both problems. The computational complexity of the proposed algorithms is evaluated and is shown to be far more efficient than the complexity of the optimal brute-force (BF) algorithm. Moreover, the paper benchmarks the performance of the proposed algorithms against the BF algorithm, the branch-and-bound (B\&B) algorithm and standard algorithms, through numerical simulations. The results demonstrate the close-to-optimal performance of the proposed algorithms. They also show that the weighted problem can be solved to provide solutions that are fair between users or to balance the load among SBSs.