Utility Maximization for Single-Station User Association in Downlink Cellular Networks

TL;DR

This paper addresses the complex problem of optimizing user association and resource allocation in cellular networks with a focus on single station association policies, providing explicit solutions, algorithms, and performance analysis.

Contribution

It introduces an explicit optimal BS allocation solution, proves the association problem's non-convexity, and offers centralized and distributed greedy algorithms for SSA.

Findings

Optimal BS allocation for SSA is a combinatorial problem.

Relaxation of the association problem has an integrality gap of one.

Greedy algorithms improve network utility in simulations.

Abstract

We study network utility maximization (NUM) in the context of cellular single station association (SSA) policies, which assigns each mobile user (MU) to a single base station (BS). We measure an SSA policy in terms of the induced \alpha-proportional fairness utility of each user's downlink rate, summed over all users. The general SSA NUM problem involves choosing an optimal association from MUs to BSs as well as an optimal allocation of BS resources to associated MUs. Finding an exact solution to such centralized user association problems is well-known to be NP-hard. Our contributions are as follows: i) we give an explicit solution for the optimal BS allocation for a given SSA, which establishes SSA NUM as a purely combinatiorial problem; ii) we establish the integrality gap for the association problem to be one, and prove the relaxation to be a non-convex optimization problem; iii) we provide both centralized and distributed greedy algorithms for SSA, both with and without the exchange of instantaneous rate information between users and stations. Our numerical results illustrate performance gains of three classes of solutions: i) SSA solutions obtained by greedy rounding of multi-station associations (a centralized convex program), ii) our centralized and distributed greedy algorithms with/without rate information exchanged, and iii) simple association heuristics.