Tier Association Probability and Spectrum Partitioning for Maximum Rate Coverage in Multi-tier Heterogeneous Networks

TL;DR

This paper investigates how to optimize user association and spectrum partitioning in multi-tier heterogeneous networks to maximize rate coverage, providing analytical insights and demonstrating minimal performance loss with joint optimization.

Contribution

It introduces a relation between derivatives of the objective function to simplify optimization and proves the optimality of equal spectrum and association probability allocation with a closed-form solution.

Findings

Joint optimization yields significant performance gains.

Equal spectrum and association probability allocation has negligible performance loss.

Analytical relation simplifies the non-convex optimization problem.

Abstract

For a wireless multi-tier heterogeneous network with orthogonal spectrum allocation across tiers, we optimize the association probability and the fraction of spectrum allocated to each tier so as to maximize rate coverage. In practice, the association probability can be controlled using a biased received signal power. The optimization problem is non-convex and we are forced to explore locally optimal solutions. We make two contributions in this paper: first, we show that there exists a relation between the first derivatives of the objective function with respect to each of the optimization variables. This can be used to simplify numerical solutions to the optimization problem. Second, we explore the optimality of the intuitive solution that the fraction of spectrum allocated to each tier should be equal to the tier association probability. We show that, in this case, a closed-form solution exists. Importantly, our numerical results show that there is essentially zero performance loss. The results also illustrate the significant gains possible by jointly optimizing the user association and the resource allocation.