Optimal base station densities for cost-efficient multi-tier heterogeneous cellular networks

Heterogeneous cellular networks have emerged to be the primary solution for overwhelming traffic demands. This study addresses the architecture optimization of multi-tier open access downlink heterogeneous cellular networks to achieve the maximum network spatial throughput under practical constraints on the network deployment cost and traffic loads of individual tiers. In particular, with the use of a stochastic geometry-based network model, the problem of optimizing the densities of base stations (BSs) in different tiers is shown to be a linear-fractional programming that can be further transformed into a linear programming by employing Charnes-Cooper transformation. Such programming can, in turn, be solved efficiently. Furthermore, for the special case of a two-tier network, the optimal BS densities are derived in closed form using the graphical method. Simulation results demonstrate significant throughput gain from the optimal deployment of multi-tier heterogeneous cellular networks.