Social Welfare Maximization in Two-Tier Heterogeneous Cellular Networks

Abstract

In this letter, an optimal bandwidth (BW) partitioning problem is studied for two-tier heterogeneous cellular networks (HCNs) with social welfare maximization (SWM) as an objective. Social welfare is represented as the sum of users’ surplus and service provider’s profit. For the SWM, the unique optimal BW-fraction is analytically obtained for the two tiers, where the spectrum is orthogonally partitioned between the tiers. By making the users indifferent to tiers for services, two different pricing schemes are presented. To ensure the feasibility of pricing schemes and the uniqueness of the optimal BW-fraction, the limits on operational cost factor are defined. It is shown that while satisfying the indifference principle, i.e., providing an equal surplus to the users from both tiers’ services, the differential pricing scheme offers a better control over the users’ surplus and service provider’s profit than the single pricing scheme. Simulations validate the analytical results. The effects of different system parameters on the optimal BW-fraction and the associated load to the different tiers are also addressed.