Exploiting cell dormancy and load balancing in LTE HetNets: Optimizing the proportional fairness utility

We consider the problem of maximizing the proportional fairness (PF) utility over heterogeneous wireless networks (HetNets) by jointly exploiting cell dormancy (cell ON-OFF) - wherein some transmission nodes from a set of interest are made inactive - and load balancing (user association) - wherein users are associated to the active transmission nodes in that set with each user being associated with only one node. We establish that this joint optimization problem which is a discrete optimization problem, is strongly NP-hard. Nevertheless, we prove that the load balancing sub-problem for any given set of active transmission nodes is not NP-hard but instead can be re-formulated as an asymmetric assignment problem and hence can be optimally solved in an efficient manner. In addition, we propose another lower complexity greedy algorithm for the load balancing sub-problem which offers a near-optimal average-case performance and a worst-case performance guarantee. We then propose a low-complexity algorithm for the joint optimization problem. Simulations over an example LTE HetNet topology reveal the superior performance of the proposed algorithms and underscore the significant benefits of jointly exploiting cell dormancy and load balancing.