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

We consider the problem of maximizing the proportional fairness (PF) system utility over heterogeneous wireless networks (HetNets) by jointly exploiting cell dormancy (cell ON-OFF)-wherein some transmission points from a set of interest can be made inactive-and load balancing (user association)-wherein users are associated to the active transmission points in that set, with each user being associated with only one point. We establish that this joint optimization problem, which is a discrete optimization problem, is NP-hard. Nevertheless, we prove that the load balancing subproblem for any given set of active transmission points is not NP-hard but instead can be reformulated as an asymmetric assignment problem and hence can be optimally solved in an efficient manner. In addition, we show that some generalized load balancing problems that incorporate multiuser diversity gains can also be optimally and efficiently solved. We propose another lower complexity greedy algorithm for the load balancing subproblem that offers a worst-case performance guarantee and describe a simple way to approximately realize a given input user association via biasing factors. We then derive low-complexity algorithms for the joint optimization problem, including one based on a successive approximation method that has hitherto been used for continuous nonconvex optimization problems. Simulations over an example Long-Term Evolution HetNet topology reveal the superior performance of the proposed algorithms and underscore the significant benefits of jointly exploiting cell dormancy and load balancing.