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We consider the problem of maximizing the proportional fairness (PF) utility over heterogeneous cellular networks (HetNets) by jointly exploiting partial muting-wherein the high power macro transmission node in a set of transmission nodes of interest can be made inactive for a specified fraction of the available time-frequency resource- and load balancing (user association)-wherein each user can be associated to (i.e., configured to receive data from) any one transmission node in that set. This joint problem is a mixed optimization problem in which there are finitely many choices for the muting fraction and the user association, but there are a continuum of ways in which each transmission node can partition the available resource among the users associated to it. While this mixed optimization problem seems intractable, we systematically construct efficient approximation algorithms, one of which is approximately optimal in that it yields a system utility that is no less than the optimal utility minus a constant. In addition, we propose another lower complexity greedy algorithm and proceed to demonstrate the superior performance of the proposed algorithms via simulations over an example LTE HetNet topology.
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Prasad et al. (2014) studied this question.
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