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This paper proposes two Pareto-optimal power control algorithms for a two-tier network, where newly-deployed Femtocell User Equipments (FUEs) operate in the licensed spectrum owned by an existing macrocell. Different from homogeneous network settings, the inevitable requirement of robustly protecting the Quality-of-Service (QoS) of all prioritized Macrocell User Equipments (MUEs) here lays a major obstacle that hinders the successful application of any available solutions. Directly targeting at this central issue, the first algorithm jointly maximizes the total utilities of both user classes. Specifically, the authors adopt the log-barrier penalty method to effectively enforce the minimum Signal-to-Interference-plus-Noise Ratios (SINRs) imposed by the macrocell, paving the way for the adaptation of load-spillage solution framework.
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