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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 utility of both user classes. Specifically, we 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. On the other hand, the second algorithm is applied to the scenario where only the sum utility of all FUEs needs to be maximized. At optimality, we show that the MUEs' prescribed SINR constraints are met with equality in this case. With the search space for Pareto-optimal SINRs substantially reduced, the second algorithm features scalability, low computational complexity, short converging time, and stable performance. We prove that the two developed algorithms converge to their respective global optima, and more importantly, they can be implemented in a distributive manner at individual links. Effective mechanisms are also available to flexibly designate the access priority to MUEs and FUEs, as well as to fairly share radio resources among users. Numerical results confirm the merits of the devised approaches.
Date of Publication: October 2012