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  • 3434 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 11, NO. 10, OCTOBER 2012

    Distributed Pareto-Optimal Power Control forUtility Maximization in Femtocell Networks

    Duy Trong Ngo, Student Member, IEEE, Long Bao Le, Senior Member, IEEE, and Tho Le-Ngoc, Fellow, IEEE

    AbstractThis paper proposes two Pareto-optimal power con-trol algorithms for a two-tier network, where newly-deployedfemtocell user equipments (FUEs) operate in the licensed spec-trum owned by an existing macrocell. Different from homoge-neous network settings, the inevitable requirement of robustlyprotecting the quality-of-service (QoS) of all prioritized macrocelluser equipments (MUEs) here lays a major obstacle that hindersthe successful application of any available solutions. Directly tar-geting at this central issue, the first algorithm jointly maximizesthe total utility of both user classes. Specifically, we adopt thelog-barrier penalty method to effectively enforce the minimumsignal-to-interference-plus-noise ratios (SINRs) imposed by themacrocell, paving the way for the adaptation of load-spillagesolution framework. On the other hand, the second algorithmis applied to the scenario where only the sum utility of allFUEs needs to be maximized. At optimality, we show thatthe MUEs prescribed SINR constraints are met with equalityin this case. With the search space for Pareto-optimal SINRssubstantially reduced, the second algorithm features scalability,low computational complexity, short converging time, and stableperformance. We prove that the two developed algorithmsconverge to their respective global optima, and more importantly,they can be implemented in a distributive manner at individuallinks. Effective mechanisms are also available to flexibly designatethe access priority to MUEs and FUEs, as well as to fairlyshare radio resources among users. Numerical results confirmthe merits of the devised approaches.

    Index TermsConvex optimization, global optimality, hetero-geneous network, interference management, Pareto optimality,power control, QoS protection, SINR optimization, utility maxi-mization.

    I. INTRODUCTION

    FEMTOCELLS have recently emerged as a promisingtechnology to increase wireless network capacity, extendcellular coverage and introduce new services [1], [2]. Fem-tocell base stations (BSs) are low-power, miniature wirelessaccess points that are typically set at a home and connectedto backhaul networks via residential wireline broadband access

    Manuscript received August 2, 2011; revised February 21, 2012; acceptedAugust 2, 2012. The associate editor coordinating the review of this paperand approving it for publication is S. Liew.

    This work is supported in part by the Natural Sciences and EngineeringResearch Council of Canada (NSERC) Grants, the Alexander Graham BellCanada Graduate Scholarship, the McGill Engineering Doctoral Award, andthe Clifford Pang Doctoral Fellowship. Part of this paper was presented atthe 2011 IEEE International Symposium on Personal, Indoor and MobileRadio Communications (PIMRC), Toronto, ON, Canada, and the 2012 IEEEVehicular Technology Conference (VTC-Fall), Quebec City, QC, Canada.

    D. T. Ngo and T. Le-Ngoc are with the Department of Electrical andComputer Engineering, McGill University, Montreal, QC, Canada H3A 0E9(e-mail: duy.ngo@mail.mcgill.ca; tho.le-ngoc@mcgill.ca).

    L. B. Le is with the Centre Energie Materiaux Telecommunications, InstitutNational de la Recherche Scientifique (INRS-EMT), Universite du Quebec,Montreal, QC, Canada H5A 1K6 (e-mail: long.le@emt.inrs.ca).

    Digital Object Identifier 10.1109/TWC.2012.090312.111454

    links, e.g., digital subscriber lines (DSL). Because femtocellscan be easily integrated into an existing cellular networkinfrastructure, their deployment requires low capital expendi-tures and operating expenses. At the same time, indoor userscan enjoy excellent wireless experience thanks to the closeproximity with their home femtocell BSs [3].

    Since femtocells operate in the licensed spectrum ownedby wireless operators and share this spectrum with macrocellnetworks, limiting the cross-tier interference from FUEs at amacrocell BS becomes an indispensable condition. Due to therandom deployment of femtocell BSs, users in a femtocellmay also suffer severe interference from nearby femtocells.One of the central research topics is to develop interferencemanagement schemes such that the QoS requirements of allMUEs are maintained, while the residual network capacityis optimally exploited by FUEs [4], [5]. Given that onlylimited signaling information can be exchanged over thebackhaul wireline network, it is always desirable in practiceto accomplish such optimization by distributed mechanisms.

    Using noncooperative game theory, the studies of [6], [7]propose distributed power control schemes for traditionalcode-division multiple access (CDMA) systems, where in-dividual users select transmit power strategies to maximizetheir own utility. For femtocell networks, power control gamesare also formulated and analyzed by [8][11]. The work in[12] develops joint power and admission control schemesfor distributed interference management in two-tier networks.Specifically, both throughput-power tradeoff optimization andsoft QoS provisioning are achieved for FUEs while thepredefined SINR targets of all MUEs are always met. Inmost instances, the underlying games settle at some Nashequilibrium (NE), a stable and predictable state at which nouser has any incentive to unilaterally change its power level.Although the achieved NE gives a steady operating point, itdoes not guarantee to be Pareto-efficient.

    A number of pricing schemes are adopted in [13][17] toimprove the efficiency of the NE. Nevertheless, it remainsunclear how far to the global optima of the original problemsthese solutions actually are. With a novel pricing scheme, thework of [18] shows that the outcome of a non-cooperativepower control game in single-cell systems can be a uniqueand Pareto-efficient NE. Various design goals can also be metby setting dynamic prices for the individual users. In multicellsettings where transmit powers of all users need to be jointlyoptimized across different cells, intercell interference, how-ever, cannot simply be treated as noise, making the solutiondevised by [18] inapplicable.

    In [19], a distributed power control algorithm is proposed

    1536-1276/12$31.00 c 2012 IEEE

  • NGO et al.: DISTRIBUTED PARETO-OPTIMAL POWER CONTROL FOR UTILITY MAXIMIZATION IN FEMTOCELL NETWORKS 3435

    that enables users to eventually achieve their fixed targetSINRs. As long as all the SINR targets are feasible, thisiterative algorithm converges to a Pareto-optimal solution ata minimal aggregate transmit power. However, a fixed SINRassignment is certainly not suitable for two-tier networks.Since femtocells typically serve data users, SINRs shouldinstead be adjusted to the extent that the system capacity canstill support. A high SINR is translated into better throughputand reliability, whereas a low SINR implies lower data rates.

    Under the proposed load-spillage framework, [20] devisesdistributed solutions to jointly optimize SINRs and powers.While guaranteeing to offer Pareto-optimal SINR assignments,the approach adopted by [20] is directly applicable to homo-geneous networks. Herein, there exist no differentiated classesof users with distinct access priority and design specifications.On the contrary, it is imperative to protect the ongoingoperation of the preferential MUEs at all times in a two-tier heterogeneous network. This critical requirement, indeed,poses a major challenge that hinders the successful applicationof any available solutions, including [20]. Specifically, thechoices of target SINRs available to the lower-tier FUEs inthis case are much more limited, which further complicate thePareto-optimal boundary of the feasible SINR region. As adirect consequence, locating a particular SINR point on such aboundary to optimize some certain system-wide design criteriais by no means a trivial task.

    Directly targeting this central issue, this paper attemptsto come up with interference management solutions wherein(i) all users attain their respective SINRs that are alwaysoptimal in Pareto sense, and (ii) macrocell and femtocellnetworks have their utilities globally maximized. To handlethe above-mentioned QoS requirements of the prioritizedMUEs, we first propose the Joint Utility Maximization withmacrocell Quality-of-Service guarantee (JUM-QoS) algorithmthat maximizes the total utility of both macrocell and femtocellnetworks. In particular, the minimum SINRs prescribed bythe MUEs are effectively enforced with the use of a log-barrier penalty function. After this key step, the Pareto-optimalboundary of the strongly-coupled feasible SINR region ischaracterized, and the load-spillage framework [20] specifi-cally adapted to find the SINR that approximately maximizesthe sum utility. Finally, the global optimum of the originalproblem is attained by properly tuning the penalty parameterin the proposed penalty approach.

    In the specific case where MUEs only need to be assuredwith some predefined minimum SINRs, we devise the Fem-tocell Utility Maximization with Macrocell SINR Balancing(FUM-MSB) algorithm. Upon observing the structure of theobjective function and the monotonicity of SINR, we confinethe Pareto-optimal SINR boundary to a much smaller space.Only then the load-spillage parametrization is applied to theFUEs, whereas the loads of all MUEs are updated accordingto a newly-developed iterative procedure. Still operating onthe Pareto-optimal SINR frontier and retaining the globaloptimality, this algorithm outperforms the general counterpartJUM-QoS in several important aspects, including scalability,computational complexity, convergence behavior, and stabilityaround the optimum.

    It is noteworthy