optimizing small cell deployment in arbitrary wireless networks with minimum service rate...

IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 13, NO. 8, AUGUST 2014 1801

Optimizing Small Cell Deployment in ArbitraryWireless Networks with Minimum Service

Rate ConstraintsHung-Yun Hsieh, Shih-En Wei, and Cheng-Pang Chien

Abstract—Femtocell technology has shifted beyond indoor residential applications to cover a wider range of scenarios includingmetropolitan and rural areas. The term “small cell” has hence been used to denote such low-power transmission points deployed forenhancing macrocell coverage and/or capacity. While deployment of femto BSs has typically followed the bottom-up paradigm drivenby the ad hoc demand of users, more and more studies have prompted a move toward a more managed deployment model for bettertradeoff between performance and cost. In this paper, we investigate an optimization problem for femtocell deployment in a densenetwork with arbitrary topology. The goal is to determine deployment locations and operation parameters of femtocells for maximizingthe number of customers supported with QoS constraints. Since the formulated problem belongs to mixed-integer non-linearprogramming (MINLP), we propose an anytime algorithm that transforms the joint problem into a cluster formation sub-problem(involving location selection and cell coverage) and a resource management sub-problem (involving power control and resourceallocation) for effectively solving all optimization variables in an iterative fashion. Compared with other approaches for femtocelldeployment, our evaluation results show that the proposed algorithm can effectively solve the target problem while striking a betterperformance tradeoff between computation complexity and solution quality.

Index Terms—Small cells, cluster formation, resource allocation, power control, coalition structure generation

1 INTRODUCTION

AS a promising technology for data traffic offloadingin cellular networks, femtocell has attracted a lot of

attention since its inception. A femto base station (BS)or femtocell is a small, short-range, and low-cost cellu-lar base station designed for providing indoor users withhigher data rate and better service coverage. Unlike otherbase stations such as macrocells and picocells, femtocellstypically rely on the wired broadband access at the userpremises for connection to the core network, and they havetypically been designed with attributes such as flexible con-figuration and self-management to allow “plug-and-play”deployment by users [1].

While femtocells have initially been deployed for res-idential and small business users, over the years theyhave expanded to encompass models of longer range andhigher capacity including metro femtocells, enterprise fem-tocells, and super femtocells. The Femto Forum has furtherstandardized femtocells into Class 1 (residential house-hold), Class 2 (enterprise) and Class 3 (metro and ruralarea) for deployment by carriers across various network

• H.-Y. Hsieh is with the Department of Electrical Engineering andGraduate Institute of Communication Engineering, National TaiwanUniversity, Taipei 106, Taiwan. E-mail: [email protected].

• S.-E. Wei and C.-P. Chien are with the Graduate Institute ofCommunication Engineering, National Taiwan University, Taipei 106,Taiwan. E-mail: {r99942074; r00942048}@ntu.edu.tw.

Manuscript received 20 Dec. 2012; revised 15 Sep. 2013; accepted19 Sep. 2013. Date of publication 17 Oct. 2013; date of current version7 July 2014.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference the Digital Object Identifier below.Digital Object Identifier 10.1109/TMC.2013.135

architectures [2]. In fact, with a radiated power of 26 dBm ormore, a metro femtocell, or metrocell, is similar in coverageto a picocell. To reflect the shift of the femtocell technol-ogy beyond residential applications and to highlight therise of such low-power transmission points deployed in awide range of scenarios for enhancing macrocell coverageand/or capacity, an umbrella term called “small cell” hashence been introduced recently [3].1

It is expected that such small cells are to be denselydeployed in large quantities in the near future. Conventionally,deployment of (indoor) femtocells has followed the bottom-up paradigm that lacks optimized planning and controlfrom the network operator. In the context of small cells withlarger capability to serve more than indoor users, however,such a deployment model may need to be revisited. Moreand more studies have prompted the idea that, instead offollowing the ad hoc customer deployment model, the net-work operator can assume more control in the deploymentof femtocells to optimize the overall system performance ina centralized fashion [4], [5]. In the WSP (wireless serviceprovider) deployment model proposed in [5], for example,users may be selected by the operator to install femtocellsin their premises for providing better services to themselvesand nearby users for potential optimization of system per-formance. While it is undesirable to incur the high cell

1. While some other low-power nodes such as picocells and remoteradio heads (RRHs) have also been considered as part of the smallcells, femtocells and variants are the main drive of the small cell tech-nology. Whenever applicable, we use the term small cell and femtocellinterchangeably in this paper, with the understanding that the latteris not limited to indoor usage.

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1802 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 13, NO. 8, AUGUST 2014

planning costs as in conventional macrocell deployment,the move towards a more managed yet plug-and-play modelfor femtocell deployment is a promising direction to strikebalance between performance and cost.

To the best of our knowledge, while related work hasproposed various solutions for optimizing performance offemtocell networks including resource allocation, interfer-ence management, power control, and access control [6]–[10], few has taken the deployment problem into the overalloptimization loop. There does exist related work that targetsdeployment of femtocells at locations inside a building [11].However, since femtocells may be densely installed atrooftops and lampposts to serve outdoor users in the neigh-borhood [12], [13], the assumptions to ignore femtocell-to-femtocell and femtocell-to-macrocell interferences as in [11]may not be applicable for outdoor deployment with highdensity. Compared to the conventional deployment prob-lem for cellular networks, since femtocell networks areexpected to be more unstructured with more complex inter-cell interference relation, solutions that assume a structured(line or grid) deployment scenario [14], [15] thus cannot bedirectly applied in the target scenario. On the other hand,while stochastic geometry for modeling the distribution offemtocells has been popularly used to analyze the perfor-mance of tiered networks [16], they are somewhat limitedin providing answers for any given network with arbitrarytopology to questions such as: where are the best locations todeploy femtocells and how should each femtocell be configured toserve users with the given spectrum resource?

As a first step towards addressing these questions, inthis paper we investigate a problem where a given numberof femto BSs are to be deployed by the operator in an arbi-trary set of neighborhood locations (households). The goalis to determine the best deployment locations and the opti-mal operation parameters (transmission power and servedhouseholds) such that the number of households that can beserved with QoS constraints is maximized. Since the formu-lated problem (involving deployment location and powercontrol) belongs to mixed-integer non-linear programming(MINLP), we then propose an anytime algorithm to solvethe problem with controllable time complexity. Specifically,based on the concept of coalition structure generation, thealgorithm decouples the problem into the cluster formationsub-problem and resource management sub-problem to findthe optimal cluster head (femto BS location), cluster size(cell selection), transmission power, and resource alloca-tion in an iterative fashion. We show through evaluationresults that the proposed algorithm can effectively solvethe problem with better tradeoff in computation complex-ity and solution quality compared to baseline approaches.To the best of our knowledge, our work is the first to inves-tigate and solve such a joint optimization problem involvingnetwork deployment and transmission configuration for femtocellnetworks with arbitrary topologies.

The rest of the paper is organized as follows: Section 2describes related work while Section 3 describes the targetscenario and problem formulation. Section 4 and Section 5present the proposed algorithm to solve the resource man-agement and cluster formation sub-problems respectively.The solution is then extended in Section 6 to addressproblems such as co-channel deployment and incremental

deployment. Section 7 presents the performance of theproposed solution and finally Section 8 concludes the paper.

2 RELATED WORK

While femtocell is a promising technology to improve theperformance of cellular networks, it introduces several newchallenges in such two-tiered networks. Firstly, spectrum(or resource) allocation techniques between the macrocelland femtocell including both orthogonal channel allocationand co-channel allocation have been investigated in relatedwork [6]. In [7], for example, the authors investigate theproblem of maximizing the area spectral efficiency (ASE)subject to a network-wide QoS constraint, and they proposean optimal spectrum partitioning strategy to determine theamount of sub-channels allocated to each tier. The authorsin [17] consider allocation of the radio resource in the unitof the physical resource block (PRB) and they propose analgorithm to assign PRBs to a group of femtocells with dif-ferent QoS classes. In these research endeavors, althoughthe focus is not on inter-tier (cross-tier) interference, it is stillchallenging to minimize intra-tier (co-tier) interference amongthe set of randomly distributed femtocells.

If the macrocell and femtocell are allocated the sameset of radio resource, inter-tier interference needs to beaddressed through techniques such as power control, inter-ference alignment, and access control. In [8], the authorsinvestigate the power control problem in two-tiered net-works and they derive a fundamental relation between thelargest feasible macrocell SINR and the given set of feasiblefemtocell SINRs. A distributed utility-based SINR adap-tation algorithm for protecting the macrocell link qualityis also proposed. The authors in [18] further investigatejoint power control and beamforming for tiered networksunder channel uncertainty. In [9], the authors show thatfemtocells can in fact improve overall network capacity ifthe macro user is allowed to connect to femtocells pro-viding better link quality. Tradeoffs between open andclosed access modes in the uplink and downlink are fur-ther investigated in [19], [20], where a hybrid access modeis also proposed that leverages the benefits of both accessmodes. To facilitate power control, however, the constraintconsidered in these papers is typically the link SINR orraw capacity without considering time sharing among multipleusers.

Since femtocell deployments are often “unstructured,”related work has typically adopted the tool of stochas-tic geometry to model the femtocell distribution using thePoisson Point Process (PPP). Owing to the nice propertiesof the stochastic model, it is possible to derive fundamen-tal and tractable analytical expressions in tiered networks.The work in [10], for example, formulates and solvesa throughput maximization problem for PPP-distributedmacro BSs and femto BSs, subject to the success probabilityand link data rate constraints under different spectrum allo-cation and femtocell access policies in tiered networks. Theauthors in [16], [21] employ stochastic geometry to obtainthe relations between the density of femto BSs, per-tieroutage probability, and transmission capacity of two-tierednetworks. Our work, instead, does not assume any stochas-tic distribution model of femto BSs, but aims to propose

HSIEH ET AL.: OPTIMIZING SMALL CELL DEPLOYMENT IN ARBITRARY WIRELESS NETWORKS 1803

solution that can be applied for any arbitrarily given networktopology in practice.

Finally, we note that while co-channel allocationallows more room for performance optimization in tierednetworks, in some scenarios it is desirable to have fem-tocells use different frequency bands from macrocells. Inparticular, FCC has recently adopted a Notice of ProposedRulemaking that makes 100 MHz of spectrum availablefor use by small cells in the 3550-3650 MHz band [22].Standards bodies have also started to investigate issueswith the dedicated resource model for supporting smallcells [12]. Since the 3.5 GHz band exhibits high penetrationloss and supports shorter transmission range compared tothe cellular band, it may not be desirable to use it for the macro-cell with large coverage. Hence, femtocells can make use ofthe available spectrum with wider bandwidth for providinga more predictable QoS to complement macrocells. Whilethe methodology proposed in this work can be applied toorthogonal and co-channel allocation of the spectrum, in thefollowing we start with the core formulation and solution of thededicated resource model and explain how it can be extendedto the shared resource model in Section 6.

3 NETWORK SCENARIO AND PROBLEMFORMULATION

3.1 Network ScenarioWe consider a set of households scattered arbitrarily in aneighborhood area, where each household has a wirelessservice subscription with a minimum downlink data raterequirement. To serve the households with the contract datarates, the network operator aims to deploy a number offemto BSs in selected locations (e.g. rooftops or lampposts)such that each femto BS serves a selected subset of nearbyhouseholds. All femto BSs are assumed to operate concur-rently on the same set of sub-channels (or OFDMA resourceblocks) through proper power control for leveraging spatialreuse. Since each femto BS may need to serve multiple sub-ordinate households, proper resource allocation also needs tobe performed by the femto BS (e.g. allocate different frac-tions of time or OFDMA symbols to different households)to meet data rate requirements of individual households.

Since the femto BSs may co-exist with the macro BSin the same geographic area, different models includ-ing the shared resource (co-channel allocation) model anddedicated resource (orthogonal channel allocation) modelmay be considered. In the shared resource model, femto-cells are typically considered as underlay of the macrocell,and hence proper interference management needs to beperformed to address inter-tier as well as intra-tier interfer-ences. In the dedicated resource model, on the other hand,femto BSs are allocated dedicated radio resource and hencedo not suffer from inter-tier interference with the macro BS.While there are trade-offs between the two models, to keepour work focused, we start with the formulation and solu-tion for the dedicated resource model as shown in Fig. 1and then explain extension for the shared resource modelin Section 6.

To minimize the number of femto BSs deployed forsupporting all households with subscriptions, transmissionpowers as well as deployment locations of femto BSs need

Fig. 1. Femtocells for serving neighborhood households.

to be optimally decided. The problem we consider thustakes physical deployment of femto BSs into the joint opti-mization problem of power control and resource allocationin the protocol stack. From the perspective of the net-work operator, since the locations, service requirements,and (long-term average) channel conditions of all house-holds can be known a priori or obtained on a periodicbasis, it is possible to optimize the overall system perfor-mance through proper network planning as we show in thefollowing.

3.2 Problem FormulationTo serve the set of households with minimum data raterequirements, our strategy is to minimize the number offemto BSs deployed and the amount of radio resourceneeded. To achieve this goal, we formulate an optimiza-tion problem that aims to maximize the number of householdssupported under the given amount of resource W and thegiven number of femto BSs m. Let H be the set of house-holds and Ci be the minimum downlink data rate for eachhousehold i ∈ H. Define binary variable Xij, ∀i, j ∈ H, asfollows:⎧⎨

⎩

Xij = 1, if household i is supported via the femto BSinstalled at household j;

Xij = 0, otherwise.

For household j where a femto BS is installed, it is requiredthat Xjj = 1. If household i is supported by household jwith a femto BS (Xij = 1), then the Shannon link capacityshould obviously be larger than data rate Ci as follows:

fiW log2

(

1 + 1�

γij

)

≥ CiXij, ∀i, j ∈ H, (1)

where fi is the fraction of resource allocated to household i,W is the bandwidth of each sub-channel, γij is the receivedSINR, and � is the SINR gap to the Shannon link capacitythat depends on the modulation technique and target biterror rate (BER) in consideration (e.g., � = − ln(5 ·BER)/1.5for M-QAM) [23]. Since all femto BSs are assumed to oper-ate concurrently on the same sub-channels, the receivedSINR γij at household i can be written as follows:

γij = PjGji

WN0 +∑k∈Hk �=j

PkGki, (2)

where Pj is the transmission power of household j, Gji is thelong-term channel gain (including proper wall penetration


loss) from household j to household i, and N0 is the AWGNspectral density. Only the household with a femto BS hasnon-zero transmission power constrained as follows:

0 ≤ Pj ≤ PFXjj, ∀j ∈ H, (3)

where PF is the upper bound of the transmission power.Variable fi in Constraint (1) accounts for the fraction of time(or resource) allocated to household i if it is supported, andhence it has the follow constraints:

∑

i∈HfiXij ≤ 1, ∀j ∈ H, (4)

0 ≤ fi ≤ 1, ∀i ∈ H. (5)

A setting of fi = 1/∑

k∈H Xkj corresponds to the specialcase of equal resource allocation (e.g. round-robin scheduling)among all households served by the femto BS.

Since the number m of femto BSs to deploy is given asa requirement, we have the following constraint:

∑

j∈HXjj = m. (6)

To facilitate femto BS management, we assume that themaximum number of households each femto BS can serveis limited by parameter n as follows:

∑

i∈HXij ≤ n, ∀j ∈ H. (7)

Finally, two additional constraints for Xij are∑

j∈HXij ≤ 1, ∀i ∈ H, (8)

and

Xij ≤ Xjj, ∀i, j ∈ H, i �= j, (9)

to ensure that a household can be served by at most onefemto BS installed in any household.

With the aforementioned constraints for data rate anddeployment requirements, the objective for maximizingthe number of supported households can be expressed asfollows:

MaximizeX, P, f

∑

i∈H

∑

j∈HXij, (10)

where the deployment location and service set (matrix X),transmission power (vector P), and resource allocation (vec-tor f) of each femto BS are to be determined. Togetherwith the objective function and pertinent constraints, wethus formulate a mixed-integer non-linear programming(MINLP) problem. While this category of problems is usu-ally NP-hard, to reduce the computation complexity, wepropose an algorithm that decouples the problem intotwo sub-problems for solving X and P, f respectively.Determination of X can be considered as a cluster formationsub-problem to decide the locations to deploy femto BSsand the subset of households each femto BS serves. On theother hand, determination of P and f can be considered as aresource management sub-problem to decide the transmissionpower of each femto BS and the fraction of resource to beallocated to each served household. We show in the follow-ing the proposed algorithm to solve the two sub-problemsin an iterative fashion.

4 INNER RESOURCE MANAGEMENTSUB-PROBLEM

Given the value of X (i.e. given a cluster structure), theinner resource management sub-problem is to determinethe optimal values of P and f. In addition, it needs to cal-culate the payoff of the given cluster structure to be used bythe outer cluster formation sub-problem for guided search.

4.1 Joint Power Control and Resource AllocationLet CS = {S1,S2, . . . ,Sm} be the given cluster structure withm clusters, where cluster Sj, j ∈ {1, 2, . . . , m}, is headed by afemto BS deployed at household lj ∈ Sj. Since the value ofX is known, the data rate constraint listed in Inequality (1)for household i in cluster Sj can be rewritten as:

fiW log2

(

1 + 1�

PjGji

WN0 +∑k �=j PkGki

)

≥ Ci, (11)

where Pj = Plj is the transmission power of femto BSj (at household lj) and Gji = Glj,i is the channel gainbetween household i and femto BS j. Similarly, the resourceallocation constraint in Inequality (4) can be rewritten as:

∑

i∈Sj

fi ≤ 1, ∀j ∈ {1, 2, . . . , m}. (12)

Note that for the given cluster structure, it is possiblethat no feasible solutions of Pj and fi exist that satisfy thepower and resource allocation constraints in Equalities (11)and (12). Therefore, it is up to the resource managementsub-problem to find whether the given cluster structureis feasible in the sense that the given households can besupported without violating constraints. In addition to fea-sibility check, it is desired that the resource managementsub-problem outputs the payoff of the given cluster structureas feedback to guide the outer cluster formation sub-problem forsearching the optimal cluster structure (that can support themaximum number of households). To achieve this goal, weset the payoff V(CS) = ∑m

i=1 |Si| − I(CS) to measure howgood the given cluster structure CS is if it is feasible (non-negative penalty I(CS) is zero only if CS is feasible). In thefollowing, we describe how we solve the resource manage-ment sub-problem while providing pertinent informationfor guided search.

4.2 An Iterative Algorithm for Power and AllocationUpdate

We propose an iterative update algorithm for finding theoptimal values of P and f for the given cluster struc-ture. Briefly, based on the interference that results fromthe power settings at iteration t − 1, each femto BS atiteration t updates its transmission power and resource allo-cation such that the minimum power is used for serving allhouseholds in its cluster. Updates of powers and resourceallocations proceed in iterations until the stopping criterionis met, where the payoff of the given cluster structure iscalculated as output to the cluster formation sub-problem.

More specifically, at iteration t, the minimal value of Pj(t)for femto BS j ∈ {1, 2, . . . , m} is obtained by solving the


Algorithm 1 Iterative power and resource allocation updateRequire: Cluster structure CS, parameters W, N0, PFEnsure: Feasibility claim, payoff V(CS), infeasibility I(CS),

hazard z(CS)

1: Power initialization, t: = 02: while

(∃j: �j(t) > ε1)

and(∃j: |Rj(t) − R(t)| > ε2

)do

3: Update femto BS powers by solving Problem (13)4: if (∃j: Pj(t) > PF) then5: Claim infeasible, and go to line 206: end if7: Update �(t), R(t), and R(t)8: t: = t + 19: end while

10: if (�(t) < ε1) then11: Pfinal: = P(t)12: else if

(R(t) converged to R(t) < 1

)then

13: Pfinal: = P(t) + R(t)�(t)1−R(t)

14: end if15: if

(�(t) < ε1 or R(t) converged to R(t) < 1

)and

(Pfinal ≤ PF) then16: Claim feasible17: else18: Claim infeasible19: end if20: Calculate V(CS), I(CS), and z(CS)

following optimization problem:

MinimizePj(t), fi

Pj(t),

subject toPj(t)Gji

�(

2Ci/(fiW)−1) ≥ WN0 + Ii(t − 1), ∀i ∈ Sj,

∑i∈Sj

fi ≤ 1,

0 ≤ Pj(t) ≤ PF,

(13)

where Ii(t − 1) = ∑k �=j Pk(t − 1)Gki is the interference at

iteration t − 1, and fi is the optimal fraction of resourceallocated to household i ∈ Sj. To solve for Pj(t), note that theminimum value occurs when all resource at the femto BS isexhaustively allocated such that

∑i∈Sj

fi = 1. Therefore, the

minimum power Pj(t) to use for femto BS j ∈ {1, 2, . . . , m}can be obtained by solving the following equation:

∑

i∈Sj

Ci/W

log2

(

1 + 1�

Pj(t)GjiWN0+Ii(t−1)

) = 1. (14)

Since the left-hand side of Equation (14) is convex andstrictly decreasing as Pj(t) increases, Pj(t) can be easilyobtained using the Newton or bisection method. We notethat given the transmission powers used in the last itera-tion, the optimization problem for each femto BS can besolved independently of any other femto BSs, and henceall femto BSs can perform the updates in parallel.

We show in Algorithm 1 the proposed iterative algo-rithm for solving the resource management sub-problem.After proper initialization of P(0), the algorithm at iterationt ≥ 1 updates Pj(t) for femto BS j by solving Equation (14).

Denote �j(t) = Pj(t) − Pj(t − 1) as the update step of femto

BS j, Rj(t) = �j(t)�j(t−1)

as the update ratio, and R(t) as the

average of Rj(t) among all m femto BSs at iteration t. Ifeither transmission powers or update ratios of all femtoBSs are converged (Line 2), the algorithm is stopped. Forthe former case (power converged) the final power is setto Pfinal = P(t), while for the latter case (ratio converged)Pfinal = P(t) + R(t)

1−R(t)�(t) if the average converged ratio

R(t) < 1. If Pfinal does not violate the maximum powerconstraint PF, the given cluster structure CS is declaredas feasible and the algorithm outputs penalty I(CS) = 0and payoff V(CS) = ∑

i |Si|. On the other hand, if Pfinalor P(t) during the update exceeds PF, or if the convergedratio R(t) ≥ 1, then CS is declared as infeasible and thealgorithm outputs penalty I(CS) = U(R(t)) based on anincreasing function U(·) and payoff V(CS) = ∑

i |Si|−I(CS).We explain in Section 5 how the cluster formation sub-problem uses the outputs of the algorithm for guided searchof the optimal cluster structure.

To understand the convergence property of the algo-rithm, note that P(t) can be written as a function of P(t−1)

such that P(t) = I(P(t − 1)), where I(·) is an “interfer-ence function.” It has been shown in [24] that if I(P) isstandard, then the iterative algorithm has the followingtwo properties: (i) P(t) will converge to a unique pointif there exists a feasible solution, and (ii) P(t) is a mono-tonically increasing sequence as t increases if we beginfrom P(0) = 0. We show in Appendix A (available online)that the iterative update (the while loop) in Algorithm 1is surely to terminate and it can be terminated immedi-ately if any P(t) exceeds PF without degrading the solutionquality.

5 OUTER CLUSTER FORMATIONSUB-PROBLEM

Based on the outputs from the inner resource managementsub-problem, the outer cluster formation sub-problem isto iterate over all candidate cluster structures to find thebest structure that maximizes the number of supportedhouseholds.

5.1 Coalition Structure GenerationThe process of grouping households into clusters is sim-ilar in concept to coalition structure generation (CSG) inthe literature. Given a set of agents, a coalition structureof size m is a partition of agents into m disjoint and exhaus-tive coalitions (groups). With the definition of the payoffV(CS) of a coalition structure CS, the CSG problem is tofind an optimal coalition structure (of any size) with themaximum payoff among the set of all possible coalitionstructures. The CSG problem has been shown to be NP-hard and many algorithms have been proposed for solvingthe problem [25]–[28].

Although the concept of coalition structure is similar tocluster structure in the target problem, there are notabledifferences: (i) There is no need to elect a “head” within acoalition in CSG, but it is essential in a cluster. The com-plexity increase due to the inclusion of cluster heads is


significant as we show in Appendix B (available online).(ii) CSG aims to partition the set of agents, but in the targetproblem it is possible that some households are excludedfrom the cluster structure due to the data rate constraints.We show in the following how we extend an algorithm forcoalition structure generation for solving the outer clusterformation sub-problem.

5.2 An Anytime Search AlgorithmSince searching for all cluster structures is practicallyimpossible, an anytime algorithm with controllable complexitythat can be interrupted at will to output a solution withinthe given time limit is desirable. We consider a stochasticlocal search algorithm, where the algorithm progressivelytraverses from one structure to its neighbor in a proba-bilistic fashion for finding the global optimal solution. Ananytime algorithm based on simulated annealing has beenproposed in related work for solving the CSG problem [29].While the algorithm has been shown to outperform otherapproaches, it cannot be directly applied for the target prob-lem but needs to be appropriately redesigned as follows.

Firstly, to define the neighborhood N (CS) for any clus-ter structure CS, related work for CSG has proposedseveral operators including split, merge, shift, extract, andexchange [28], [29]. In the target problem, however, theoptimal cluster structure must consist of exactly m femtoBSs. Given an initial structure of m clusters, the neighbor-hood operators hence should not change the total numberof clusters. In addition, it is possible that a householddoes not belong to any cluster for being unsupported. Wethus construct two new operators called add and discard tomove a unsupported household into and to move a sup-ported household out of a cluster respectively. To searchfor optimal cluster heads through neighbor traversal, wealso construct a third operator called rotate to change thelocation of the head within a cluster.

Secondly, since the CSG problem typically does not haveinfeasible structures, it suffices to consider the payoff V(CS)

for stochastic search. In the target problem, however, a clus-ter structure may be infeasible as claimed by Algorithm 1.We hence propose the use of a penalty metric I(CS) to avoidbeing stuck in infeasible solutions. Specifically, denote CSnas a chosen neighbor (to be detailed later) in N (CS) of thecurrent cluster structure CS. To decide if CSn is accepted toreplace CS for the next iteration, the following conditionsare considered based on V(CS), V(CSn), I(CS), and I(CSn)

as shown in Algorithm 2:

(1) If CS is feasible and CSn yields a better payoffsuch that V(CSn) > V(CS), then CSn is acceptedfor the next iteration. If CSn has a worse payoffthan CS, then it is still accepted with probabilitye(V(CSn)−V(CS))/t. The temperature t decreases witheach iteration according to an annealing schedulet: = αt with 0 < α < 1.

(2) If CS is not feasible but CSn is feasible, then CSn isobviously accepted. If both CS and CSn are infeasi-ble, then CSn is accepted if it is “less infeasible” suchthat I(CSn) < I(CS); otherwise (CSn is worse), CSnis still accepted with a probability e(I(CS)−I(CSn))/t.

Finally, to “guide” (expedite) the search for goodsolutions, we propose a hazard vector z(CS) as an additional

Algorithm 2 Solving the overall MINLP problemRequire: Iteration limit cmax, initial temperature tinit, cool-

ing ratio α

Ensure: Best cluster structure CSbest and best payoff vbest1: c: = 0, t: = tinit2: CS: = initial cluster structure, CSbest: = CS

3: Use Algorithm 1 to get V(CS), I(CS), and z(CS)

4: vbest: = V(CS)

5: while (c < cmax) do6: Randomly select CSn in N (CS) guided by z(CS)

7: Use Algorithm 1 to get V(CSn), I(CSn), and z(CSn)

8: if (CS is feasible and V(CSn) > V(CS)) or(CS is infeasible and CSn is feasible) or(both CS and CSn are infeasible and I(CS) > I(CSn))

then9: CS: = CSn

10: if (CSn is feasible and V(CSn) > V(vbest)) then11: CSbest: = CSn, vbest: = V(CSn)

12: end if13: else14: if (both CS and CSn are infeasible) then15: CS: = CSn with probability e

I(CS)−I(CSn)t

16: else17: CS: = CSn with probability e

V(CSn)−V(CS)t

18: end if19: end if20: c: = c + 1, t: = αt21: end while22: return CSbest, vbest

output from Algorithm 1. The hazard zj in z = [z1 z2 . . . zm]for femto BS j is defined as follows:

zj =m∑

k=1k �=j

∑

i∈Sk

fiPjGji

WN0 +∑mr=1 PrGri

. (15)

For femto BS j, it can incur interference on households ofother clusters, and the portion of interference on household

i ∈ Sk, k �= j, contributed by femto BS j isfiPjGji(

WN0+∑m

r=1 PrGri

) .

The “hazard” of femto BS j as defined in Equation (15) thuseffectively describes how bothering femto BS j is (from theperspective of households outside its cluster). Therefore,it can be used to guide (bias) the selection of the neigh-bor structure. The cluster to perform the discard operation,for example, can be chosen with a probability proportionalto its hazard value. In addition, once the target cluster ischosen, instead of randomly selecting a household to dis-card, the SINRs of individual households in the clustercan be used for a biased selection. Similar techniques canbe applied on the add and rotate operators for achievinga better solution quality within the designated number ofiterations. We show in Section 7 the performance of theproposed algorithm when z(CS) is used.

6 EXTENSION

We have thus far described the formulation and algorithmfor solving the femto BS deployment problem in Section 3.


In this section, we describe how the proposed approach canbe extended for solving variants of the problem.

6.1 Co-Channel DeploymentIn Section 3.2, the femtocell and macrocell are assumed touse orthogonal sub-channels, and hence inter-tier interfer-ence is not considered. In some scenarios, however, it mightbe desirable to adopt co-channel allocation for potentialspatial reuse. We present in this section how we solve forsuch a shared resource model.

Denote H = {1, 2, . . . , |H|} as the set of households andC = {C1, C2, . . . , C|H|} as the vector of data rate require-ments for all households as before. Let i = 0 be the macrouser served by the macro BS and C0 be its data rate require-ment. In addition, let P0 be the downlink transmissionpower of the macro BS to be decided with the followingconstraint:

0 ≤ P0 ≤ PM, (16)

where PM is the maximum transmission power of the macroBS. Since the macro user needs to be supported with a min-imum rate C0 by the macro BS, we have the following datarate constraint for the macro user (closed access mode):

W log2

(

1 + 1�

P0G00

WN0 +∑k∈H PkGk0

)

≥ C0, (17)

where G00 is the channel gain from the macro BS to themacro user and Gk0 is the channel gain from femto BSdeployed at lk ∈ H to the macro user. For each house-hold i ∈ H, since the macro BS incurs interference on thereceived signal, the SINR expressed in Equation (2) needsto be changed as follows:

γij = PjGji

WN0 + P0G0i +∑k∈Hk �=j

PkGki, (18)

where G0i is the channel gain from the co-channel macroBS to household i ∈ H. By replacing Equation (2) withEquation (18) and adding Constraint (17) for the macro useras well as Constraint (16) for the macro BS, the problem for-mulated in Section 3.2 for the dedicated resource model canbe translated into a problem for the shared resource model.

In the shared resource model, while only one additionalvariable (P0) is introduced, the challenge in solving the opti-mization problem is that the location of the macro user is notknown or fixed. That is, unlike the case for households wherethe locations are fixed and can be known before deploy-ment, the macro user that the macro BS serves may change astime proceeds. In this case, the channel gains G00 and Gk0 inConstraint (17) become variable for the optimization prob-lem. To address such a problem, one conceivable approachis to adopt a probabilistic approach by assuming the loca-tion distribution function of the macro user and then usesstochastic optimization (such as the chance-constrainedmodel) to ensure the probability that Constraint (17) failsfor the given stochastic geometry model is below a giventhreshold [30]. In this paper, however, we adopt a differentapproach to ensure that the data rate of any macro user in thetarget serving area of the macro BS is satisfied. While such anapproach may seem conservative as far as the deployment

strategy of the femto BSs is concerned, it can work irrespec-tive of the specific scheduling decision adopted by the macroBS under any condition.

To proceed, note that since the femto BSs are deployedto provide service to users in the household, we assumethe macro user to be outside the premises of each house-hold (e.g. outside the building). To ensure that the data raterequirement of the macro user is satisfied, Constraint (17)needs to be satisfied for any macro user located inside itsservice area:

Rc = R \|H|⋃

j=1

rj, (19)

where R is the coverage area of the macro BS and rj isthe premises area of household j. To solve the problem,note that since the macro user is served exclusively by themacro BS (closed access), the cluster formation sub-problemremains the same as the dedicated resource model (sincethe sub-problem concerns only how individual householdsare served by femto BSs). The resource management sub-problem as presented in Section 4, however, needs to bechanged. Nonetheless, by considering the macro BS as onespecial “femto BS” and the macro user as one of its serv-ing “households” populated in Rc, the solution can still bederived from the iterative update framework proposed inSection 4.

Specifically, at iteration t, each femto BS j ∈ {1, 2, . . . , m}updates its power and resource allocation vector by solvingProblem (13) as before, except for the change that the inter-ference becomes Ii(t − 1) = P0(t − 1)G0i +∑

k �=j Pk(t − 1)Gkito include the additional interference from the macro BS.The macro BS also updates its transmission power P0(t) toensure that any macro user in its coverage area meets theminimum data rate constraint C0 as follows:

P0(t) = �(

2C0/W − 1)

· max

{WN0 +∑m

j=1 Gj0Pj(t − 1)

G00

}

,

(20)

where the maximum is taken over all locations in Rc spec-ified in Equation (19). Since the transmission powers andlocations of all femto BSs are known, the channel gain Gj0and G00 can be expressed as functions of the unknown loca-tion (x, y) ∈ Rc of the macro user. Hence, the macro BSpower can be obtained by finding the values of x and ythat maximize Equation (20). After the transmission pow-ers of the macro BS and all femto BSs are updated, thealgorithm proceeds to the next iteration until it is stoppedas described in Algorithm 1 earlier.2

We note that while we have described a closed accessmode for the shared resource model, it is possible to extendto an open access mode if so desired. In the open accessmechanism, the macro user can be served through either

2. We note that at each iteration, the location of the macro user withthe lowest SINR may change. However, this is similar to the case thateach femto BS at each iteration needs to update its power to accom-modate the data rate requirement of the household with the lowestSINR (of which the location also changes over iterations.) Hence, theconvergence property for the shared resource model follows that forthe dedicated resource model proved in Appendix A (available online)similarly.


the macro BS or any nearby femto BS depending on theprovided data rate. To serve the macro user, however,each femto BS needs to reserve a portion β, 0 ≤ β ≤ 1,of its resource for use by the macro user. The data raterequirement in open access thus can be written as follows:

min0≤j≤m

βjW log2

⎛

⎜⎝1 + 1

�

PjGj0

WN0 +∑mk=0k �=j

PkGk0

⎞

⎟⎠ ≥ C0, (21)

where P0 = P0, G00 = G00, β0 = 1, and βj = β for 1 ≤ j ≤ m.Similar to closed access, this problem can be solved byadding Equation (20) in the power update algorithm, withthe change that the maximum is taken over a reducedarea Ro instead of Rc. More specifically, at iteration t, afterthe powers of all femto BSs have been updated as before,the coverage area Rj of each femto BS j ∈ {1, 2, . . . , m} isupdated to include the locations where femto BS j can pro-vide a macro user with the desired data rate requirementC0. Afterwards, the service area Ro of the macro BS can bewritten as

Ro = Rc \m⋃

j=1

Rj. (22)

The macro BS then applies Equation (20) to meet the datarate requirement of the macro user with the lowest SINRin Ro.

In such an open access mode, if the reserved resourceβ = 0, Constraint (21) essentially reduces to Constraint (17)for the closed access mode. If β > 0, the capability of eachfemto BS to serve its households is reduced since

∑

i∈HfiXij ≤ 1 − β, ∀j ∈ H. (23)

However, the potential benefit is that the macro BS can use asmaller transmission power (owing to a smaller service areaRo), thus resulting in lower interference to the households.We show in Section 7 the performance trade-offs betweenthe dedicated resource model and shared resource model(closed and open access) for femto BS deployment.

6.2 Post-Deployment OptimizationAs Section 3.1 describes, the problem we consider is todeploy femto BSs for providing the data rates subscribedby households in the neighborhood. While any networkdeployment needs to start with some initial planning [15],[31], [32], it is possible that the demand (e.g. the set ofhouseholds or subscription rates) is changed (possibly inthe time span of months) after the femto BSs have beendeployed. In this case, a possibly different yet optimal setof femto BSs can be solved for the new demand (describedby the new set of households H and the data rate vectorC). However, since physical installation of femto BSs incursmore overheads than internal reconfiguration of femto BSs(e.g. changing the powers or service sets), it might not bedesirable to change the locations of deployed femto BSsfrequently for any slight change in the network scenario.We discuss in this section how the proposed approachaddresses such a problem after initial deployment has beenmade.

In solving the cluster formation sub-problem inSection 5, optimal locations of femto BSs are determinedthrough a stochastic traversal of cluster structures from aninitial structure. While the neighborhood operators add, dis-card, and rotate allow an initial structure to traverse to anyother structures, it is possible to confine the search space toensure that the final cluster structure meets the desiredproperty. More specifically, assume initially that a set offemto BSs have been optimally deployed at householdslj ∈ H based on a given topology H and rate requirementsC. After the scenario has been changed to H′ and C′, wepropose to find the solution for the new scenario by usingAlgorithm 2 as before but with the following modifications:

(1) Initial input: The current cluster structure is used asthe input to the algorithm.

(2) No rotate operator: Starting from the initial structureCS, its neighbor N (CS) can be reached only throughthe add and/or discard operators.

The maximum number of households that can be sup-ported through reconfiguration (e.g. change of transmissionpowers or service sets) of the deployed femto BSs can beobtained as the output of the algorithm. If any householdis left unsupported, then it is necessary to deploy addi-tional femto BSs to serve those households. In this case, wefirst calculate the sum of excess demands ej for each deployedfemto BS j ∈ {1, 2, . . . , m} as follows:

ej =∑

i

C′i − Ci

W log2

(1 + 1

�γij

) , (24)

where C′i is the new data rate, γij is the received SINR of

household i, and the summation is over all households forwhich femto BS j provides the largest SINR. The householdwith the largest excess demand in the cluster with the largestvalue of ej is chosen as the initial location to deploy theadditional femto BS. Then, Algorithm 2 is executed again,where the new femto BS is allowed to be rotated to anotherhousehold (while keeping the locations of existing femtoBSs intact) for finding the optimal deployment location.

Note that since we disallow femto BSs lj ∈ H alreadydeployed to be rotated, the final cluster structure could besub-optimal (possibly requiring more number of femto BSs)compared to the case where all femto BSs can be freelyrotated. Despite, since our formulation aims to minimizethe number of femto BSs to serve all households, such anincremental deployment strategy could still achieve compara-ble performance as we show in Section 7. It is possible that aselected subset of deployed femto BSs are allowed to rotateif there is a significant change in topology H or demandC, but it is up to the network operator to strike a bal-ance between re-deployment cost and overall deploymentefficiency.

6.3 Discrete Allocation of Resource BlocksIn determining the fraction of resource to be allocated toeach served household, the variable fi as introduced inInequality (4) is assumed to be continuous. In the contextof OFDMA resource allocation, however, each householdshould be allocated an integer multiple of resource blocksand hence fi should be discrete. In this case, let B be the


Fig. 2. Progression of power update for a given cluster structure with 15femto BSs.

total number of resource blocks in an allocation period, andf ′i ∈ Z be the number of resource blocks allocated to house-

hold i. Problem (13) for resource allocation within clusterj ∈ {1, 2, . . . , m} can now be rewritten as follows:

MinimizePj(t), f ′

i ∈Z

Pj(t),

subject toPj(t)Gji

�

(

2CiB/(f ′i W)−1) ≥ WN0 + Ii(t − 1), ∀i ∈ Sj,

∑i∈Sj

f ′i ≤ B,

0 ≤ Pj(t) ≤ PF.

(25)

To solve this problem, we first solve Problem (13) to getfi and set f ′

i = ⌊Bfi⌋

. For each of the remaining B −∑i∈Sj

f ′i

resource blocks, the household k ∈ Sj in cluster j that hasthe lowest achievable data rate is allocated an extra resourceblock, where

k = arg maxi

�(

2CiB/(f ′i W) − 1

)

Gji(WN0 + Ii(t − 1)) . (26)

The process continues until all available resource blocks areallocated. Note that allocating the extra resource block tothe constraining household allows the transmission powerPj(t) of femto BS j to be further reduced. We show theimpact of discrete allocation on the overall performance inSection 7.

7 PERFORMANCE EVALUATION

To evaluate the performance of the proposed approach,we randomly distribute 250 households in an area. Thedensity of the households thus deployed is about 6329households per square kilometer to stress-test a hyper-dense, interference-limited scenario [13], [33]. Based on thesimulation settings in [34], [35], the maximum transmis-sion powers of the macro BS and the femto BS are set toPM = 46 dBm and PF = 20 dBm respectively. The path lossis set to 131.1 + 42.68 log(d) dB for a distance separationof d kilometers. We assume that femto BS are deployedoutside the household (e.g. rooftop), and hence an addi-tional −3 dB wall penetration loss is added to the path lossmodel for indoor receivers [20]. We set the channel band-width W = 10 MHz, noise PSD N0 = −174 dBm/Hz, and

Fig. 3. Benefits of using the hazard metric for guided stochastic search.

the SINR gap � = 1 in Inequality (1) for calculating theachievable data rate. The rest of the simulation parametersfollow the settings in the 3GPP specification [34]. To com-pare closed access and open access modes, we note that theaverage size of households in the world varies from 76.0 m2

(United Kingdom) to 214.6 m2 (Australia) as shown in [36].Therefore, the premises area of each household (macro userprohibition zone) used in Equation (19) is modeled as a circlewith a minimum radius d = 5 m.

7.1 Evaluation of the Proposed AlgorithmWe first investigate the performance of the proposed algo-rithm for solving the resource management and clusterformation sub-problems. We then show the computationcomplexity compared to baseline approaches.

7.1.1 Iterative Update for the Resource ManagementSub-Problem

To observe the convergence property of the iterative updatealgorithm in Algorithm 1, we show in Fig. 2 a particulartrace of the power update progress for a given cluster-ing structure with 15 femto BSs. For the case with equalresource allocation (labeled “PC only”), only transmissionpowers of individual femto BSs need to be updated. It canbe observed that there is no feasible setting of transmissionpowers for the given structure as the maximum power con-straint is violated for some femto BS after 6 iterations. Onthe other hand, if resource allocation together with trans-mission power can both be optimized (labeled “PC+RA”),it becomes possible to support the given cluster structureas indicated by the converged ratio of the update step withR(t) < 1. (The final power and allocation vectors can bedetermined after only 6 iterations.) In addition, it can beobserved from the figure that, compared to the case of equalresource allocation, allowing resource allocation to be opti-mized can reduce the transmission powers of all femto BSs forsupporting the same number of households.

7.1.2 Guided Search for the Cluster FormationSub-Problem

To investigate the performance of the anytime search algo-rithm in Algorithm 2, we show in Fig. 3 the requirednumber of iterations with or without the use of hazard


Fig. 4. Computation time of the proposed algorithm. A unit computationtime is defined as the time needed for the approach labeled as “Coalitionstructure” to solve a scenario of 20 households.

defined in Equation (15). Specifically, we focus on the dis-card operator, where a target cluster (to perform discard) israndomly selected with equal probability if hazard is notused [29]; if hazard is used, on the other hand, a targetcluster is randomly selected with a probability value pro-portional to the hazard of the cluster head. It is clear fromthe figure that the solution quality and the required num-ber of iterations are significantly improved with the use ofhazard. For example, for the case with 6000 iterations, 4741iterations (79.0%) find feasible CSs with the use of hazard;only 3366 iterations (56.1%) find feasible CSs without theuse of hazard. The reason is that the use of hazard can avoidconsecutive long, inefficient discards that take too manyiterations to get back to the feasible region from infeasiblesolutions.

7.1.3 Runtime Complexity of the Overall AlgorithmTo compare the computation complexity of the proposedtwo-stage algorithm against baseline approaches, we con-sider an instance of the algorithm including joint powercontrol and cluster formation (i.e., equal resource allocationamong all households served by a femto BS). We compareagainst several baseline approaches for solving the MINLPproblem formulated in Section 3 as follows:

(a) MINLP: Use of an MINLP solver (bonmin) to solvethe MINLP problem directly [37];

(b) MIP: Use of an MIP (mixed-integer linear program-ming) solver (CPLEX) to solve the problem afterproper linearization of nonlinear constraints such asInequality (1) as shown in [38].

(c) Coalition Structure: Use of a two-stage algorithmsimilar to Algorithm 2 but based on the conceptof the coalition structure instead of the clusterstructure [38].

We measure computation complexity as the computa-tion time for each approach to solve a problem normalizedto the time used by the “Coalition Structure” approach tosolve a problem with 20 households. It is clear from Fig. 4that directly solving the MINLP problem incurs significantcomputation complexity. While linearizing the nonlinearconstraints into an MIP problem helps reduce the compu-tation time, the complexity still increases drastically as the

Fig. 5. Supporting ratio vs. data rate requirement of each household.The number of femto BSs is fixed at 50 and each data point is anaverage over 10 random topologies.

number of households increases. The two-stage algorithmbased on the conventional coalition structure shows notice-able reduction in complexity. However, it is still limitedby the requirement to solve the MIP power control sub-problem [38]. On the other hand, it can be observed thatthe proposed algorithm has a very low complexity com-pared to other approaches without notable degradation insolution quality (attaining an objective value at least 98%of the best solutions obtained by using other approachesfor all scenarios in the figure). Hence the proposed algo-rithm including problem decomposition, iterative update, andguided stochastic search is much more efficient and scalablecompared to baseline approaches.

7.2 Performance Gain for Joint OptimizationTo substantiate the benefits of joint optimization for deploy-ing femto BSs, in the following we first compare theproposed approach against different alternatives and thenshow the impact of discrete resource allocation.

7.2.1 Minimum Data Rate SupportWe consider the following five alternative approaches fordeploying femto BSs:

(a) Baseline: Locations of femto BSs are pre-determinedby using the k-means method [39], and householdsselect the serving femto BSs based on the receivedsignal strength, where the transmission power of afemto BS is set to PF [40].

(b) CF+PC (no head rotation): Locations of femto BSsare pre-determined by using the k-means method,and Algorithm 2 is used for femto BSs to decidetransmission powers and for households to selectserving femto BSs. In other words, Algorithm 2 isused with neighborhood operators {add, discard} (norotate) and equal resource allocation.

(c) CF+PC: Locations and transmission powers offemto BSs as well as household selections of serv-ing femto BSs are optimally decided by runningAlgorithm 2 (but with equal resource allocation).

(d) CF+PC+RA (no head rotation): Same as (b) but withresource allocation optimization.


Fig. 6. Comparison of continuous allocation (fi is continuous) and dis-crete allocation (fi is discrete such that each household gets an integernumber of the resource blocks).

(e) CF+PC+RA: Same as (c) but with resource allocationoptimization (i.e., the proposed approach).

Fig. 5 compares the performance of the five approachesas the data rate requirement varies. It can be observed thatwith the proposed approach almost all households can besupported up to 6 Mbps data rate when 50 femto BSs aredeployed. The baseline approach without joint optimiza-tion, on the other hand, can support 250 households eachwith less than 1 Mbps rate. While deploying more femtoBSs can increase the performance of all approaches, giventhe data rate requirements of households, the proposedapproach can significantly reduce the minimum number offemto BSs.

7.2.2 Impact of Discrete AllocationTo investigate the impact of discrete allocation, Fig. 6 showsthe performance when each household is allocated an inte-ger multiple of resource blocks. It can be observed thatas the total number of resource blocks B in Problem (25)increases from 30 to 480, the performance of discrete allo-cation approaches that of continuous allocation. In a typicalconfiguration where the length of a resource block is on theorder of 1 ms, and the period of allocation is on the orderof 1s (or more), the solution obtained by assuming con-tinuous allocation is a good approximation to the actualsolution based on discrete allocation.

7.3 Post-Deployment OptimizationAs we have described in Section 6.2, it might not bedesirable to change the locations of femto BSs frequentlyonce they are deployed. In the following, we investigatethe performance of the proposed approach for incrementaldeployment under changes in the data rate requirement Cand the set of household H respectively.

7.3.1 Change in the Data Rate RequirementWe consider a scenario where initially 250 households havethe same data rate requirements of 3 Mbps and the opera-tor determines the optimal number and locations of femtoBSs as before. Afterwards, a subset of households are ran-domly selected to increase the subscription rate to 4 Mbps.The optimal solutions that allow completely different sets

Fig. 7. Performance of incremental deployment as the number ofhouseholds with data rate change (from 3 Mbps to 4 Mbps) increases.

of femto BSs to be deployed can be obtained by run-ning Algorithm 2 anew, where the numbers of femto BSsrequired for different scenarios are shown in Fig. 7. Thenumber of femto BSs required under incremental deploy-ment (the original set of femto BSs is retained) as describedin Section 6.2 is also obtained for comparison.

As we observe from the figure, when the number ofhouseholds with increased traffic demand is less than20, it is possible to re-configure existing femto BSs (e.g.through power adjustment, resource re-allocation, andcell re-association) without adding new femto BSs. Whileincreasing transmission powers of femto BSs for meetingthe increased demand may result in decreased SINR (espe-cially to those households far away from serving femtoBSs), a closer look of the solution reveals that the fractionof resource allocated by each femto BS to those house-holds increases, at the expense of reduced allocations tohouseholds closer to each femto BS. Still, support ratiodoes not change (the household with the minimum SINR isnot dropped) as long as such resource re-allocation insideeach cluster is possible. If the number of households withincreased demand keeps increasing, it becomes necessaryto deploy additional femto BSs. In this case, it is clear thatincremental deployment requires more femto BSs comparedto the optimal solution. As the figure shows, however,the gap is still moderate, where the number of femto BSsneeded is 43 and 45 for incremental and optimal deploy-ment respectively when almost half of the households showincreased demand. In addition, we find that, for the sce-nario of 30 households with increased demand, the optimalsolution requires a total of 38 femto BSs (including 3 newfemto BSs), but only 9 femto BSs remain at the same loca-tions while the other 26 femto BSs are moved to differentlocations. In contrast, incremental deployment requires onemore femto BS (a total of 4 new femto BSs), but the existing35 femto BSs are kept at their initial locations, thus avoidingthe cost of re-deployment.

7.3.2 Change in Network TopologyIn addition to change in the subscription data rate, wealso investigate the impact when the set of householdsto serve changes after initial deployment. We start with ascenario with 250 households and 3 Mbps service rate asbefore. After femto BSs have been optimally deployed, we


Fig. 8. Performance of incremental deployment as additional house-holds are added to the network topology.

randomly distribute from 0 to 60 new households to the net-work (each with a data rate of 3 Mbps). Fig. 8 thus showsthe difference between the optimal solution and incremen-tal deployment. It can be observed that the results aresimilar to Fig. 7, meaning that it is possible to minimize theoverheads of re-deploying femto BSs through incrementaldeployment. The reason for not increasing the number ofrequired femto BSs as additional households are added (e.g.the flat region between 10 and 30 households) is similar tothe case shown in Fig. 7. While re-configuration of femtoBSs may result in reduced excess data rate for some house-holds as Fig. 8 shows, no additional femto BSs are requiredas long as all households can be provided with the mini-mum data rates. We conclude that incremental deploymentis an effective measure for post-deployment optimization.

7.4 Dedicated vs. Shared Resource ModelsWe have so far focused on the dedicated resource modelwithout inter-tier interference. We show in this section theperformance comparison between dedicated and sharedresource models following the discussion in Section 6.1.

7.4.1 Setup for Supporting the Macro UserWe assume the macro user is outdoor that can be locatedanywhere inside the area Rc defined in Equation (19). Theobjective is to support the macro user with rate C0 inaddition to the set of households with minimum data raterequirements by using one of the following three models:

(a) Dedicated Resource Model: The total bandwidth Wis divided into two orthogonal portions: the macroBS uses βW while the femto BSs use (1−β)W, where0 ≤ β < 1. To ensure that the macro user is sup-ported, β is a function of the macro BS power P0 asfollows:

β ≥ C0

W log2

(

1 + P0G†00

�WN0

) , (27)

where G†00 is the channel gain between the macro

BS and the farthest point inside the macro BS ser-vice area Rc (i.e. the point on the cell boundary).While the macro BS can use any power withoutinterfering with the femto BSs, for fair comparison,

Fig. 9. Comparison of the dedicated and shared (open and closedaccess) resource models as the amount of resource reserved for themacro BS varies.

we do not assume the macro BS to use the max-imum transmission power PM; the average powerlevel obtained in the shared model (closed access)is used for determining β in the dedicated modelinstead.

(b) Shared Resource Model (Closed Access): The macroBS and all femto BSs share the same bandwidth W,and the macro user can be served only by the macroBS. The optimal transmission powers of the macroBS and all femto BSs are obtained as described inSection 6.1.

(c) Shared Resource Model (Open Access): The setupis similar to (b), except that the macro user can beserved through either the macro BS or any nearbyfemto BS. As described in Section 6.1, the abilityof each femto BS to serve the macro user dependson the portion of resource βW reserved. We vary β

during simulation to see its impact on performance.

7.4.2 Impact of Resource Division RatioWe randomly distributed 250 households in the networkand the data rate of each household is set to 3 Mbps asbefore. The data rate requirement of the macro user is set to300 kbps by following similar settings in [20]. The effectiveradius of the household premises area used in Equation (19)is set to d = 8 m, which corresponds approximately to thesize of households (201.5 m2) in the United States [36]. Thetotal bandwidth W is shared between femto BSs and themacro user and we vary the proportion of bandwidth βWreserved for the macro user for investigating the performancedifference between different deployment models. As Fig. 9shows, in the dedicated resource model, initially 35 femtoBSs are sufficient for supporting all households. However,as the bandwidth (1−β)W allocated to femto BSs decreases,the support ratio decreases. The numbers shown besides thecurve for the dedicated resource model are the minimumtransmission powers of the macro BS (under different allo-cated bandwidths) for serving the macro user with the targetdata rate. For example, if the macro BS has a transmissionpower of 0 dBm, then less than 10% bandwidth is neededfor serving the macro user with the target data rate.

For the shared resource model, the closed access modedoes not require femto BSs to reserve bandwidth for serving


Fig. 11. Visualization of the cluster structures for femto BS deployment under different resource allocation models. (a) Dedicated Model. (b) SharedModel (Closed Access). (c) Shared Model (Open Access).

the macro user, so the curve is flat. Due to interference fromthe macro BS, however, its support ratio is lower than thededicated model in the target scenario. For the open accessmode, on the other hand, variation of β shows an interest-ing impact on its performance. Note that when β = 0, openaccess degrades to closed access since no femto BSs canserve the macro user. With sufficient amount of resourcereserved at femto BSs, the macro user can potentially beserved by a nearby femto BS, and hence the transmissionpower of the macro BS can potentially be reduced due tothe reduced service area in Equation (22). In this way, sincethe interference on femto BSs are reduced accordingly, thesupport ratio for households can increase. However, as β

keeps increasing, the household support ratio starts to fallas the impact of bandwidth reduction (for femto BSs) out-weigh the impact of interference reduction from the macroBS. When the resource reserved for households is lowerthan 62%, for example, the support ratio in open access fallsbelow that of closed access. Despite, it has to be noted thatopen access as described in Section 6.1 actually allows morethan one macro user to be supported in the network (eachby a nearby femto BS with sufficient resource). For example,it has been observed that the total number of macro usersthat can be supported with rate C0 = 300 kbps increasesfrom 7 to 29 as β increases from 5% to 10% (saturated at 36for β ≥ 20%). Therefore, the open access mode could havebetter performance gain from the perspective of total datarates (throughputs) supported per unit bandwidth. Furtherinvestigation of this topic, however, is beyond the scope ofthis paper.

Fig. 10. Impact on different resource models as the effective servicearea of the macro BS varies.

7.4.3 Impact of the Macro BS Service AreaFor the shared resource model, the transmission power ofthe macro BS is dependent on the size of its service areawhere the macro user may appear. To show the impact ofrestricting the macro user in different service areas, we varythe radius of the premises area such that the macro user islimited to be at least d meters away from each femto BS.Fig. 10 thus compares the performance of the three mod-els when 20% of bandwidth is reserved for the macro BS. Itcan be observed that as the “prohibition zone” of the macrouser increases, the household support ratio for the closedaccess mode increases significantly due to the reduction inthe transmission power of the macro BS (from 49 dBm to25 dBm as d increases from 5 to 15). While the support ratiofor the open access mode also increases, the improvementis less pronounced compared to closed access. The reasonis that as d increases, the performance gain of open accessfor allowing femto BSs to serve the macro user decreases(the macro user is effectively farther away from the femtoBS as d increases). Therefore, the reserved bandwidth atfemto BSs becomes a pure minus to the support ratio with-out yielding positive gain. At d = 12 m and beyond, thesupport ratio of open access is lower than that of closedaccess. While we do not delve into details of the perfor-mance trade-offs, we do show that the proposed approachcan provide a unified framework for comparing the performanceof different resource allocation models.

7.4.4 Contours of SupportFinally, we show the snapshots of the cluster structuresunder different resource models in an arbitrary network.For ease of comparison, the locations of femto BSs in allthree models are kept the same and only a square area oflength 140 m around the macro BS is shown. In additionto the support status of each household, a contour of sup-port is also plotted for each cluster that shows how thehousehold with the minimum SINR in each cluster can bemoved without being dropped by the femto BS. As shownin Fig. 11, the dedicated model has the highest supportratio (0.96), while closed access has the lowest (0.75). Dueto inter-tier interference from the macro BS, several house-holds far from individual serving femto BSs are dropped(marked as red rectangles) as we move from the dedicatedmodel (a) to the shared closed access model (b). Some ofthese households are salvaged in the shared open accessmodel due to the reduction in the transmission power of


the macro BS. Reduction of the macro BS interference canalso be inferred from the figure since the contours of sup-port for some femto BSs (especially for those closer to themacro BS) are expanded as we move from closed access (b)to open access (c). The proposed optimization frameworkthus provides a useful tool for femto BS deployment in anyarbitrarily given network.

8 CONCLUSION

In this paper, we have formulated a joint optimizationproblem for femto BS deployment, including location selec-tion, cell association, power control, and resource allocation,to serve a set of households with minimum rate require-ments. Since the formulated problem belongs to MINLP,we have proposed an anytime two-stage algorithm for solv-ing the problem with reduced complexity. We have shownthrough simulation results that the proposed algorithmcan effectively solve the target problem compared to base-line approaches. Finally, we have shown that the proposedformulation and algorithm can be extended for differentresource allocation models as well as post-deployment opti-mization. The proposed approach thus provides a unifiedand useful tool for optimizing femto BS deployment inarbitrary two-tier femtocell networks.

ACKNOWLEDGMENTS

This work was supported in part by funds from theNational Science Council, National Taiwan Universityand Intel Corporation under Grants NSC-102-2219-E-002-009, NSC-102-2911-I-002-001, NTU-103R7501, and NTU-103R890842.

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Hung-Yun Hsieh received the Ph.D. degreein electrical and computer engineering fromGeorgia Institute of Technology, Atlanta, GA,USA. He is currently an Associate Professorin the Department of Electrical Engineeringand Graduate Institute of CommunicationEngineering, National Taiwan University, Taiwan.His current research interests include wirelesscommunications and mobile computing.

Shih-En Wei received the M.S. degree in com-munication engineering from National TaiwanUniversity, Taiwan, in 2012. His current researchinterests include computer networks and algo-rithms.

Cheng-Pang Chien is currently a M.S. stu-dent a the Graduate Institute of CommunicationEngineering, National Taiwan University, Taiwan.His current research interests include wirelesscommunications.

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