distributed power and channel allocation for cognitive...

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 4, APRIL 2017 3475

Distributed Power and Channel Allocation forCognitive Femtocell Network Using a Coalitional

Game in Partition-Form ApproachTuan LeAnh, Nguyen H. Tran, Member, IEEE, Sungwon Lee, Member, IEEE, Eui-Nam Huh, Member, IEEE,

Zhu Han, Fellow, IEEE, and Choong Seon Hong, Senior Member, IEEE

Abstract—The cognitive femtocell network (CFN) integratedwith cognitive-radio-enabled technology has emerged as one ofthe promising solutions to improve wireless broadband coveragein indoor environments for next-generation mobile networks. Inthis paper, we study a distributed resource allocation that consistsof subchannel- and power-level allocation in the uplink of thetwo-tier CFN comprised of a conventional macrocell and multi-ple femtocells using underlay spectrum access. The distributedresource allocation problem is addressed via an optimization prob-lem, in which we maximize the uplink sum rate under constraintsof intratier and intertier interference while maintaining the aver-age delay requirement for cognitive femtocell users. Specifically,the aggregated interference from cognitive femtocell users to themacrocell base station (MBS) is also kept under an acceptablelevel. We show that this optimization problem is NP-hard andpropose an autonomous framework, in which the cognitive femto-cell users self-organize into disjoint groups (DJGs). Then, insteadof maximizing the sum rate in all cognitive femtocells, we onlymaximize the sum rate of each DJG. After that, we formulatethe optimization problem as a coalitional game in partition form,which obtains suboptimal solutions. Moreover, distributed algo-rithms are also proposed for allocating resources to the CFN.Finally, the proposed framework is tested based on the simulationresults and shown to perform efficient resource allocation.

Index Terms—Coalitional game, cognitive femtocell network(CFN), game theory, power allocation, resource allocation, sub-channel allocation.

I. INTRODUCTION

IN recent years, the number of mobile applications de-manding high-quality communications has tremendously

increased. For instance, high-quality video calling, mobilehigh-definition television, online gaming, and media-sharing

Manuscript received October 31, 2014; revised February 6, 2016; acceptedFebruary 20, 2016. Date of publication March 1, 2016; date of current ver-sion April 14, 2017. This work was supported by Basic Science ResearchProgram through National Research Foundation of Korea (NRF) funded bythe Ministry of Education (NRF-2014R1A2A2A01005900). The review ofthis paper was coordinated by Dr. F. Gunnarsson. (Corresponding author:Choong Seon Hong.)

T. LeAnh, N. H. Tran, S. Lee, E.-N. Huh, and C. S. Hong are with theDepartment of Computer Science and Engineering, Kyung Hee University,Yongin 446-701, South Korea (e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]).

Z. Han is with the Department of Electrical and Computer Engineering,University of Houston, Houston, TX 77004-4005 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2016.2536759

services always have connections with high-quality of services(QoS) requirements among devices and service providers [1].To adapt to these requirements, the Third-Generation Partner-ship Project (3GPP) Long-Term Evolution Advanced (LTE-Advanced) standard has been developed to support higherthroughput and better user experience. Moreover, to accom-modate a large amount of traffic from indoor environments,the next mobile broadband network uses the heterogeneousmodel, which consists of macrocells and small cells [2], [3]. Thesmall-cell model (such as femtocells) is one way of increasingcoverage in dead zones in indoor environments, reducing thetransmit power and the size of cells and improving spectrumreuse [4], [5].

In practice, a two-tier femtocell network can be implementedby spectrum sharing between tiers, where a central macrocellis underlaid with several femtocells [6]. This network modelis also called the cognitive femtocell network (CFN) [7], [8].The CFN can be deployed successfully and cost-efficientlyvia two different spectrum-sharing paradigms: overlay andunderlay [8]–[10]. The overlay access paradigm enables thecognitive femtocell user equipment (CFUE, secondary user)to transmit their data only in spectrum holes where macrocellusers (primary users) are not transmitting. A CFUE vacates itschannel if it detects an occupancy requirement of macro userequipment (MUE). In the underlay access, CFUEs are allowedto operate in the band of the macrocell network, whereas theoverall interference from CFUEs occupancy on the same chan-nel should be kept below a given threshold. Moreover, in thisparadigm, entities in CFN are assumed to have knowledge ofthe interference caused by transmitters in the macrocell network[6], [9]. In this paper, we focus on the resource allocationin underlay CFN where the channel usages are based on theunderlay cognitive transmission access paradigm [6], [8], [11].

In the CFN deployment, interference is a major challengecaused by overlapping area among cells in a network area andcochannel operations. The interference can be classified as:intratier (interference caused by macro-to-macro and femto-to-femto) or intertier (interference caused by macro-to-femtoand femto-to-macro) [12], [13]. Specifically, the intertier in-terference, which is caused by using the underlay spectrumaccess, needs to be considered to protect the macrocell network[6]. To mitigate interference, some works have studied thedownlink direction [12], [14]–[16]. Suppression of intratier in-terference using the coalitional game is studied in [12]. In [14],

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3476 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 66, NO. 4, APRIL 2017

a frequency-division multiple access (FDMA) is employed interms of the area spectral efficiency and subjected to a sensibleQoS requirement. The power and subcarrier allocations fororthogonal FDMA (OFDMA) femtocells based on underlaycognitive radios in a two-tier network are mentioned in [15]. Aself-organization strategy for physical resource block allocationwith QoS constraints to avoid cochannel and cotier interferenceis investigated in [16]. However, the CFN uplink using the un-derlay paradigm is also an important challenge that needs to beconsidered [3]–[5]. In the uplink direction, the uplink capacityand interference avoidance for two-tier femtocell network weredeveloped in [7]. In [17], an interference mitigation was pro-posed by relaying data for macro users via femto users, basedon the coalitional game approach and leasing channel. Thepower control under QoS and interference constraints in femto-cell networks was studied in [18]. The distributed power controlfor spectrum-sharing femtocell networks using the Stackelberggame approach was presented in [6]. However, most of theaforementioned works only focus on single-channel operationand do not mention the channel allocation to the femto users.In [19], the uplink interference is considered in OFDMA-basedfemtocell networks with partial cochannel deployment withoutthe power control of femtocell users. Additionally, channelallocations are based on an auction algorithm for macrocellusers and femtocell users. Clearly, the channel allocation in [19]is not efficient where users can reuse the channels by powercontrol, as in [6] and [18].

In this paper, we study an efficient distributed resourceallocation for the CFN uplink in two-tier networks to overcomethe drawbacks of the existing literature. The efficient distributedresource allocation in the multiple-channel environment is rep-resented by solving an optimization problem. The objective ofthis optimization problem is the uplink sum rate. The intratierand intertier interference are considered with constraints inthe optimization problem. Additionally, the guaranteed averagedelay requirements are at the minimum for the connected cog-nitive femtocell users, and the total interference at the macrocellbase station (MBS) is kept under acceptable levels as well. Weshow that this optimization problem is an NP-hard optimizationproblem. Motivated by the design of self-optimization networks[4], [5], [8], [20], we propose a self-organizing framework inwhich CFUEs self-organize into disjoint groups (DJGs). Bydoing so, instead of maximizing the sum rate in whole cognitivefemtocells, we only maximize the sum rate of each DJG wherethe computation of the original optimization is decomposed tothe formed DJGs. Then, to solve the optimization problem ateach DJG, we formulate this optimization problem as a coali-tional game in the partition form, which obtains near-optimalsolutions along with efficient resource allocation in a distributedway. The coalitional game is defined by a set of players who arethe decision-makers seeking to cooperate to form a coalitionin a game [12], [21]. One kind of game expression is thecoalitional game in the partition form that captures realistic in-tercoalition effects in many areas, particularly in wireless com-munication networks [21], [22]. In this paper, CFUEs can joinand leave a coalition to obtain the maximum data rate (denotedby individual payoff). The joining and leaving of CFUEs haveto satisfy some constraints of the aforementioned optimization

problem. Specifically, the proposed game is solved based onthe recursive core method [21], [22]. Throughout this method,the stability of the coalition formation is a result of the optimalchannel and power allocation. The optimal power allocationto CFUEs corresponding to the network partition is obtainedfrom sharing payoffs of CFUEs in a coalition. The geometricprogramming and dual-decomposition approaches, which arebased on [18], [23]–[25], are proposed to determine the optimalpower allocation in the coalition. Simulation results show thatthe proposed framework can be implemented in a distributedmanner with an efficient resource allocation. Furthermore, thesocial welfare of the usable data rate in CFN under our solutionis also examined via our simulation results. In addition, we alsoestimate the gap between the global optimal solution and thesuboptimal solution using proposed cooperative approach.

The main contributions of this paper are summarized asfollows.

• We investigate an efficient resource allocation for theunderlay CFN uplink that is addressed via an NP-hardoptimization problem.

• The NP-hard optimization problem is simplified by di-viding the network into DJGs. Then, it is solved byformulating the optimization problem as a coalition gamein a partition form.

• We propose algorithms to allocate resources in a dis-tributed way, in which the CFN implementation is self-organized and self-optimized.

The remainder of this paper is organized as follows.Section II explains the system model and problem formulation.The optimization problem of the efficient resource allocationis formulated in Section III, as is the DJGs formation. InSection IV, we address the solutions to solve this optimizationproblem based on a coalitional game in the partition formapproach. Section V provides simulation results. Finally, con-clusions are drawn in Section VI.

II. SYSTEM MODEL AND PROBLEM FORMULATION

First, we provide the system model followed by the prob-lem formulation of primary network protection. Second, weconsider the data transmission model in the uplink of CFUEs.Third, we analyze a queuing model of CFUEs. Finally, wediscuss some problems of licensed subchannel reuse amongCFUEs in the CFN.

A. System Model

We consider an uplink CFN based on the underlay spec-trum access paradigm, in which N cognitive femotocell basestations (CFBSs) are deployed as in Fig. 1. These CFBSs areunderlaid to the macrocell frequency spectrum and reuse theset of licensed subchannels of the uplink OFDMA macrocell.In the primary macrocell, there exist M subchannels, whichare correspondingly occupied by M MUE in the uplink di-rection. Let N = {1, . . . , N} and M = {1, . . . ,M} denotea set of all CFBSs and MUEs, respectively. A subchannelcan contain one resource block or a group resource with the

LEANH et al.: DISTRIBUTED POWER AND CHANNEL ALLOCATION FOR CFN USING COALITIONAL GAME 3477

Fig. 1. System architecture of a CFN.

single-carrier FDMA (SC-FDMA) technology in the LTE sys-tem [26]. Every CFBS n ∈ N is associated to the same L num-ber of CFUEs. Let Ln = {1, . . . , L} denote the set of CFUEsserved by a CFBS n ∈ N . Furthermore, cognitive modules areadded to CFUEs and CFBSs to support self-organization, self-optimization as in [8]. Moreover, CFUEs and CFBSs exchangeinformation via dedicated reliable feedback channels or wiredbackhauls.

B. Primary Network Protection

In the underlay CFN, the MBS of the macrocell needs tobe protected against overall interference from CFUEs, as in[27]–[29]. The protection on subchannel m at the MBS isaddressed as follows:∑

l∈Ln,n∈Nαmlnh

mln,0P

mln ≤ ζm0 ∀m ∈ M (1)

where αmln is a subchannel allocation indicator defined as

αmln =

{1, if l ∈ Ln is allocated to subchannel m

0, otherwise(2)

hmln,0 denotes the channel gain between CFUE l ∈ Ln and the

he primary MBS, Pmln is the power level of CFUE l ∈ Ln

using subchannel m, and ζm0 is the interference threshold at theprimary receiver MBS on subchannel m.

C. Data Transmission Model in Uplink

In our considered model, the data transmission of CFUEs isaffected by the interference from the MUE and other CFUEsin other femtocells. Each CFUE is assumed assigned to one

subchannel for a given time. The transmission rate of CFUE l ∈Ln on subchannel m follows the Shannon capacity as follows:

Rmln = Bwlog (1 + Γm

ln) (3)

where Bw is the bandwidth of subchannel m ∀m ∈ M, andΓmln is the SINR of the CFUE l ∈ Ln using subchannel m as

follows:

Γmln =

hmlnP

mln

Imn + n0. (4)

In (4), Imn denotes the total interference at CFBS n on sub-channel m

Imn =∑

l′∈Ln′ ,n′∈Nhml′nP

ml′n′ + hm

m,nPmm0 (5)

where n′ �= n; hmln, hl′n, and hm

m,n are the channel gains be-tween CFUE l and CFBS n, CFUE l′ ∈ Ln′ and CFBS n, andMUE m and CFBS n, respectively; n0 is the noise varianceof the symmetric additive white Gaussian noise; hm

m,nPmm0

is the intertier interference at CFBS n from MUE m; and∑l′∈Ln′ ,n′∈N hm

l′nPml′n′ is the total intratier interference from

CFUEs at the other CFBSs that use the same subchannel m.To successfully decode the received signals at the CFBS of

the CFUE transmission, the SINR at CFBS n from CFUE l ∈Ln has to satisfy [30]

Γmln ≥ γ (6)

where γ is the SINR threshold to decode received signals at theCFBS ∀n ∈ N ∀m ∈ M.

Because the transmission on the CFUE–CFBS link can bedropped due to a certain outage event, the successful transmis-sion of CFUEs can be computed based on the probability ofmaintaining the SINR above a target level γ, which is given by

ξln = Pr (Γmln > γ) . (7)

This outage value can be reduced by employment of thehybrid automatic-repeat-request protocol with chase combiningat the medium access layer [31]. According to this protocol,packets will be retransmitted if they have not been successfullyreceived at the receiver. This retransmission can occur up toKmax times until the successful data transmission. Hence, ifarrivals to CFUE l ∈ Ln follow a Poisson process with arrivalrate λln, the effective arrive rate λln with a maximum of Kmax

retransmissions is computed as follows:

λln = λln

Kmax∑k=1

ξln(1 − ξln)k−1 (8)

where (1 − ξln) is the error packet transmission probabilityof the connected link CFUE l ∈ Ln to CFBS n, which iscalculated based on (7), and

∑Kmax

k=1 ξln(1 − ξln)k−1 is the

successful transmission probability of a data packet of CFUE lwith a maximum of Kmax retransmissions.

Clearly, through (8), congestion at the queue of the CFUEoccurs when the departure rate or data rate on the CFUE–CFBS


Fig. 2. M/D/1 queueing model for data transmission of CFUEs.

link is lower than the acceptable threshold. This congestionleads to delaying data packets in the queueing model of theCFUE data transmission. The queueing model for CFUEs willbe discussed in the following.

D. Queuing Model Analysis for Guaranteeing theCFUE Demands

Here, we address the data transmission of the CFUE usingthe M/D/1 queuing model [32], as shown in Fig. 2. In thisqueueing model, the arrival rate λln depends on the data ratefrom the upper layer of CFUE l. Based on Little’s law, theaverage waiting time of a packet in CFUE l can be calculatedas follows:

Dmln =

λln

2Rmln

(Rm

ln − λln

) (9)

where Rmln is considered the service rate in the M/D/1 queuing

model determined by (3).Assuming that, at the beginning of each time slot, the max-

imum delay requirement for each CFUE l ∈ Ln is given byDm

ln ≤ Dmaxln , the condition

Rmln ≥ Rth

ln (10)

has to be guaranteed. From (9) and the maximum delay valuerequirement Dm

ln = Dmaxln , the data rate requirement Rmin

ln iscalculated as follows:

Rminln =

((Dmax

ln λln

)2

+ 2Dmaxln λln

) 12

+Dmaxln λln

2Dmaxln

. (11)

From (3), (4), and (10), we have the constraint of totalinterference to guarantee the minimum delay requirement ofeach CFUE as follows:

Imn + n0 ≤ hmlnP

mlnχln (12)

where χln = (2Rminln /Bw − 1).

Intuitively, from (3) and (10), in order to satisfy the minimumaverage delay requirement, the CFUE needs to increase itspower greater than a power level threshold. However, thisincrease may produce harmful interference to other CFUEs,which leads to a reduced data rate of other CFUEs using thesame subchannel, as in (3). Additionally, the increasing powerlevel at the CFUEs using the same subchannel m will increase

Fig. 3. Interference model for reusing a licensed subchannel among CFUEs.

the overall interference at the MBS, as mentioned in (1).Therefore, when the power allocation to CFUEs cannot satisfyconstraints (1), (3), and (10), CFUEs have an incentive to findanother opportunity for selecting the subchannel from a set ofsubchannels.

E. Channel Reuse in the CFN

In the CFN, a subchannel m that allocated to a CFUE ncan be reused at other CFUEs if it overcomes the intratierinterference constraints as considered in [16]. Certainly, toallocate a subchannel efficiently, the unlicensed subchannelsneed to be reused among CFUEs that are based on parameterαmln as follows:

αml′n′ =

{0, if l′ ∈ Ln′ , n′ ∈ Tm

ln , m ∈ M1, if l′ ∈ Ln′ , n′ /∈ Tm

ln , m ∈ M(13)

where Tmln is a set of the CFBSs lying within the interference

range (IR) of CFUE l ∈ Ln on subchannel m. The CFBS n′ ∈Tmln if and only if

IRmln,n′ ≥ γ (14)

where the IR IRmln,n′ is determined based on the SINR level

from observing the surrounding CFBSs of CFUE l ∈ Ln asfollows:

IRmln,n′ =

hln′Pm,maxln

hmn′Pmm0 + n0

(15)

and Pm,maxln is the maximum transit power of CFUE l ∈ Ln

that can be allocated on subchannel m. To illustrate the reuse ofsubchannels among CFUEs and to form table Tm

ln , we present asimple example as follows.

Example 1: Let us consider reusing a licensed subchannelm = 1 among three CFUEs as shown in Fig. 3, in whicheach CFBS serves one CFUE. The table Tm

ln of each CFUE isconstructed by considering the IR of the CFUEs based on (14)and (15). Then, the CFBSs that belong to the table of CFUEs11, 12, and 13 are T 1

11 = {1, 2}, T 112 = {2}, and T 1

13 = {2, 3},respectively. From (13), if subchannel m = 1 is allocated toCFUE 11, then α1

11 = 1, α112 = 0, and α1

13 = 1. This means


that subchannel 1 cannot be reused at CFUE 12 from CFUE 11,but CFUE 13 can reuse this subchannel. Similarly, we considerprinciples for CFUEs 12 and 13, respectively. The detail of thetable Tm

ln formation is discussed in Section III-B.To illustrate the subchannel and power allocation efficiently

and optimally, we address an optimization problem in thefollowing.

III. OPTIMIZATION PROBLEM AND DISJOINT

GROUP FORMULATION

Here, we first discuss an optimization problem that repre-sents an efficient resource allocation for the underlay CFNuplink. Second, we address the network partition into DJGs todecompose the computation of the optimization problem intodistributed computations at DJGs.

A. Optimization Problem Formulation

The objective is to maximize the uplink sum rate of thewhole CFN. The constraints include minimization of the in-tratier and intertier interference levels with similarly minimalaverage delay requirements for connected CFUEs. Specifically,the total interference at the MBS is also kept under acceptablelevels. Moreover, the subchannels are efficiently reused amongCFUEs. From the discussion of our considered problems inSection II, the optimization problem is formulated as follows:

OPT1:

maximize(αm

ln,Pmln)

∑m∈M

∑n∈N

∑l∈Ln

αmlnR

mln (16)

subject to (1), (12), (13)

0 ≤∑m∈M

αmln ≤ 1, n ∈ N , l ∈ Ln (17)

αmln = {0, 1}, m ∈ M, n ∈ N , l ∈ Ln (18)

Pm,minln ≤ Pm

ln ≤ Pm,maxln ∀m,n, l. (19)

The purpose of OPT1 is to allocate the optimal subchannelsand power levels for CFUEs to maximize the CFN uplinksum rate. Constraints (1), (6), (12), and (13) are addressed inSection II. Moreover, some conditions of subchannel allocationindicator αm

ln are represented in (17)–(19). Constraint (17)shows that each CFUE l ∈ Ln is only assigned one subchannelat a given time, and (18) is represented as in (2). Constraint (19)represents the power range of each CFUE l ∈ Ln, which hasto be within the threshold range. The thresholds Pm,max

ln andPm,minln indicate the limitations of the power range of CFUE

l ∈ Ln on each licensed subchannel m.Clearly, OPT1 is an NP-hard optimization problem because,

to find the optimal solution, we must allocate subchannels withmixed-integer variable αm

ln and noninteger variable Pmln along

with mixed linear and nonlinear constraints [33], [34]. TheNP-hard optimization problem along with the huge numberof CFUEs makes it infeasible to find an optimal solution. Tosolve OPT1, we propose a solution that is based on the DJGs’formation and coalitional game in the partition form approach.

Fig. 4. Proposed structure for solving OPT1 based on the DJGs’ formation andcoalitional form in the partition form.

A summary of the proposed solution is shown in Fig. 4.First, CFUEs in the network self-organize into DJGs usingAlgorithm 1 (to be discussed in Section III-B), in which theinterference from CFUEs transmission in a DJG is not affectedby CFUEs transmission among other DJGs. The purposes ofthis division are to reduce feedback among network entities anddecompose the computation in OPT1 into distributed compu-tations at DJGs. Second, CFUEs in DJGs will be consideredplayers in the coalitional game. CFUE cooperates with otherCFUEs to choose subchannel and power levels to form stablecoalitions using Algorithms 2 and 3 (described in Section IV-C).In the following, we simplify the optimization problem OPT1by addressing the DJGs’ formation.

B. DJGs Formation

In the CFN deployment, depending on the aims of networkdesigners and mobile user equipment, the locations of CFBSsand CFUEs are distributed randomly in a network area. Somefemtocells are less affected by interferences from others femto-cells. Thus, CFUEs can self-organize into DJGs as addressed inAlgorithm 1.

At the beginning of each period, the CFBS broadcasts a mes-sage that contains CFBS identification (ID) and interferencefrom MUEs (line 1). The CFUE decodes the received messages(lines 2, 3) and detects the surrounding CFBSs within the IRusing (14) and (15). The detected CFBSs are stored in table Tm

ln

and then form table Tln = {tln′}M×|Nl | (line 4); here, tln′ = 1if n′ ∈ Tm

ln , else tln′ = 0, and Nl is the set of CFBSs detectedby CFUE l. Then, the CFUE sends its information Tln to itsCFBS n (line 5). The CFBS n collects information Tln ofall its CFUEs and constructs table Tn = {tml,n′}

M×max(|Nl|)×Ln

(line 6). Here, {ttml,n′} equals to 1 if n′ ∈ Tln; otherwise, it

equals to 0. Simultaneously, the CFBSs exchanges informationthe table Tn with the CFBSs n′ ∈ Tn to form a DJG g (line 7).Then, the CFBSs build a subchannel reuse table among CFUEsbased on (13) (lines 8, 9). For convenience, let denote Tg ={αm

ln}(|Lg |×|Lg |×M the reuse table of CFUEs at DJG g. Here,denoting by Lg = ∪n∈Ng

Ln is the set of CFUEs in DJG g,and Ng is the set of CFBSs belonging group g. Clearly, someCFUEs can be self-organized into DJG g.


Fig. 5. DJG formulation in example 2.

Algorithm 1 The self-organization of CFUEs into DJGs

1: Initially, Tln = ∅, Pmln = Pm,max

ln , ∀m∈M, ∀n ∈ N ,l ∈ Ln. The CFBSs broadcast TxCFemtoBS-ID

messages based on pilot channels as discussed in [16].∗ At the CFUE, ∀ l ∈ Ln, ∀n ∈ N , do:2: decode TxCFemtoBS-ID message of the surrounding

CFBSs.3: estimate hln′ , n′ �= n based on received RSSIs.4: construct table Tln based on (14).5: send table Tln to its CFBS.∗ At the CFBS n, ∀n ∈ N , do:6: collect Tln from its CFUEs.7: construct table Tn based on table Tln, ∀ l ∈ Ln.8: exchange Tn � Tn′ , ∀n′ ∈ Tn.9: self-organize into groups.

10: construct tables Tg based on condition (13) then sends itto the network coordinator.

After CFUEs form DJGs, CFUEs only exchange informationfor group formation if and only if the network has new eventssuch as the CFUEs’ location or new joining CFUEs. In addition,exchanging information among CFBSs in the DJG formationcan be processed via asynchronous intercell signaling [35], [36].A femtocell signals its status information to neighbor femto-cells periodically and updates its CFUEs’ local information uponreception of the other femtocells signaling. For clear under-standing of DJG formation, we provide Example 2 as follows.

Example 2: Let us consider a CFN model consisting of fiveCFBSs, as shown in Fig. 5, in which each CFBS contains anCFUE. Assume that the IRs of CFUEs are determined andexist as shown in Fig. 5 (Steps 1–3). Intuitively, table Tln isconstructed as in Table I (Step 4), where “1” indicates the CFBSbelongs to the CFUE’s IR, “0” represents the CFBS that doesnot belong to the IR of the CFUE, and ∅ indicates that the CFUEdoes not receive the CFBS’s pilot signals. Because we onlyconsider one subchannel, the tables T1, T2, T3, T4, and T5 arealso represented as T 1

11, T 112, T 1

13, T 114, and T 1

15 as in Table II,respectively. To obtain databases of tables of the surroundingCFBSs, the CFBS n exchanges table Tn with other CFBSsn′ ∈ Tn. By doing so, the CFUEs {11}, {12}, and {13} have thesame database as in Table II and form a DJG, namely DJG-1.

TABLE ITABLE Tln FORMULATION OF ALL CFUES

TABLE IISUBCHANNEL REUSE TABLE Tg AMONG CFUES

Moreover, DJG-2 is formed by CFUEs {14} and {15}. Afterfinishing DJG formation, subchannel reuse tables for DJGs areformed based on (13) and exist as shown in Table II. Here, “1”denotes two CFUEs that can reuse subchannel 1, “0” denotestwo CFUEs that cannot reuse subchannel 1, and the ∅ denotetwo CFUEs belonging to different DJGs.

After establishing DJGs, without loss of generality, we findthe local optimal solution of OPT1 by finding an optimalsolution of OPT1g in each DJG g, which is taken from OPT1as follows:

OPT1g : max .(αm

ln,Pmln)

∑m∈M

∑n∈Ng

∑l∈Ln

αmlnR

mln (20)

s.t.∑

l∈Ln,n∈Ng

αmlnh

mln,0P

mln ≤ ζm0 , m ∈ M (21)

Imn,g + n0 ≤ hmlnP

mlnχln ∀n,m, l (22)

αml′n′ =

{0, if l′ ∈ Ln′ , n′ ∈ Tm

ln , m ∈ M1, if l′ ∈ Ln′ , n′ /∈ Tm

ln , m ∈ M(23)

0 ≤M∑

m=1,

αmln ≤ 1, n ∈ Ng, l ∈ Ln (24)

αmln = {0, 1}, n ∈ Ng, l ∈ Ln, m ∈ M (25)

Pm,minln ≤ Pm

ln ≤ Pm,maxln ∀n,m, l (26)


where Ng denotes the set of CFBSs that belong to the DJGg. Constraint (23) is taken from (13), and n, n′ ∈ Ng. Herein,the network size is decreased, but OPT1g is still an NP-hardoptimization problem. In the following, we discuss in detailhow to find the optimal solution of OPT1g .

We note that, the intratier interference Imn,g in (22) is deter-mined based on (3) as follows:

Imn,g = Zmn,g + Zm

n,g′ + hmm,nP

mm0 (27)

where Zmn,g =

∑l′∈Ln′ ,n′∈Ng

hml′nP

ml′n′ is the intratier interfer-

ence from CFUEs inside DJG g to CFBS m on subchannelm, and Zm

n,g′ =∑

l′′∈Ln′′ ,n′′∈N\Nghml′′nP

ml′′n′′ is the intratier

interference from CFUEs outside DJG g to CFBS n on subchannel m.

IV. RESOURCE ALLOCATION BASED ON COALITIONAL

GAME IN PARTITION FORM

Herein, the problem OPT1 is solved based on a coalitiongame approach where CFUEs are players as follows. First, theOPT1g of each DJG g is formulated as a coalitional game inpartition form. Second, we present the recursive core methodto solve the proposed game. Third, we address an implemen-tation of the recursive core method to determine the optimalsubchannel and power allocation in a distributed way. Finally,we consider the convergence and existence of the Nash-stablecoalitions in the game.

A. Formulation OPT1g as a Coalitional Game inPartition Form

The coalitional game is a kind of cooperative game that isdenoted by (Lg, ULg

), in which individual payoffs of a set ofplayers Lg are mapped in a payoff vector ULg

. The playershave incentives to cooperate with other players, in which theyseek coalitions to achieve the overall benefit or worth of thecoalitions. The coalitional game in partition form is one suchgame expression, which is studied and applied in [21], [37],and [38]. The worth of coalitions depend on how the playersoutside of the coalition are organized and on how the coalitionsare formed. In the coalitional game, the cooperation of playersto form coalitions is represented as the nontransferable utility(NTU) game, which is defined as follows [38].

Definition 1: A coalitional game in partition form with NTUis defined by the pair (Lg , ULg

). Here, ULgis a mapping

function such that every coalition Sm,g ⊂ Lg , ULg(Sm,g, φLg

)

is a closed convex subset of �|Sm,g |, which contains the payoffvectors available to players in Sm,g .

The mapping function ULgis defined as follows:

ULg(Sm,g, φLg

)

={x ∈ �|Sm,g ||xln(Sm,g, φLg

) = Rmln(Sm,g, φLg

)}

(28)

where xln(Sm,g, φLg) is the individual payoff of player l ∈ Ln,

which corresponds to the benefit of a member in Sm,g inpartition form φLg

of group g. The CFUE l ∈ Ln belongs tocoalition Sm,g, depending on the partition φLg

in a feasible setΦLg

of players joining coalitions.

Remark 1: The singleton set ULg(Sm,g, φLg

) is closed andconvex [23].

In summary, the players make individual distributed deci-sions to join or leave a coalition to form optimal partitionsthat maximize their utilities and bring the overall benefit ofcoalitions. Based on the characteristics and principles of thisgame, we model the OPT1g as a coalitional game in partitionform. Instead of finding the global optimal that cannot be solveddirectly, CFUEs will cooperate with other CFUEs to achievesuboptimal solution of the optimization problem OPT1g .

Proposition 1: The optimization problem OPT1g can bemodeled as a coalitional game in partition form (Lg, ULg

).Proof: CFUE l ∈ Ln and its data rate Rm

ln in a certainDJG g are considered player l ∈ Ln and individual payoffxln(Sm,g, φLg

) in the game, respectively. A set of CFUEs thatbelong to DJG g is represented as Lg . The data rate Rm

ln ismapped in a payoff vector ULg

as in (28). To address formationof a certain coalition Sm,g , we assume that there are onlyM + 1 candidate coalitions Sm,g that CFUEs can join, i.e.,m ∈ M∪ {0}. Here, S0 means that CFUEs in this coalitionare not allocated to any subchannel. Furthermore, each joiningor leaving coalition of CFUEs has to satisfy the constraints ofthe optimization problem OPT1g . The total data rate of CFUEsusing the same subchannel bring the overall benefit or worthof a coalition. To find a suboptimal value in OPT1g , CFUEshave incentives to cooperate with other CFUEs. The coopera-tion information consists of the subchannels and power levelsallocated to CFUEs. Intuitively, if CFUEs do not exchangetheir information with other CFUEs, the system performancewill be degraded due to unsatisfied constraints (21)–(26), asmentioned in Section III-A. Moreover, from (27), the individualpayoff of each CFUE depends on CFUEs belong toLg using thesame subchannels. In addition, the individual payoff of CFUEsdepend on using subchannels of CFUEs at other DJGs. Hence,to improve the individual payoff value of CFUEs, incentivesto cooperate among CFUEs are necessary [12], [38], [39].Therefore, the OPT1g can be solved based on modeling as acoalitional game in partition form. �

To solve this game, we simplify the coalition formation byassuming the value of the coalition depends on the outsidecoalitions, which is intratier interference from other DJGs.Then, we apply the recursive core method that is introducedin [22] and [37] to solve this proposed game. Different from thecore of Shapley value in the characteristic form, a recursive coreallows modeling of externalities for games in partition form[22]. The details of the solution are discussed in the following.

B. Recursive Core Solution

As discussed in [22] and [37], the NTU game in partitionform is very challenging to solve. However, we can use theconcept of a recursive core to solve the proposed game [22].Normally, the recursive core is defined for games with trans-ferable utility (TU), where a real function captures the benefitof a coalition instead of mapping [22], [37]. Moreover, sincethe mapping function in (28) is a singleton set, we can definean adjunct coalition game as (Lg , v) for the proposed gamein which the benefit of each coalition Sm,g is captured over a


real line v(Sm,g). By doing so, the original game (Lg, ULg) is

solved via the adjunct coalition game (Lg, v) that is similar togames with TU as studied in [12], [17], and [39].

Whenever a CFUE detects a coalition Sm,g that it can join,it compares its payoff in the current coalition and payoff incoalition Sm,g . If the payoff in Sm,g is greater than the currentthen CFUE will join it; otherwise, it will stay in the currentcoalition. In the NTU game, payoffs are a direct by-product ofthe game itself due to power allocation of CFUEs on subchannelm to avoid violation of MBS protection (21) and providingguaranteed QoS to CFUEs in coalition as in (22). However,the payoff values of players are not determined solely by thedata rate that CFUEs can achieve because of the CFUEs are thesubscribed users of the wireless service providers. Meanwhile,the wireless service providers are the operators of the networks;therefore they can control the payoffs of the players via net-work coordinator from two aspects. First, service providerscan physically provide different services to cooperative andnoncooperative users using rewards and punishment. Second,the CFUEs are stimulated to act cooperatively and improvethe overall performance of the formed coalition Sm,g or net-work while guaranteeing the MBS protection and CFUEs’QoS,which can be obtained via division of the single TU valuev(Sm,g) [22], [37]. Whenever Sm,g belongs to φLg

, the func-tion value v(Sm,g, φLg

) ∈ v of the our game is determined asfollows:

v(Sm,g, φLg)=

⎧⎨⎩

∑ln∈Sm,g

xln, if (21), (22), and |Sm,g| ≥ 1

0, otherwise.(29)

We can see that the mapping vector of the individual payoffvalue of CFUEs in (28) is uniquely given from (29), and thecore in TU game is nonempty [37]. Thus, we are able toexploit the recursive core as a solution concept of the originalgame (Lg, ULg

) by solving the game (Lg, v) while restrictingthe transfer of payoffs according to the unique mapping in(28). Here, the value v(Sm,g, φLg

) is the sum rate of CFUEsallocated to the same subchannel m in partition φLg

. Throughcooperating and sharing, the payoff among CFUEs in thecoalition m, CFUEs achieve their optimal power allocation tomaximize each coalition Sm,g to which they belong (details arediscussed in Algorithm 2 of Section IV-C). Then, based on theresults in each coalition, the optimal subchannel allocations aredetermined by finding the core of the game using the recursivecore definition.

Before describing the recursive core definition, we define aresidual game that is an important intermediate problem. Theresidual game (R, v) is a coalitional game in partition form thatis defined on a set of CFUEs R = Lg\Sm,g. CFUEs outside ofR are deviators, whereas CFUEs inside of R are residuals [22],[37]. The residual game is still in partition form and can besolved as an independent game, regardless of how it is gener-ated [38]. For instance, when some CFUEs are deviators thatreject an existing partition, they have incentives to join anothercoalition that satisfy (23)–(25) and subchannel reuse table Tg.Naturally, their decisions will affect the payoff values of theresidual CFUEs. Hence, the residual game of CFUEs forms a

new game that is a part of the original game. CFUEs in theresidual game still have the possibility to divide any coalitionalgame into a number of residual games, which, in essence,are easier to solve. The solution of a residual game is knownas the residual core [22], [37], which is a set of possible gameoutcomes, i.e., possible partitions of R. The recursive coresolution can be found by recursively playing residuals games,which are defined as follows (mentioned in [22, Def. 4]):

Definition 2: The recursive core C(Lg, v) of a coalitionalformation game (Lg , v) is inductively defined as follows:

1) Trivial Partition. The core of a game with Lg is only anoutcome with the trivial partition.

2) Inductive Assumption. Proceeding recursively, considerall CFUEs belonging to the DJG g, and suppose theresidual core C(R, v) for all games with at most |Lg| − 1CFUEs has been defined. Now, we define A(R, v) asfollows:A(R, v) = C(R, v), ifC(R, v) �= ∅; A(R, v) =Ω(R, v), otherwise. Here, let Ω(R, v) denote a set of allpossible outcomes of game (R, v).

3) Dominance. An outcome (x, φLg) is dominated via coali-

tion Sm if at least for one (yLg\Sm,g, φLg\Sm,g

) ∈ A(Lg\Sm,g, v) there exists an outcome ((ySm,g

,yLg\Sm,g),

φSm,g∪ φLg\Sm,g

) ∈ Ω(Lg, v), such that (ySm,g,

yLg\Sm,g) Sm,g

x. The outcome (x, φLg) is dominated

if it is dominated via a coalition.4) Core Generation. The recursive core of a game of |Lg| is

a set of undominated partitions, denoted by C(Lg , v).

In Step 1, the core of a trivial partition is initialized withCFUEs belonging to coalition 0. Step 2 is an inductive as-sumption that establishes the dominance for a game of |Lg| − 1CFUEs through inductive steps of the formed coalitions. Forinstance, subchannel allocation permits assigning subchannelsto CFUEs to bring dominance. Step 3 is the main step forchecking and finding dominant coalitions, which captures thevalue of a coalition depending on partitions. We define xas the payoff vector of players, and φSm,g

as the partitionof the user set Lg. The payoff vector x is an undominatedcoalition if there exists a way to partition that brings an outcome((ySm,g

,yLg\Sm,g), φSm,g

∪ φLg\Sm,g) that achieves greater re-

ward to CFUEs of Sm,g , compared with x. Corresponding toeach DJG partition, the individual payoffs of all CFUEs in thegame are uniquely determined and undominated. Furthermore,the coalitions in the recursive core are formed to provide thehighest individual payoffs or data rates of CFUEs, as detailedin Step 4.

C. Implementation of the Recursive Core at Each CoalitionalGame Formation in Partition Form at DJGs

We address implementation of the recursive core methodto solve the proposed game, which is sketched in Fig. 6. Asdiscussed earlier, the game (Lg, Ug) is solved via the game(Lg, v). According to this alternative, the coalition Sm,g in apartition φLg

is represented by a real function v(Sm,g, φLg) as

in (29). Corresponding to the subchannel allocation of CFUEs,some CFUEs can be allocated into the same subchannel m,which forms a coalition Sm,g. Then, CFUEs optimize theirindividual payoffs by sharing with other CFUEs in the same


Fig. 6. Determination of the optimal solution of OPT1g based on the coali-tional game in partition form.

coalition Sm,g . In this case, CFUEs cooperate with othersin coalition m to maximize the individual payoff and valuev(Sm,g, φLg

). Sharing is achieved by finding optimum powervalues of each CFUE in the following optimization problem:

OPT1Sm,g ,φLgmaximize

Pmln

v(Sm,g, φLg) (30)

subject to∑

ln∈Sm,g

hmln,0P

mln ≤ζm0 (31)

Zmn,g+Zm

n,g′+hmm,nP

mm0+n0≤hm

lnPmlnχlnl ∈ Ln, ln ∈ Sm,g

(32)

Pm,minln ≤ Pm

ln ≤ Pm,maxln , ln ∈ Sm,g, l ∈ Ln. (33)

The constraint (32) is taken from (22) and (27). When CFUEl ∈ Ln belongs the coalition Sm,g, αm

ln is set to 1; otherwise,it is set to 0. Therefore, without loss of generality, we ignoreparameter αm

ln in OPT1Sm,g ,φLg. By finding the optimal power

allocation to CFUEs, they will achieve an optimum individualpayoff value that maximizes the worth of coalition Sm,g . Theoptimal solution of OPT1Sm,g,φLg

can be found in a centralizedor distributed way. We find the optimal solution in a distributedway. We solve the optimization problem by modeling as a geo-metric convex programming problem [18], [24], [29]. Then, the

optimum values can be found using Karush—Kuhn—Tucker(KKT) conditions [18], [23], [24], [40], as follows:

Pmln = ey

mln =

1 + μln

βhmln,0 + ηln − ςln

(34)

where [a]+ = max{a, 0}; the Lagrange multipliers β, μln, ηln,ςln, and the consistency price ϑln for all CFUE ln ∈ Sm,g areupdated as

β(t) =

⎡⎣β(t− 1) + s1(t)

⎛⎝ ∑

∀ln∈Sm,g

hmln,0e

ymln − ζm0

⎞⎠⎤⎦+

(35)

ηln(t) =[ηln(t− 1) + s3(t) (ymln(t)− logPm,max

ln )]+ (36)

ςln(t) =[ςln(t− 1) + s4(t)

(−ymln(t) + logPm,min

ln

)]+(37)

ϑln(t) =[ϑln(t− 1) + s5(t)

(Zmn,g − ez

mn,g

)]+(38)

and (39), shown at the bottom of the page.We use the changing logarithm of the variables ymln =

logPmln . The parameter si(t) represents the step size satisfying

∞∑t=0

si(t)2 < ∞, and

∞∑t=0

si(t) = ∞ ∀i = 1, 2, 3, 4, 5

(40)which leads to the convergence of algorithms [23]. Addition-ally, the variable zmn,g is also calculated from the KKT necessaryconditions as follows:

ezmn,g =

ϑln

(Zmn,g′ + hm

m,nPmm0 + n0

)1 − ϑln + μln

(41)

where zmn,g = log(Zmn,g).

The details of finding the optimum value Pmln and ez

mn,g in

OPT1Sm,g ,φLgis expressed in [41]. The updating of values ez

mn,g

and Pmln are expressed in Algorithm 2.

Algorithm 2 Distributed power allocation for CFUEs in thecoalition Sm,g ⊆ φLg

∗ Initialization:1: Initialize t = 0, β(0) > 0, μln(0) > 0, ηln(0) > 0,ςln(0) >, 0, ϑln(0) > 0, Pm

ln (0) ∈ [Pm,minln , Pm,max

ln ], χln,∀ln ∈ Sm,g.∗ At CFBS n, ∀n ∈ Sm,g:2: Measure the interference Imn,g.3: Calculate the variable ez

mn,g as in (41).

4: Update the Lagrange multiplier μln(t+ 1) and consis-tency price ϑln(t+ 1) using (39) and (38), respectively.

μln(t) =

[μln(t− 1) + s2(t) log

(e−ym

ln

hmln

(ez

mn,g + Zm

n,g′ + hmm,nP

mm0 + n0

))− log(χln)

]+(39)


5: Transmit μln(t+ 1) to CFUE l ∈ Ln.∗ At CFUE l ∈ Ln, ln ∈ Sm,g:6: Estimate channel gain hm

ln,0 and compute the total inter-ference at the MBS; Receive the updated value μln, ϑln.7: Update the Lagrange multipliers β, ηln, and ςln from(35), (36), and (37), respectively.8: Calculate the power value Pm

ln (t+ 1) as in (34).9: Send power value Pm

ln (t+ 1) and hmln,0(t+ 1) to other

CFUEs in the coalition Sm,g.∗ Output: Optimal transmit power level Pm∗

ln and optimalvalue v(Sm,g, φLg

)m∗ of the formed coalition m.

In Algorithm 2, the information being exchanged amongCFUEs and CFBSs is based on feedback, such as ACK/NACK.This information can be exchanged in forms such as wiredbackhauls, dedicated control channels, or pilot signals. TheCFBS measures the intratier interference and intertier interfer-ence on subchannel m (Step 2). Then, the CFBS updates thevalue ez

mn,g(t+ 1) (Step 3). The Lagrange multiplier μln(t+ 1)

and consistence price ϑln(t+ 1) are updated (Step 4). Afterthat, the CFBS transmits μln(t+ 1) to CFUE l (Step 5). CFUEl ∈ Ln estimates channel gain hm

ln,0 and the aggregated inter-ference at the MBS (Step 6). Simultaneously, CFUE l ∈ Ln

gets updated values of β(t+ 1), i.e., ϑln(t+ 1), from CFBSn. We note that the value threshold ξm0 is updated from MBSvia a weighted interference vector depending on the formedcoalition. Then, the remaining Lagrange multipliers are updatedvia (35)–(37) (Step 7). After that, the CFUE updates the powervalue at time t+ 1, as in Step 8. Then, the CFUE sends itsthe newest power value Pm

ln (t+ 1) and newest channel gainhmln,0(t+ 1) to other CFUEs that belong to coalition Sm,g

(Step 9). OPT1Sm,g ,φLgis transformed to the convex optimiza-

tion problem, the optimal duality gap is equal to zero, and stepsizes satisfy (40). Therefore, the solution P ∗

ln will converge tothe optimal solution under Algorithm 2.

After finishing Algorithm 2, in general, coalition Sm,g guar-antees the optimal sharing payoffs among members CFUEs.Simultaneously, we also find the optimum worth v(Sm,g, φLg

)of coalition Sm,g. Based on the steps in the Definition 2, wepropose Algorithm 3 to find recursive core, which leads to thedistributed subchannel and power allocation.

Algorithm 3 Distributed algorithm for subchannel and powerallocation in cognitive femtocell network.

∗ Initialization:1: CFUEs and CFBSs form DJGs ← Algorithm 1; Formtable Tg; φ

(0)Lg

= {{1}, {2} . . . , {|Lg|}} in which CFUEsare randomly allocated subchannel and transmit power withnoncooperative among FUEs.

∗ Coalition formation at each DJG g:2: CFUEs operate in cooperative mode and join into poten-tial coalitions φLg

= {{0}, {1} . . . , {|M|}} that satisfy thetable Tg.3: for player {nl} ∈ Lg do4: for Sm,g ∈ {φ(k−1)∗

Lg\{nl}} do

5: Set φ(k)Lg

:= {φ(k−1)∗Lg

\Sm,g,S′m,g= Sm,g ∪ {nl}}.

6: Find v(S′m,g, φ

(k+1)Lg

) ← based on (29) and Alg.2.7: if

∑m∈M∪{0} v(S′

m,g, φ′Lg) >∑

m∈M∪{0} v(Sm,g, φLg)

then8: Set φ(k)∗

Lg= φ

(k)Lg

.9: Update αm∗

ln , Pm∗ln .

10: end if11: end for12: end for∗ Output: Output the stable core of game (Lg, v) consistingof both the final partition φ∗

Lg, subchannel allocation decision

αm∗ln , and transmit power level Pm∗

ln .

To obtain a partition in the recursive core, the CFUEs inLg use Algorithm 3. In the initial step, the information onsubchannel reuse table Tg of DJG g is formed at the net-work coordinator (Step 1). The network coordinator makesdecision to allocate subchannel to CFUEs with the assuranceto protect MBS and provide guaranteed QoS to CFUEs. Theindividual payoff values of CFUEs in (28) are mapped to theformed coalitions via (29). Then, in the coalition formation,the value of whole game in group g (

∑m∈M∪{0} v(Sm,g, φLg

))is captured at the network coordinator. Network partitions ofDJG g are controlled by network coordinator that makes adecision to assign CFUEs into coalition Sm,g ∀m ∈ M∪ {0}(Step 2). Additionally, network partitions of DJG g have tosatisfy the principles in the subchannel reuse table Tg andSteps 3, 4, and 5. After that CFUEs find the optimal transmitpower and individual payoff value based on Algorithm 2 toadopt their delay requirement and the MBS protection (Step 6).The network coordinator updates the undominance partitionvia Step 3 of Definition 2 (Steps 7 and 8). The algorithmis repeated until it converges to the stable partition φ

(k)∗Lg

,which results in an undominated partition in the recursive core.Whenever undominated partition φ

(k)∗Lg

is updated at time k, thenetwork coordinator updates subchannel allocation to CFUEs(Step 9). The CFBS of each femtocell shares the resourceusage information among each other when they get the updatedinformation from its CFUEs. Sharing of these confirmationcauses overhead in the system. However, we have mitigatedthe amount of messages exchange by forming DIGs. By doingthis, only CFUEs inside a DJG are permitted to exchangeinformation. In addition, observation of the value v(Sm, φLg

)is done by network coordinator such as the femtocell gateway[39]. We note that the subchannel and power allocation ofCFUEs are updated whenever a network partition is transferredfrom partition (k − 1) to partition (k), which produces Paretodominates S(k)

m,g. The convergence and Nash-stable coalitions inAlgorithm 3 are discussed in following.

D. Convergence and Stable Analysis of the Proposed Game

Convergence of the proposed game through four steps of therecursive core method is guaranteed as follows.


Propriety 1: Starting from any initial partition φLg, using

the Algorithm 3, coalitions of CFUEs merge together by Paretodominance, which results in a stable network partition and liesin the nonempty recursive core C(Lg, v).

Proof: Let φ(k)Lg

be the formed partition at iteration kthat is based on principles of residual game (Steps 4 and 5 ofAlgorithm 3). The individual payoff of CFUE l ∈ Ln via a func-tion v(k)(S(k)

m,g, φ(k)Lg

) as (29) is denoted by x(k)(S(k)m,g, φ

(k)Lg

).Therefore, each distributed decision made by the CFUE inAlgorithm 3 can be seen as a sequential transformation of thecomposition of the network partition as follows:

φ(0)Lg

→ φ(1)Lg

→ φ(2)Lg

→ . . . → φ(k)Lg

→ . . . (42)

where the decision of making a partition is managed by thenetwork coordinator, and φ

(k)Lg

is the network partition in DJG g

after k transfers. Every transfer operation from partition (k − 1)to partition (k) is an inductive step, which produces Pareto

dominates S(k)m,g as follows:

φ(k−1)Lg

→ φ(k)Lg

⇔∑

S(k)m,g∈φ(k)

Lg

v(S(k)m,g, φ

(k)Lg

)>

∑S(k−1)m,g ∈φ(k−1)

Lg

v(S(k−1)m,g , φ

(k−1)Lg

).

(43)

We note that each CFUE gradually selects the coalitionbased on reuse table Tg and conditions (23)–(25). Hence, thevalue of coalition will be set to zero if any condition of theformed coalition is violated, and the value of other coalitionsremains unchanged. Therefore, in Algorithm 3, when any twosuccessive steps k − 1 and k are successful, then we havev(φ

(k)Lg

) =∑

S(k)m,g∈φ(k)

Lg

v(S(k)m,g, φ

(k)Lg

) is Pareto dominated by

φ(k)Lg

.Therefore, Algorithm 3 ensures that the overall network

utility sequentially increases by Pareto dominance. In addition,the sum of values of the coalitions in each group g increaseswithout decreasing the payoffs of the individual CFUEs andthe whole network as well. Since the number of partitions ofLg CFUEs into M + 1 coalitions is a finite set given by theBell number [37]; thus, the number of transmission steps in(42) is finite. Hence, the sequence in (42) will terminate aftera finite number of inductive steps and will converge to a finalpartition. �

After DJG g partition converges to a final partition φLg, it is

still not guaranteed analytically that the partition is Nash-stable.A partition φLg

is Nash-stable if no player can get benefit intransferring from its coalition (Sm,g, φLg

) to another existingcoalition Sm′ , which can be mathematically formulated basedon [42] as follows.

Definition 3: The partition φLgis Nash-stable with Pareto

dominance if ∀ ln ∈ Lg , such that ln ∈ Sm,g,Sm,g ∈ φLg;

thus, (Sm,g, φLg) �ln (Sm′ ∪ {ln}, φ′

Lg) for all Sm′ ∈ φLg

∪{∅} with φ′

Lg=(φLg

\{Sm,g, Sm′}∪{Sm,g\{ln}, Sm′∪{ln}).Hence, the stability of partition φLg

in the proposed gamecan be considered as follows.

Proposition 2: Any final partition φLgbelongs to the core

C(Lg, v) of the DJG in Algorithm 3 and always converges to aNash-stable partition.

Proof: Consider a partition φcLg

belongs to coreC(Lg , v),which is found according to the four steps in Definition 2. If thispartition is not Nash-stable, then there exists a CFUE ln ∈ Lg

with ln ∈ Sm,g, Sm,g ∈ φcLg

, and a coalition Sm′ ∈ φcLg

suchthat y(Sm′ ∪ {ln}, φ′

Lg) ln x(Sm,g, φLg

), and CFUE l ∈ Ln

can move to coalition Sm′ . Here, φ′Lg

= (φLg\{Sm,g, Sm′} ∪

{Sm,g\{ln}, Sm′ ∪ {ln}}). However, this contradicts with thefinal partition φLg

in Propriety 1. On the other hand, afterfinishing the recursive core formation, we can see that CFUEshave no incentive to abandon their coalitions, because anydeviation can be detrimental. As a result, a partition φLg

in therecursive core is also stable since it ensures the highest possiblepayoff for each CFUE with no incentive to leave this partition,as studied in [42]. Thus, any partition φLg

that belongs to thecore of Algorithm 3 is Nash-stable. �

With respect of computational complexity, related to central-ized solution, it is worth mentioning that finding a partition isstrongly challenged by the exponentially growing number ofrequired iterations and the signaling overhead traffic that wouldrapidly congest the backhaul and dedicate channels. Moreover,femtocell does not have reliable centralized control due tounreliable backhaul [9]. Due to these characteristics, femtocelldeployment needs distributed solutions with automatic channelselection, power adjustment for autonomous interference coor-dination, and coverage optimization. In our distributed solution,the complexity can be significantly reduced by considering thefollowing aspects. First, in our game, the network partitionis managed by network coordinator of each DJG. Moreover,cooperation is established only among those CFUEs who areusing the same subchannel in their DJG is often small. Further,the network partition formation does not depend on the orderin which the CFUEs in coalition are evaluated, the number ofiterations is further reduced. Second, the network partition isobtained by running residual games in each DJG with checksin subchannels reusing table, significantly reducing the searchspace and amount of exchanged information.

Obviously, the recursive core method applied to our proposedgame always converges to a final DJG partition. Moreover, thenetwork partition based on residual game always converges toa Nash-stable partition.

V. SIMULATION RESULTS

As shown in Fig. 7, we simulate an MBS and 16 CFBSs withthe coverage radii of 500 and 30 m, respectively. To allocatesubchannels to the femtocells, we utilize three SC-FDMAlicensed subchannels, which are allocated to uplink transmis-sion of three MUEs, each with bandwidth Bw = 360 kHz (byusing two subcarriers for each licensed subchannel) and a fixedpower level of 500 mW. Moreover, the interference thresholdat the MBS for each licensed subchannel equals to −70 dbmW.Each CFBS has two CFUEs: A pilot signal with power equals500 mW. Each CFUE has an arrival rate equals to 1.5 Mb/s,and the delay must be less than or equal to 10 m. In addition,each CFUE has a maximum power level constraint (Pmax) of


Fig. 7. Self-organization of CFUEs in the CFN to six DJGs according toAlgorithm 1. DJG-1, DJG-2, DJG-3, DJG-4, DJG-5 and DJG-6 are composedof CFUEs belonging to the groups CFBS {1}, {2, 3, 12, 14}, {4, 15}, {5, 11,13}, {6, 7, 8, 9, 10}, and {16}, respectively.

Fig. 8. Maximum power levels of CFUEs on three licensed subchannels.

100 mW. We assume that distance-dependent path-loss shad-owing according to the 3GPP specifications [43] affects thetransmissions.

After the network is initialized, the CFBS and MBSperiodically broadcast the pilot signal to CFUEs. CFUEsmeasure the received signal strength indication (RSSI) of thepilot signals and estimate channel gain to the surroundingCFBSs. Additionally, the CFUE also estimates its channelgain to the MBS based on the messages broadcast from theMBS. Independently, the CFUE estimates the maximum powerlevel for each licensed subchannel based on its own observedchannel gain to the MBS and (1), in which the maximum powerlevel on each licensed subchannel is determined by Pm,max

ln =[min(Pmax, ζm0 /hm

ln,0)]+ ∀m ∈ {1, 2, 3}. The maximum

power level of CFUEs on licensed subchannels are shown inFig. 8. CFUEs in CFBS-16 have the highest maximum powerlevel because the distance to MBS is too far from CFUEswhere the MBS lies outside the interference threshold range.

Fig. 9. Subchannel reuse tables among CFUEs in DJGs of the CFN. The value“0” means two CFUEs cannot be reused the subchannels; else, it has a valueequal to “1.”

Fig. 10. Optimal subchannel allocation in DJG-1 and DJG-5.

To find DJGs, we run Algorithm 1. The self-organizationDJGs are shown in Fig. 7, in which CFUEs self-organize intosix DJGs. Simultaneously, the subchannel reuse tables amongCFUEs of DJGs are also formed. The subchannel reuse tablesof all DJGs are depicted in Fig. 9, in which value “0” meanstwo CFUEs cannot be reused; else, it has a value equal to “1.”

In Fig. 10, we compare our proposal to a random subchannelallocation scheme. Specifically, we consider DJGs 1 and 5. In-tuitively, by using Algorithm 3, DJG-5 needs 20 time steps, andDJG-1 needs five time steps to converge to the optimum value.On the other hand, by randomly allocating the subchannels, thesum rate of each DJG-1 and DJG-5 is not stable and are lowerthan the optimum value. This examination is the same for allDJGs in the network. We also see that the sum rate in each DJGusing our scheme is greater than that of the random subchannelallocation scheme. Therefore, our scheme is more efficient thanthe random subchannel allocation scheme.

The convergence of DJGs after applying coalitional gameapproach via Algorithm 3 is shown in Fig. 11. By using thecoalitional game, in each time step, all CFUEs will cooperate


Fig. 11. Convergence of each DJG.

Fig. 12. Optimal subchannel allocation of CFUEs.

Fig. 13. Optimal power allocation of CFUEs.

with other CFUEs in its formed coalition and form DJGs withjoining and leaving principles to maximize the sum rate ofDJGs. Clearly, using the coalitional game approach, we canachieve a local optimum. We also see that the convergence ofAlgorithm 3 is achieved after around 18 time steps, as shownin Fig. 11.

The results of the subchannel and power allocation basedon the core of the game are shown in Figs. 12 and 13, re-spectively. In each group, some CFUEs may not be allocated

Fig. 14. Social welfare of CFUEs in OPT1 with different power allocationschemes.

to any subchannel because these allocations do not satisfy theconstraints of the minimum delay and protection at the MBS.Additionally, the power of CFUEs in CFBS-16 are allocatedwith the maximum power level because the MBS is outside ofthe IR of CFUEs in CFBS 16. Furthermore, this group is notaffected by interference from other CFUEs in other DJGs or byinterference from the MUEs.

To leverage subchannel variations and network stochasticrealizations, the results are averaged over a large number ofsimulations. We consider our problem in 30 periods, and weestimate the social welfare of CFUEs by the utilitarian measure((1/N × L)

∑Ll=1

∑Nn=1 Rln) for each period. There are three

schemes considered: our proposal given in Algorithm 3, sub-channel allocation using Algorithm 3 with the fixed maximumpower level of CFUE (CA+maximum power allocation), andsubchannel allocation using Algorithm 3 with random powerlevel allocation to each CFUEs (CA+random power allocation).The results are shown in Fig. 14. Intuitively, our proposedscheme always achieves a higher social welfare utilities forall CFUEs compared with the other methods. Hence, sharingthe individual payoff among CFUEs using Algorithms 2 isnecessary to find the optimal solution of OPT1.

Next, we estimate the social welfare of CFUEs(∑L

l=1

∑Nn=1 Rln) with respect to different interference

thresholds of the MBS. Fig. 15 shows that for any interferencethreshold at the MBS, the social welfare of the proposed ap-proach is always higher than those of the (CA+maximum powerallocation) and (CA+random power allocation) schemes.Further, in Fig. 15, we have numerically compared theproposed approach with the optimal solution, in which CFUEsare allocated subchannel and transmit power in a centralizedfashion. The social welfare of all the schemes grows with theincrease in interference thresholds at the MBS. The comparisonshows that performance of the proposed is close to centralizedsolution. In addition, gaps between the proposed approachand centralized solution are 4.56% and 4.96% when theinterference thresholds are of −70 dBmW and −40 dBmW,respectively.

To see the social welfare versus the numbers of licensedsubchannels, we fix the positions of CFUEs and CFBSs. Then,


Fig. 15. Social welfare of CFUEs in OPT1 versus the interference threshold atthe MBS.

Fig. 16. Average data rates of CFUEs follow number of the subchannels.

we increase the number of licensed subchannels that are allo-cated to CFN in the uplink direction. We examine OPT1 withdifferent methods, as shown in Fig. 16. When the number ofsubchannels is less than or equal to 11, the social welfare ofCFUEs in our scheme is higher than that of the other twoschemes. With increasing number of licensed subchannels, thesocial welfare is increased because more CFUEs are allocatedto subchannels. The saturation point is achieved when thenumber of subchannels is greater than or equal to 11 because,at this point, all CFUEs are allocated to the optimal subchanneland power level formed in the core of the proposed game. Thescheme “Optimal CA+random power allocation” always hasthe smallest value because some CFUEs, which are allocatedwith random power level do not satisfy the conditions to protectMBS or the minimum delay requirement of each CFUE. In suchcases, the subchannel is not allocated to these CFUEs, whichdramatically decreases the sum rate of all CFUEs, as well asthe social welfare in the network.

VI. CONCLUSION

In this paper, we have investigated an efficient distributedresource allocation scheme for uplink underlay CFN. The ef-ficient resource allocation is characterized via an optimizationproblem. We identified the optimal subchannels and power

levels for CFUEs to maximize the sum rate. The optimiza-tion problem guaranteed the intratier and intertier interferencethresholds. Specifically, the aggregated interference from fem-tocell users to the MBS and the maximum delay requirementof the connected CFUE are kept under the acceptable level.To solve the optimization problem, we simplified the CFNby forming DJGs and suggested a formulation optimizationproblem as a coalitional game in partition form in each formedDJG. The convergence of algorithms was also carefully inves-tigated. Simulation results showed that the CFUEs can be self-organized into DJGs. Additionally, the sum rate in the proposedframework is achieved by the optimal subchannel and powerallocation policy with all CFUEs’ average delay constraintsbeing satisfied. Moreover, the efficient resource allocation istested, with the sum rate of the proposed framework alwaysbeing close to optimal solution and better than those of the otherframeworks.

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Tuan LeAnh received the B.Eng. and M.Eng. de-grees in electronic and telecommunication engineer-ing from Hanoi University of Technology, Hanoi,Vietnam, in 2007 and 2010, respectively. He is cur-rently working toward the Ph.D. degree with theDepartment of Computer Science and Engineering,Kyung Hee University, Seoul, South Korea.

Since 2007, he has been an Engineer withthe Vietnam Posts and Telecommunications Group,Hanoi. His research interests include queueing, op-timization, control, and game theory to design,

analyze, and optimize the cutting-edge applications in communication net-works, such as cognitive radio, heterogeneous, small-cell, and content-centricnetworks.

Nguyen H. Tran (S’10–M’11) received the B.S.degree from Ho Chi Minh City University of Tech-nology, Ho Chi Minh City, Vietnam, and the Ph.D.degree in electrical and computer engineering fromKyung Hee University, Seoul, South Korea, in 2005and 2011, respectively.

Since 2012, he has been an Assistant Professorwith the Department of Computer Science and Engi-neering, Kyung Hee University. His research inter-ests include the design, analysis, and optimizationof the cutting-edge applications in communication

networks, such as cloud, mobile-edge computing, datacenters, smart grid,Internet of Things, and heterogeneous and small-cell networks.

Sungwon Lee (M’13) received the Ph.D. degreefrom Kyung Hee University, Seoul, South Korea.

He is currently a Professor with the Departmentof Computer Science and Engineering, Kyung HeeUniversity. From 1999 to 2008, he was a Senior En-gineer with the Telecommunications and NetworksDivision, Samsung Electronics Inc. His research in-terests include mobile broadband networks and com-munication protocols.

Dr. Lee is a member of the Korean Institute ofInformation Scientists and Engineers, Korean Infor-

mation and Communications Society, and Korean Information Processing So-ciety. He serves as the Editor for the Journal of Korean Institute of InformationScientists and Engineers: Computing Practices and Letters.

Eui-Nam Huh (M’14) received the B.S. degree fromBusan University, Busan, South Korea, in 1990; theM.S. degree from the University of Texas at Austin,Austin, TX, USA, in 1995; and the Ph.D. degreefrom Ohio University, Athens, OH, USA, in 2002.

Since 2011, he has been a Professor with theDepartment of Computer Science and Engineering,Kyung Hee University, Seoul, South Korea. He isthe founding Director of Realtime Mobile Cloud Re-search Center (RmCRC) and the Chair of ISOC AsiaPacific Advanced Network (APAN). His research

interests include cloud computing, Internet of Things, wireless sensor networks,high-performance computing, and real-time mobile cloud computing.

Dr. Huh is a member of the Association for Computing Machinery and theInformation Processing Society, as well as several other technical committees.He serves several highly reputed journals as an Editor, including, but notlimited to, the KSII Transactions on Internet and Information Systems and theInternational Journal of Distributed Sensor Networks.


Zhu Han (S’01–M’04–SM’09–F’14) received theB.S. degree in electronic engineering from TsinghuaUniversity, Beijing, China, in 1997 and the M.S. andPh.D. degrees in electrical and computer engineeringfrom the University of Maryland, College Park, MD,USA, in 1999 and 2003, respectively.

From 2000 to 2002, he was a Research and De-velopment Engineer with JDSU, Germantown, MD.From 2003 to 2006, he was a Research Associatewith the University of Maryland. From 2006 to 2008,he was an Assistant Professor with Boise State Uni-

versity, Boise, ID, USA. He is currently a Professor with the Department ofElectrical and Computer Engineering and with the Department of ComputerScience, University of Houston, Houston, TX, USA. His research interests in-clude wireless resource allocation and management, wireless communicationsand networking, game theory, wireless multimedia, security, and smart gridcommunication.

Dr. Han is currently an IEEE Communications Society Distinguished Lec-turer. He received a National Science Foundation Career Award in 2010, theFred W. Ellersick Prize from the IEEE Communication Society in 2011, theEURASIP Best Paper Award for the Journal on Advances in Signal Processingin 2015, and several best paper awards at IEEE conferences.

Choong Seon Hong (AM’95–M’07–SM’11) re-ceived the B.S. and M.S. degrees in electronicengineering from Kyung Hee University, Seoul,South Korea, in 1983 and 1985, and the Ph.D. degreefrom Keio University, Tokyo, Japan, in 1997.

In 1988, he joined KT, where he worked onbroadband networks as a Member of the TechnicalStaff. In September 1993, he joined Keio University.He had worked for the Telecommunications NetworkLaboratory, KT, as a Senior Member of TechnicalStaff and as a Director of the Networking Research

Team until August 1999. Since September 1999, he has been a Professor withthe Department of Computer Science and Engineering, Kyung Hee University.His research interests include future Internet, ad hoc networks, network man-agement, and network security.

Dr. Hong served as a General Chair, Technical Program Commit-tee Chair/Member, or an Organizing Committee Member for internationalconferences such as the IEEE/IFIP Network Operations and ManagementSymposium; the IEEE/IFIP International Symposium on Integrated NetworkManagement; the Asia–Pacific Network Operations and Management Sym-posium; the IEEE Workshops on End-to-End Monitoring Techniques andServices; the IEEE Consumer Communications and Networking Conference;the International Workshop on Assurance in Distributed Systems and Networks;the International Conference for Parallel Processing; the IEEE InternationalWorkshop on Data Integration and Mining, Web Information and ApplicationConference; the IEEE/IFIP International Workshop on Broadband ConvergenceNetworks; the Telecommunications Information Networking Architecture Con-ference; the IEEE/IPSJ International Symposium on Applications and theInternet; and the International Conference on Information Networking. Hecurrently serves as an Associate Editor for the IEEE TRANSACTIONS ON SER-VICES AND NETWORKS MANAGEMENT, the International Journal of NetworkManagement, and the Journal of Communications and Networks. He is alsoan Associate Technical Editor for the IEEE COMMUNICATIONS MAGAZINE.He is a member of the Association for Computing Machinery; the Instituteof Electronics, Information, and Communication Engineers; the InformationProcessing Society of Japan; the Korean Institute of Information Scientists andEngineers; the Korean Information and Communications Society; the KoreanInformation Processing Society, and OSIA.

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