Interference Mitigation in Resource Allocation forOFDMA-based Macro/Femtocell Two-tier Wireless

NetworksShiying Han, Boon-Hee Soong and Quang Duy La

INFINITUS, School of Electrical and Electronic EngineeringNanyang Technology University, Singapore 937553

Email: ebhsoong@ntu.edu.sg

Abstract—In this paper, we present the OFDMA-basedmacro/femtocell wireless system as a geometric model, basedon which we propose a resource allocation (RA) scheme thatmitigates cross-tier and inter-femto interference. To mitigate thecross-tier interference, the neighboring area where the macromobile station (MMS) is regarded as neighboring MMS (NMMS)is decided according to the average signal-to-interference-ratio(ASIR) threshold; then the total spectrum resource is partitionedby the femtocell and its NMMS. Subsequently, RA for each femto-cell is implemented as a strategic non-cooperative game by whichthe inter-femto interference is mitigated. Simulation results showthat better performance can be achieved in terms of macrocellthroughput, femtocell throughput on each subcarrier, MMS andfemto mobile station (FMS) CDF of signal-to-interference-plus-noise ratio (SINR), with negligible femtocell throughput sacrifice.

Index Terms—OFDMA, QoS, interference mitigation, subcar-rier exclusion, non-cooperative game

I. INTRODUCTION

With higher demand of multimedia content service (e.g.LTE/DTV) stimulated by the tremendous development ofsmart mobile terminals, various levels of QoS should beguaranteed in the next generation wireless networks. Femtocellnetworks [1], which have several useful features such asshort range, low power, low cost and customer own, enhancemacrocell to provide better multimedia services. Lots of re-search have demonstrated its application in LTE cellular andmultimedia broadcasting networks, such as Single FrequencyNetworks [2][3]. To fully utilize its advantages, femtocell isusually deployed near the edge of macrocell, thereby makingits nearby MMS suffer from high downlink interference, i.e.,cross-tier interference. Cross-tier interference can be canceledby applying open access strategy, but it deteriorates systemcapacity when Closed Subscriber Group (CSG) is applied,which implies that only authorized mobile user can accessits corresponding femtocell. In addition, the inter-femto in-terference cannot be ignored since femtocells are frequentlyserving in cluster, for instance, in a building or community.Therefore, under the scenario of co-channel and CSG accessstrategy, most effort should be directed to the challenge ofinterference mitigation.

In Orthogonal Frequency Division Multiple Access (OFD-MA) wireless networks, the orthogonality nature of subcar-riers makes Fractional Frequency Reuse (FFR) effective to

avoid cross-tier interference [4] [5]. However, the frequencyreuse factor in conventional FFR is fix and less than onewhich results in insufficient exploration of spectrum efficiencyof OFDMA system. Moreover, the proposed escape carrierscheme [6] which dedicates NMMS to the subcarriers un-used by FMSs forces MMS lose its priority, and thus QoSrequirements may not be guaranteed. On the other hand, powercontrol is also applied for cross-tier interference mitigation[7]-[9]. Nevertheless, dramatic reduction of power as distancefrom MBS increases hampers fulfilling enhancement of indoorcapacity and coverage.

In our scheme, we adopt the available spectrum resourcefor each femtocell dynamically according to macrocell RA,which guarantees priority of MMS in accordance with thefact that femtocell can be turned on or off by customerwhile macrocell is operating all the time. By dynamicallyexcluding the subcarriers that are occupied by its NMMS,femtocell spectrum efficiency can be larger than traditionalFFR scheme. Furthermore, for complexity reduction, we definethe neighboring area as where the average SIR received byenclosed MMS exceeds the given threshold. Thus the MMSlocated in the neighboring area will be treated as NMMS.With the whole spectrum resource partitioned by the femtocelland its NMMS, subcarriers occupied by NMMS will neverbe allocated by FBS to its FMS. By doing this, the mostdominant cross-tier interference from FBS to MMS has beentotally canceled.

To mitigate the inter-femtocell interference, game theoryis proven to be a powerful tool since FBS is operating ina self-organized way and it allocates physical resource in adistributed manner [10]. In this paper, we model the femtocellRA as a non-cooperative game and adopt a utility functionthat not only considers the benefit from subcarrier and powerallocated to FMSs, but also the total interference received fromother femtocells and posted to other femtocells. The existenceof the Nash Equilibrium Point can be guaranteed by the proofof the game being a Exact Potential Game.

The structure of the present paper can be summarizedas follows. In section II, the system model is introducedwhich is followed by section III and section IV that presentthe cross-tier and inter-femto interference mitigation scheme,respectively. The simulation results are provided in section V

and the paper is concluded in section VI.

II. SYSTEM MODEL

In the geometric model illustrated in Fig.1, N FBSs servingKn FMSs each are operating within a macrocell with asingle macro base station (MBS) located in the center. Km

MMSs are randomly distributed in macrocell, where someof them are located near or inside femtocells. The shape ofmacrocell is assumed to be hexagonal with radius of Rm,and that of femtocell is assumed to be circular with radiusof Rf . The distance from MBS to FBS is d. We adopt CSGspectrum access policy and co-channel resource reuse withtotal bandwidth of B shared by F subcarriers. Without lossof generality, we assume all the MMSs are outdoor users inthis paper.

We will define the neighboring area and denote its radius asRc which is indicated by dashed circle in Fig.1. We assumethat the inter-macrocell interference can be handled by anothertier of RA, and thus will be ignored here. Thus, in this paperwe only focus on two kinds of interferences: one is cross-tierinterference from femtocell to macrocell, and the other one isintra-cell interference that exists among different femtocells,i.e. inter-femto interference.

The channel gains without considering path loss for eachmobile user k and subcarrier f from MBS to MMS, FBS toFMS, MBS to FMS, FBS to FMS in the other femtocells isrepresented by Hm

k,f ,Hnk,f ,Hmn

k,f and Hnlk,f , respectively, where

m represents macrocell, n and l represent the nth and lth fem-tocell, respectively. We assume they are perfect and availableto FBS and MBS via either feedback or preamble, and FBScommunicate with MBS via IP-based backhaul networks, somacrocell subcarrier allocation matrix Am = {amk,f}Km×Fand power allocation matrix Pm = {pmf }1×F are known byeach FBS. We represent the maximum transmission power ofMBS and FBS are Pm

max and Pnmax. During the femtocell

resource allocation procedure, we introduce subcarrier alloca-tion matrix An = {ank,f}Kn×F , whose element ank,f ∈ {0, 1}represents the occupation for kth FMS on f th subcarrier innth femtocell. Accordingly, the power allocation matrix isrepresented by Pn = {pnf }1×F whose element is pnf ≥ 0representing the power allocated on f th subcarrier in nthfemtocell.

III. CROSS-TIER INTERFERENCE MITIGATION

Macrocell resource allocation can be realized by traditionaloptimization problem allowing for the QoS satisfaction ofeach user, e.g., minimum rate and SINR requirement. Withoutloss of generality, we assume each MMS is allocated withthe same amount of subcarriers and equal power on eachsubcarrier. Then, we can focus on the femtocell resourceallocation problem in this study.

A. Neighboring area definition

Since the MMS that is close to the edge of femtocell isprone to suffer a high level of interference from FBS, theywill be treated as NMMS if the interference level reaches

Fig. 1. System Model

an intolerable level. We introduce an average signal to in-terference ratio (ASIR), i.e. SIR, to determine the radius ofneighboring area Rc within which the MMS is treated asNMMS. Because the distance from MBS to FBS d is muchlarger than femto radius Rf , the shape of neighboring area canbe approximated to be circle although it should be amoebic.Taking channel fading coefficient, path loss and penetrationloss into account, the average SIR that will be suffered byMMS with the distance of Rc from FBS can be derived as,

SIR =Ef∈F

[∑Km

k=1 amk,fp

mf H

mk,f/PLmm(d)

]Ef∈F

[∑Km

k=1 amk,fp

nfH

nmk,f /PLfm(Rc)

] (1)

PLmm and PLfm is the MBS to MMS path loss functionand FBS to MMS path loss function, respectively. To deriveRc, firstly, the ASIR threshold is defined as δ. Generally,δ is chosen no less than 20 (13dB) so that the cross-tierinterference suffered by MMS beyond Rc can be ignored. ThusRc can be derived according to Eq. (2), where PLmf−1(·) isthe inverse function of PLfm.

Rc = PLfm−1

δEf∈F

[∑Km

k=1 amk,fp

nfH

nmf

]Ef∈F

[∑Km

k=1 amk,fp

mf H

mf /PLmm(d)

](2)

B. Cross-tier interference mitigation

When Rc is obtained, the total MMSs will be classifiedinto two categories: one is the NMMS whose distance toFBS is smaller than Rc and the others are non-NMMSswhich are located beyond Rc. To mitigate the femto-to-macrointerference based on matrices of Am and Pm obtained fromMBS, FBS needs to recognize the subcarriers that have beenoccupied by its NMMSs, excludes them from the availablespectrum resource and allocates the remained subcarriers toits FMSs. This method is equivalent to sharing the wholespectrum resource within the coalition formed by femtocelland its NMMSs. By doing this, the most dominant femto-to-macro interference has been totally canceled.

IV. NON-COOPERATION GAME BASED CO-TIERINTERFERENCE MITIGATION

A. Game model

Based on the distributed nature of femtocell, we modelthe femtocell resource allocation problem as a strategic non-cooperative game. Firstly, we model an original game asG = {N, {Sn}n∈N , {un}n∈N}, where players are the NFBSs, strategy Sn = An × Pn is composite strategy, inwhich An = {An| ank,f ∈ {0, 1},

∑Kn

k=1 ank,f ≤ 1}, and

Pn = {Pn| 0 ≤∑F

f=1 pnf ≤ Pn

max}. We denote the powerallocated on f th subcarrier for kth FMS in nth femtocell asonk,f = ank,fp

nf . The interference power from lth femtocell to

nth femtocell on f th subcarrier is denoted by olnk,f = ank,fplf .

Thus, the utility function un can be shown in Eq.(3).

un(Sn, S−n) = β

Kn∑k=1

F∑f=1

log2

(1 +

onk,fGnk,f

pmf Gmnk,f + σ2

)

−N∑l 6=n

Kn∑k=1

F∑f=1

olnk,fGlnk,f −

N∑l 6=n

Kl∑k=1

F∑f=1

onlk,fGnlk,f (3)

The first term of G which represents a benefit for the playercomes from the subcarrier and power allocated to the FMSin nth femtocell; while the second and third terms whichrepresent the costs are the interference introduced by otherfemtocells and interference imposed to other femtocells. Weintroduce β to balance the importance of the benefit. Here,Gn

k,f = Hnk,f/PLff(dnk ) implies the channel gain from

femtocell n to FMS k on subcarrier f , where PLff is theindoor path loss function and dnk is the distance from FBSn to its FMS k. Accordingly, Gm

k,f is the macrocell channelgain, and Gln

k,f is the channel gain from FBS l to FMS k infemtocell n.

In game G, all the subcarriers will be allocated to FMS,whereas in our subcarrier exclusion scheme, some of thesubcarriers will not used by the FBS. To exactly model theFBS RA in the proposed scheme, we model the sub-gameof the game G as Γ = {N, {Sn}n∈N , {un}n∈N}, whereSn = An×Pn, An ⊆ An, Pn ⊆ Pn, n ∈ N , which means thestrategy space of the sub-game is the subset of that of originalgame. The utility function of Γ is denoted by u(Sn, S−n)which is the same with Eq. (3).

B. Convergence of the original game and its sub-game

The existence of Nash Equilibrium Point of the originalgame G can be guaranteed by the fact that game is a ExactPotential Game. Exact Potential Game is featured by the theexistence of potential function. Meanwhile, the increment ofthe utility function will be equal to that of the potentialfunction, if a player unilaterally changes its strategy, whichis illustrated by Eq. (4).

F (S′

nS−n)−F (Sn, S−n) = un(S′

n, S−n)−un(Sn, S−n) (4)

We propose the potential function of G as in Eq. (5), andwill prove the Eq. (4) holds with this potential function.

F (Sn, S−n) =

N∑n=1

β Kn∑k=1

F∑f=1

log2

(1 +

onk,fGnk,f

pmf Gmnk,f + σ2

)

−1

2

N∑l 6=n

Kn∑k=1

F∑f=1

olnk,fGlnk,f −

1

2

N∑l 6=n

Kl∑k=1

F∑f=1

onlk,fGnlk,f

(5)

Proof: Rewrite utility function as

un(Sn, S−n) = βX(S) + Y (S) (6)

where,

X(S) =

Kn∑k=1

F∑f=1

log2

(1 +

onk,fGnk,f

pmf Gmnk,f + σ2

)(7)

Y (S) = −N∑l 6=n

Kn∑k=1

F∑f=1

olnf Glnk,f −

N∑l 6=n

Kl∑k=1

F∑f=1

onlk,fGnlk,f (8)

Therefore, potential function shown in Eq. (5) can be writtenas,

F (Sn, S−n) = β

N∑n=1

X(S) +1

2

N∑n=1

Y (S) (9)

Then we derive∑N

n=1X(S) and∑N

n=1 Y (S) as in Eq. (10)and Eq. (12), respectively.

N∑n=1

X(S) =

N∑n=1

Kn∑k=1

F∑f=1

log2(1 +onk,fG

nk,f

pmf Gmnk,f + σ2

)

=

Kn∑k=1

F∑f=1

log2(1 +onk,fG

nk,f

pmf Gmnk,f + σ2

)

+

N∑q 6=n

Kn∑k=1

F∑f=1

log2(1 +oqk,fG

qk,f

pmf Gmqk,f + σ2

)

= X(S) +W (S−n) (10)

where

W (S−n) =

N∑q 6=n

Kn∑k=1

F∑f=1

log2(1 +oqk,fG

qk,f

pmf Gmqk,f + σ2

) (11)

N∑n=1

Y (S) = −N∑

n=1

N∑l 6=n

Kn∑k=1

F∑f=1

olnk,fGlnk,f +

Kl∑k=1

F∑f=1

onlk,fGnlk,f

= −

N∑l 6=n

Kn∑k=1

F∑f=1

olnk,fGlnk,f −

N∑l 6=n

Kl∑k=1

F∑f=1

onlk,fGnlk,f

−N∑

q 6=n

N∑l 6=q

Kn∑k=1

F∑f=1

olqk,fGlqk,f +

Kl∑k=1

F∑f=1

oqlk,fGqlk,f

= −

N∑l 6=n

Kn∑k=1

F∑f=1

olnk,fGlnk,f −

N∑l 6=n

Kl∑k=1

F∑f=1

onlk,fGnlk,f

−N∑

q 6=n

Kn∑k=1

F∑f=1

oqnk,fGqnk,f −

N∑q 6=n

Kl∑k=1

F∑f=1

onqk,fGnqk,f

−N∑

q 6=n

N∑l 6=q,n

Kn∑k=1

F∑f=1

oqlk,fGqlk,f +

Kl∑k=1

F∑f=1

olqk,fGlqk,f

= −2

N∑l 6=n

Kn∑k=1

F∑f=1

olnk,fGlnf − 2

N∑l 6=n

Kl∑k=1

F∑f=1

onlk,fGnlf

−N∑

q 6=n

N∑l 6=q,n

Kn∑k=1

F∑f=1

oqlk,fGqlf +

Kl∑k=1

F∑f=1

olqk,fGlqf

= 2Y (S) + V (S−n) (12)

where,

V (S−n) = −N∑

q 6=n

N∑l 6=q,n

Kn∑k=1

F∑f=1

oqlk,fGqlf +

Kl∑k=1

F∑f=1

olqk,fGlqf

(13)

Substitute Eq. (10) - (13) into Eq. (9), we have,

F (Sn, S−n) = βX(S) + Y (S) + βW (S−n) +1

2V (S−n)

= un(Sn, S−n) + βW (S−n) +1

2V (S−n) (14)

If the strategy Sn is transferred to S′

n, with S−n remainsthe same, according to Eq. (14), we can get,

F (S′

n, S−n) = βX(S′) + Y (S

′) + βW (S−n) +

1

2V (S−n)

= un(S′

n, S−n) + βW (S−n) +1

2V (S−n) (15)

Compared Eq. (14) with Eq. (15), we can get,

F (S′

n, S−n)− F (Sn, S−n) = un(S′

n, S−n)− un(Sn, S−n)(16)

Thus, we can come to the conclusion that the original gameG is an Exact Potential Game, and F (Sn, S−n) is one of thepotential function of game G.

From the above proof, the existence of Nash EquilibriumPoint of game G is guaranteed by the fact that the originalgame G is an Exact Potential game. It should be notedthat the proof made no assumption of the strategy space,we can safely get the conclusion that its sub-game Γ ={N, {Sn}n∈N , {un}n∈N} is also a potential game, becausethe strategy set for each player is a subset of the strategy setof original game G. Thus, we can confirm the existence ofNash equilibrium point of game Γ.

C. Solution of game

To avoid the extremely high complexity of joint subcarrierand power allocation, we adopt the iterative play to allo-cate subcarrier and power, respectively. In such a play, eachplayer chooses the myopic best strategy based on the currentknowledge of other players’ strategies. In our system, all the

TABLE IMACROCELL PARAMETER

parameter valueLayout of macrocell Hexagonal, Rm=500mNumber of macrocell SingleNumber of MMS 6Subcarrier bandwidth 200kHzNumber of subcarriers 50Carrier frequency 2.5/2.3GHzPath loss [11]Penetration loss 18.3db (reinforced wall)Noise density -174dBm/HzMBS antenna patten / gain Omnidirection / 0dBiMBS transmission power 43dBmTraffic mode Full buffer

available subcarriers will be allocated, therefore, choosing themyopic best strategy can be realized by best allocating eachsubcarrier in a greedy way. Given the transmission powerallocation, for each available subcarrier f , FBS will choosethe best FMS so that the utility function can be maximized,which is shown in Eq. (17).

ank0,f = 1, if k0 = arg max∑Kn

k=1ank,f≤1

ank,f∈{0,1}

un(Sn, S−n) (17)

Given the subcarrier allocation for each iteration, the powerallocation problem can be derived from the convex optimiza-tion problem by solving Karush-Kuhn-Tucker (KKT) condi-tion as in Eq. (18), since the utility function is a concavefunction of pnf .

maxpnf

un(Sn, S−n)

s.t.∑F

f=1 pnf ≤ Pn

max

pnf ≥ 0

(18)

Thus, we can get Eq. (19) for power allocation, where λ isthe Lagrangian multiplier for the maximum power constraint.

pnf = (β∑N

l 6=nGnlk,f + λ

−pmf G

mnk,f + σ2

Gnk,f

, 0)+ (19)

V. NUMERICAL RESULT

A. System parameters

The system parameters of macrocell and femtocell forsimulation are summarized in Table 1 and Tabble 2 respec-tively. We adopt the path loss model of suburban deploymentindicated in [11]. Moreover, we adopt the maximum totalFBS transmission power less than 20dBm-23dBm which isthe allowable maximum FBS transmission power in standard,allowing for the effect of distance between MBS and FBS,and the density of MMS on the neighboring area.

TABLE IIFEMTOCELL PARAMETER

parameter valueLayout of femtocell Circle, Rf=10mNumber of femtocell 2Number of FMS 5Path loss [11]FBS antenna patten / gain Omnidirection / 0dBiFBS Transmission power 10dBm

B. Simulation results

We show the system performance of proposed scheme, andcompare the performance with that of Femto-Centric (FC)scheme [7]. In FC scheme, each femtocell allocates all theradio resource to its FMS aiming to maximize its throughputwithout considering its nearby MMS. Fig. 2, Fig. 3 and Fig.4 illustrate the throughput of macrocell, femtocell and eachfemtocell effective subcarrier, respectively. From the plots, wecan observe that the effect of dynamic subcarrier exclusionis threefold: 1) The improvement of macrocell throughput byimplementing the proposed scheme with respect to FC schemecomes from the cancelation of dominant cross-tier interferenceof neighboring MMSs by the subcarrier exclusion. 2) Due tosubcarrier exclusion, femtocell’s available subcarrier resourceis less than that of FC scheme; thus, there is a decrease of fem-tocell system throughput. However, the percentage of decreaseis so small that can be ignored (around 1.3%). Moreover, thedecrease is also alleviated by playing the potential game. 3)Due to less subcarrier available, power that can be allocated toeach effective subcarrier is increase. Therefore the throughputfor each subcarrier of femtocell is increased compared to theFC scheme.

The SINR performance of MMS and FMS is also investi-gated by simulation as shown in Fig. 6 and Fig. 7. where dfofrepresents the distance between FBSs. It can be observed thatthe MMS SINR under the proposed scheme is much betterthan that under FC scheme, which results in the better outageperformance of macrocell. Meanwhile, the outage performanceof FMS under proposed scheme is improved a little. Thisimplies that when there is femtocell installed in the edgeof macrocell, with the proposed scheme, the performance ofMMS, especially for the user near the cell edge, will not beaffected.

The convergence performance of the propose scheme is alsoinvestigated and provided in Fig. 5, from which we can see thepotential function for the 2-femtocell system can be convergedin around 3-4 iterations.

VI. CONCLUSION

In this work, we investigate the interference mitigation prob-lem for the macro/femtocell two-tier system. By introducingthe concept of neighboring area, MMSs are classified intoNMMS and non-NMMS, where the subcarriers occupied byNMMS will be excluded by its related femtocell. In thisway, the dominant femto-to-macro interference is canceled.

Fig. 2. Macrocell performance Fig. 3. Femtocell performance

Fig. 4. Femtocell throughput pereffective subcarrier

Fig. 5. Convergence

Fig. 6. MMS SINR performance

Fig. 7. FMS SINR performance

To mitigate the inter-femtocell interference, the femtocellRA problem is modeled as an Exact Potential Game whoseequilibrium point can be reached by the iterative play andcorresponding power allocation. This scheme is more suitablein the suburban scenario where the density of MMS is lowand the system is not overload. Simulation results show itsadvantage in system performance with respect to FC scheme.We will investigate more about the neighboring area modelin the multiple MBS scenario, as well as the dynamic FBSpower adaptation scheme according to location of FBS anddistribution of MMS in the future work.

ACKNOWLEDGMENT

The financial support of Mediacorp-NTU Joint R&D forDTV Signal Survey project is gratefully acknowledged.

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