IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 2, NO. 2, APRIL 2013 179

Power Control Based on Subcarrier Exclusion to MitigateDownlink Cross-Tier Interference in OFDMA Tiered Networks

Shiying Han, Student Member, IEEE, Boon-Hee Soong, Senior Member, IEEE,and Quang Duy La, Student Member, IEEE

Abstract—In this letter, we propose a novel power controlscheme based on subcarrier exclusion in OFDMA macro/femtotwo-tier networks implemented by femto base station (FBS).The FBS derives its optimal transmission power and radius ofneighboring area (NA) according to its own location and themacro mobile station (MMS) distribution to maximize its ergodiccapacity under the constraints of maximum FBS transmissionpower and MMS performance requirement. Moreover, the macroneighboring area is derived, within which the FBS avoidsits deployment. Our simulation verifies the applicability andefficiency of the proposed scheme.

Index Terms—Neighboring area, OFDMA tiered networks,power control, subcarrier exclusion.

I. INTRODUCTION

FEMTOCELL [1] is proven to be an effective solutionof indoor coverage overlaid on the macrocell that pro-

vides high throughput due to its advantages of shorter path,lower power, self-configuration and self-organization. With thelimited availability of spectrum resource, permitting femtocellto access the whole spectrum, which results in co-channeldeployment, improves the spectral efficiency of the systemcompared to partial spectrum access scheme, such as theFractional Frequency Reuse. However, the interference acrossdifferent tiers, i.e., cross-tier interference, caused by the co-channel deployment will degrade the system performance,even making the users suffer from intolerable bit error rateor outage probability. To mitigate such interference, opensubscriber group (OSG) is implemented, making it possiblefor a mobile user to hand over to the base station (BS)that provides better service. It obviously results in frequenthandoff; and moreover, since the femtocell is usually featuredby the private service, close subscriber group (CSG), whichforbids the user without authorization to access the FBS, ismore applicable.

To this end, this work focuses on the solution of downlinkcross-tier interference mitigation when co-channel deploymentand CSG are adopted. The contribution of this work canbe summarized as follows. Based on the subcarrier exclu-sion scheme proposed in [4], we introduce a power controlscheme to adjust the amount of excluded subcarriers accordingto system parameters with the help of convex optimization

Manuscript received August 23, 2012. The associate editor coordinatingthe review of this letter and approving it for publication was L. Le.

This work was supported in part by project DTV Signal Survey, and Qualityof Service Multicasting routing in Ad Hoc Networks.

The authors are with the School of Electrical and Electronic Engineering,Nanyang Technological University, Singapore (e-mail: ebhsoong@ntu.edu.sg).

Digital Object Identifier 10.1109/WCL.2012.122612.120611

method, in order to maximize the femto ergodic capacity. Theoptimization problem takes into account the FBS location,maximum transmission power, MMS distribution and MMSperformance requirement. The minimum distance betweenFBS and macro BS (MBS) is also derived. It should be notedthat the power control is implemented according to the macroresource allocation status transmitted to FBS via a wiredbackhaul. Thus, it guarantees the priority of the macro service.

II. SYSTEM MODEL AND PROBLEM FORMULATION

The macro/femto tiered system model is shown in Fig. 1,where the deployment areas of macrocell and femtocell areboth circular with radii of Rm and Rn, respectively. Thedistance between MBS and FBS is denoted by d. The femtoand macro NA indicated by the dashed circles are defined asfollows. Femto-NA (F-NA) is defined as the area within whichthe MMS is treated as neighboring MMS (NMMS). Similarly,macro-NA (M-NA) is defined as the area within which thefemtocell cannot guarantee the Quality of Service (QoS) of itsfemto mobile user (FMS), and thus will avoid being deployedthere. The radii of F-NA and M-NA are represented with Rn

c

and Rmc , respectively. Based on the definition of F-NA and M-

NA, we define the macro and femto average-signal-to-average-interference ratio (M-ASAIR, F-ASAIR) as follows.

M-ASAIR, SIRm, is defined as the average received signalpower from MBS over the average interference from FBS atthe border of F-NA, which can be represented as

SIRm =E[pmf Hm

f d−αm ]

E[pnfHnmf (Rn

c )−αnGPL]

≥ δm (1)

where pmf and pnf are the transmission power from MBS andFBS on subcarrier f , respectively. Hm

f and Hnmf are the

channel responses from MBS and FBS to MMS on subcarrierf , respectively. GPL is the penetration loss and δm is theM-ASAIR threshold. αm and αn are path loss exponent ofmacro and femto, respectively. Similarly, F-ASAIR, SIRn, isdefined as the average received signal power from FBS overthe average interference from MBS at the border of M-NA,which can be represented as

SIRn =E[pnfH

nf (Rn)

−αn ]

E[pmf Hmnf (Rm

c )−αmGPL]≥ δn (2)

where Hnf and Hmn

f are the channel responses from FBSand MBS to FMS on subcarrier f , respectively. δn is the F-ASAIR threshold. To formulate the power control problem,several important assumptions should be highlighted. Firstly,the MMS distribution is modeled as Spatial Poisson Point

2162-2337/13$31.00 c© 2013 IEEE

180 IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 2, NO. 2, APRIL 2013

mcR

mR

nR

ncR

fD

dMMS

MMS

NMMS

Fig. 1. Geometric model of two-tier networks.

Process (SPPP) with intensity of ρm. Secondly, macrocell pro-vides only the best effort service, i.e., all the spectrum resourcewill be allocated to MMS without any idle subcarriers. Thirdly,a single FMS per femtocell is served. The power allocated oneach subcarrier for FMS is equal, i.e., pnf = p0. Last, the M-NA and F-NA are approximated to be circular [2]. Based onthe above definitions and assumptions, we introduce the powercontrol based on subcarrier exclusion (SE-PC) scheme asfollows. The FBS optimizes its ergodic capacity by choosingthe optimal transmission power p0 and F-NA radius Rn

c underthe constraints of maximum FBS transmission power Pn

max andM-ASAIR threshold δm. The subcarrier occupied by NMMSwhich is located inside F-NA will be excluded by FBS fromthe allocable spectrum resource. Furthermore, M-NA radiusRm

c will be calculated based on the achieved p0. Thus, theproblem can be formulated as

max E

⎡⎣ F∑f=1

I(ϕf ) log(1 + p0g

nf

)⎤⎦ (P1)

s.t.

{E[∑F

f=1 I(ϕf )p0] ≤ Pnmax

SIRm ≥ δm

where gnf =Hn

f R−αnn

Γ(In+N0B0), In is the interference from MBS to

FMS, and Γ = − ln(5BER)1.5 is SINR gap [3]. I(ϕf ) log(1+p0g

nf )

is the instantaneous data rate on subcarrier f , where I(ϕf ) isthe indication function given by

I(ϕf ) =

{1, if ϕf > 0

0, otherwise(3)

where ϕf = Df − Rnc , and Df is the distance between FBS

and the MMS who holds subcarrier f , which is also indicatedin Fig. 1. It should be noted that the determination of NMMSis also implemented by each FBS individually when multipleFBS’s coexist in the system. The key point is the modifica-tion of F-NA radius which will take the interference fromother FBS’s into consideration. Because I(ϕf ) is functionof random variable depending on the MMS distribution andlog(1+p0g

nf ) is function of random variable depending on the

FMS channel gain, they are independent. Thus, the objectivefunction in (P1) can be written as

∑Ff=1 E[I(ϕf )]E[log(1 +

p0gnf )].

In the next section, we will derive E[I(ϕf )] and solve(P1). With the solution of (P1), we provide the optimization

algorithm accordingly.

III. OPTIMIZED FBS TRANSMISSION POWER AND F-NARADIUS

A. Derivation of E[I(ϕf )]

To derive E[I(ϕf )], we first calculate P{ϕf > 0}. Based onthe first assumption, the probability that m MMS are locatedoutside F-NA and that n MMS are located inside F-NA are

P (M = m) =e−λ1(λ1)

m

m!P (N = n) =

e−λ2(λ2)n

n!(4)

where λ1 and λ2 are the average number of MMS locatedoutside and inside F-NA, respectively. They can be calculatedas λ1 = ρm(|M| − |F-NA|) and λ2 = ρm|F-NA|, where |M|and |F-NA| are the areas of macrocell and F-NA, respectively.Based on the last assumption, |M| = π(Rm)2 and |F-NA| =π(Rn

c )2. Moreover, the probability that one of the n MMS

occupies subcarrier f when there are m MMS outside NAand n MMS inside F-NA is

P {ϕf ≤ 0|M = m,N = n} =

(n1

)(m+n

1

) =n

m+ n. (5)

Then, the probability of P{ϕf > 0} can be derived as

P{ϕf > 0} = 1−∞∑

n=0

∞∑m=0

P{ϕf ≤ 0|M = m,N = n}

P{M = m,N = n} (6)

which equals to

P{ϕf > 0} =λ1

λ1 + λ2(7)

The mathematical derivation details of (7) are shown inAppendix. Thus, we can get E[I(ϕf )] as

E[I(ϕf )] =

∫ ∞

−∞I(ϕf )f(ϕf )dϕf = P{ϕf ≥ 0} =

λ1

λ1 + λ2.

(8)

By letting a = λ1

λ1+λ2and D =

Rαnm E[pm

f Hmf d−αm ]

E[Hnmf GPLδm] , (P1) can

be written as

max

F∑f=1

aE[log(1 + p0g

nf

)](P2)

s.t.

{ ∑Ff=1 ap0 ≤ Pn

max

p0 ≤ D(1− a)αn2 .

Next, we will focus on solving for p0 and a, and thenpropose the related algorithm.

B. Optimization of p0 and a

Let o0 = ap0. The convexity of the objective function andthe constraints in (P2) can be verified by checking its 2 × 2Hessian matrix [6]. By assigning Lagrangian multipliers λ andγ to each of the constraints, we can form the Lagrangian

f(o0, a) =E

⎡⎣ F∑f=1

a log(1 +o0agnf )

⎤⎦− λ

⎛⎝ F∑

f=1

o0 − Pnmax

⎞⎠

− γ(o0a

− (1− a)αn2 D

). (9)

HAN et al.: POWER CONTROL BASED ON SUBCARRIER EXCLUSION TO MITIGATE DOWNLINK CROSS-TIER INTERFERENCE IN OFDMA TIERED . . . 181

By differentiating f(o0, a) with respect to o0 and a, we have

∂f(o0, a)

∂o0=E

⎡⎣ F∑f=1

(gnf

1 + o0gnf /a)

⎤⎦ − λF − γ

a(10)

∂f(o0, a)

∂a=E

⎡⎣ F∑f=1

log(1 +o0g

nf

a)−

F∑f=1

(o0g

nf

a+ o0gnf)

⎤⎦

+ γo0a2

− γDαn

2(1− a)

αn2 −1. (11)

Since the femto path loss is much smaller than macrocelldue to femto shorter path property, (10) and (11) can beapproximated by ignoring 1 in the logarithmic formula andfractional items as the gap is tight at high SINR region[5].Letting (10) and (11) equal to zeros gives⎧⎨⎩

p0 = FaFaλ+γ

log(

FaFaλ+γ

)− Fλa

Faλ+γ − γDF

αn

2 (1− a)αn2 −1 + Z

F = 0

(12)where Z = E[

∑Ff=1 log(g

nf )] is a constant and can be

numerically calculated. Since it depends on the cdf profile offading channel, such as Rayleigh, Log-normal or Nakagamichannel, the allocated power will be different under differentfading conditions. It is difficult to get the closed form of ain (12). However, it can be solved by numerical method. Wepropose a gradient-based algorithm that solves for p0 and anumerically in Alg. 1. The optimal p0 and a can be obtainedby finding the optimal Lagrangian multipliers λ∗ and γ∗ asso-ciated with constraints

∑Ff=1 ap0 ≤ Pn

max, p0 ≤ D(1− a)αn2 .

Its complexity is bounded by log(max[Δ1,Δ2]ε ), where Δ1 and

Δ2 are the gaps between the initial and optimal value of ap0and that of p0(1− a)

−αn2 . ε is a small error tolerance [7].

Algorithm 1 SE-PC SchemeInitialize λ, γ, calculate a and p0 by solving (12).while

∑Ff=1 ap0 < Pn

max and p0(1− a)−αn/2 < D doincrease λ and γ by small steps: λ = λ+Δλ, γ = γ+Δγcalculate a and p0 by solving (12)

end whilereturn a and p0

IV. DERIVATION OF M-NA RADIUS

In this section, we derive the M-NA radius Rmc which is

also the minimum distance between FBS and MBS in SE-PCscheme. By substituting p0 derived in the previous section into(2), Rm

c can be derived as

Rmc ≥

(Ef [p

mf Hmn

f GPLδn]

Ef [p0Hnf (Rn)−αn ]

)1/αm

. (13)

According to (13), FBS should avoid being deployed withinM-NA with radius of Rm

c , when it is near MBS. Otherwise,the FMS QoS may be unable to be guaranteed.

TABLE ISIMULATION PARAMETERS

Symbol Parameter ValueRm, Rn macrocell, femtocell radius 1 km, 10 mρm MMS density 2.2× 10−4/m2

F number of subcarrier 1000B0 subcarrier BW 10 kHzPmmax, Pn

max max power of MBS, FBS 43 dBm, 20 dBmGPL penetration loss 20 dB [8]αm, αn macro, femto path loss exponent 4, 3.2/3.4

200 400 600 800 1000

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance between FBS and MBS, d(m)F

em

toce

ll ra

te r

atio

SE−PC (αn=3.2, δ

m=10)

SE−PC (αn=3.4, δ

m=10)

FC−DPC (αn=3.2, δ

0=1)

FC−DPC (αn=3.4, δ

0=1)

200 400 600 800 10000.88

0.9

0.92

0.94

0.96

0.98

1

Distance between FBS and MBS,d(m)

Macr

oce

ll ra

te r

atio

SE−PC (αn=3.2, δ

m=10)

SE−PC (αn=3.4, δ

m=10)

FC−DPC (αn=3.2, δ

0=1)

FC−DPC (αn=3.4, δ

0=1)

Fig. 2. Femto and macro achieved rate to ideal rate ratio.

V. NUMERICAL RESULTS

A. Simulation Parameters

The SE-PC scheme is compared with the femto-centricscheme with distance-based power control (FC-DPC) [6],under two femto path loss exponent profiles, i.e., αn = 3.2and 3.4. In the FC-DPC scheme, FBS allocates subcarrier andpower to maximize the femto capacity, while decreasing itstransmission power according to the distance between FBSand MBS as given by

E[pmf d−αm

]= δ0p0R

−αnn GPL (14)

s.t. F · p0 ≤ Pnmax.

The power control scheme in (14) indicates the ratio ofreceived power from MBS to the interference from FBS atthe outside of femtocell wall equals to δ0 which is the macroSIR threshold. Noted that δ0 is different from δm, i.e., the M-ASAIR threshold at the border of F-NA radius, as indicatedin section II. Other parameters are summarized in Table I.

B. Simulation Results

We first evaluate the femto and macro performance in termsof their achieved data rates normalized by their ideal datarates in Fig. 2. Femto ideal data rate is achieved when Pn

maxis utilized, while the macro ideal data rate is achieved whenthe interference of FBS is ignored. Moreover, the FBS trans-mission power on each allocated subcarrier is studied in Fig.3a. It is observed that as d increases, SE-PC permits highertransmission power on each allocated subcarrier compared toFC-DPC, resulting in higher femto capacity, while the macrorate ratios are almost the same for both schemes. This indicatesthat although more power is allocated in SE-PC scheme, theinterference to macrocell does not increase.

182 IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 2, NO. 2, APRIL 2013

200 400 600 800 1000−55

−50

−45

−40

−35

−30

−25

−20

−15

−10

Distance between FBS and MBS,d(m)

FB

S t

ran

smis

sio

n p

ow

er

pe

r a

lloca

ted

su

bca

rrie

r (d

Bm

)

SE−PC (αn=3.2, δ

m=10)

SE−PC (αn=3.4, δ

m=10)

FC−DPC (αn=3.2, δ

0=1)

FC−DPC (αn=3.4, δ

0=1)

Fig. 3a. FBS transmission power

200 400 600 800 10007.5

8

8.5

9

9.5

10

10.5

11x 10

6

Distance between FBS and MBS,d(m)

En

erg

y e

ffic

ien

cy

SE−PC (αn=3.2, δ

m=10)

SE−PC (αn=3.4, δ

m=10)

FC−DPC (αn=3.2, δ

0=1)

FC−DPC (αn=3.4, δ

0=1)

Fig. 3b. System Energy efficiency.

10 20 30 40 50 60 70 80 90 1000

20

40

60

80

100

Distance between FBS and MBS, d(m)

Mac

roce

ll N

A ra

dius

(m)

αn=3.2

αn=3.4

d=Rcm

Fig. 4. Radius of MBS NA.

As SE-PC permits more power allocated, we would be moreconcerned with the system energy efficiency expressed as

Een =Rmacro +Rfemto

Pmacrototal + P femto

total

(15)

which truly reflects the efficiency of SE-PC scheme. The resultin Fig. 3b shows that SE-PC reaches higher system energyefficiency compared to FC-DPC. The difference becomes evenmore obvious when d is getting larger.

Finally, the M-NA radius Rmc is also investigated when FBS

is deployed near the MBS, i.e., d ranges from 10m to 100m.When αn = 3.2, if d < 25m, the performance of FMS will notbe guaranteed. Likewise, when αn = 3.4, the performance ofFMS will not be guaranteed if FBS is located within d = 35m.

VI. CONCLUSION

In this letter, we present a power control scheme based onsubcarrier exclusion in a tiered OFDMA system. This schemepermits higher transmission power on each subcarrier in orderto increase the femto capacity while guaranteeing the macroperformance. The high achievable system energy efficiency in-dicates its better efficiency compared to previous approaches.Moreover, the radius of M-NA also is calculated based onthe optimized FBS transmission power, which indicates theminimum distance between FBS and MBS that guarantees theFMS performance.

APPENDIX ADERIVATION OF (7)

Since the distribution of MMS outside and inside F-NA isSPPP, combined with (4) and (5), we can calculate P{ϕf ≤ 0}

P{ϕf ≤ 0} =

∞∑n=0

∞∑m=0

P{ϕf ≤ 0|M = m,N = n}

=

∞∑n=0

∞∑m=0

n

m+ n

e−λ1λm1

m!

e−λ2λn2

n!. (16)

To make the summation with respect to m tractable, we firstderive the summation of its derivative with respect to λ1, andthen integrate the summation. Thus, (16) becomes

P{ϕf ≤ 0} = e−(λ1+λ2)∞∑

n=1

(∫ ∞∑m=0

λm+n−11

m!dλ1

)λn2

(n− 1)!λn1

= e−(λ1+λ2)∞∑

n=0

(∫eλ1λn

1 dλ1

)λn+12

n!λn+11

. (17)

By exchanging the order of integral and the summation withrespect to n, and making some algebraic manipulations, (17)becomes

P{ϕf ≤ 0} = e−(λ1+λ2)λ2

λ1

∫ ( ∞∑m=0

λn1 e

λ1λn2

n!tn

)dλ1|t=λ1

= e−(λ1+λ2)λ2

λ1

∫eλ1e

λ1+λ2t dλ1|t=λ1 =

λ2

λ1 + λ2. (18)

Therefore, we get the conclusion that

P{ϕf > 0} = 1− P{ϕf ≤ 0} =λ1

λ1 + λ2. (19)

ACKNOWLEDGMENT

The authors would like to thank the reviewers for theirprecious comments and suggestions that improve the qualityof paper.

REFERENCES

[1] V. Chandrasekhar and J. G. Andrews, “Femtocell networks: a survey,”IEEE Commun. Mag., vol. 46, no. 9, pp. 59–67, Sep. 2008.

[2] I. Guvenc, M.-R. Jeong, F. Watanabe, and H. Inamura, “A hybridfrequency assignment for femtocells and coverage area analysis for co-channel operation,” IEEE Commun. Lett., vol. 12, no. 12, pp. 880–882,Dec. 2008.

[3] S. Sadr, A. Anpalagan, and K. Raahemifar, “Radio resource allocation al-gorithms for the downlink of multiuser OFDM communication systems,”IEEE Commun. Survey Tuts., vol. 11, no. 3, pp. 92–106, 2009.

[4] S. Han, B.-H. Soong, and Q. D. La, “Interference mitigation in re-source allocation for OFDMA-based macro/femtocell two-tier wirelessnetworks,” in Proc. 2012 IEEE BMSB.

[5] S. T. Chung and A. J. Goldsmith, “Degree of freedom in adaptivemodulation: a unified view,” IEEE Trans. Commun., vol. 49, no. 9, pp.1561–1571 Sep. 2001.

[6] M.-S. Kim, H. W. Je, and F. A. Tobagi, “Cross-tier interference miti-gation for two-tier OFDMA femtocell networks with limited macrocellinformation,” in Proc. 2010 IEEE Globecom, pp. 1–5.

[7] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge Univer-sity Press.

[8] 3GPP R4-092042, “Simulation assumptions and parameters for FDDHeNB RF requirement,” Alcatel-Lucent, picoChip Design and Vodafone.