Area Spectral Efﬁciency of Co-Channel Deployed OFDMA ...gssst.iitkgp.ac.in/uploads/faculty/File 6.pdf · Area Spectral Efﬁciency of Co-Channel Deployed OFDMA Femtocell Networks

3524 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 13, NO. 7, JULY 2014

Area Spectral Efficiency of Co-Channel DeployedOFDMA Femtocell Networks

Prabhu Chandhar, Student Member, IEEE, and Suvra Sekhar Das, Member, IEEE

Abstract—Deployment of femtocells is expected to increasethe capacity of cellular networks several folds. However, sincefemtocells operate within the available spectrum of the macro-cellular network, the arising uncontrolled interference may limitthe achievable gain. For the successful operation of femtocells,the area spectral efficiency (ASE) performance needs to be stud-ied for useful insights. In this paper, we derive the ASE fororthogonal-frequency-division-multiple-access-based cochannel-deployed macrocell–femtocell networks considering uniformlydistributed femtocell locations. The ASE is obtained from the areaaveraged signal to interference plus noise ratio (SINR) distribu-tions of macrocell and femtocell networks. Since strength of theco-channel interference received by a user terminal is related toload condition in neighboring cells, the ASE is derived consideringactivity due to fractional load of interfering cells. We then inves-tigate the impact of femtocell density, transmit power, and load offemtocells as well as macrocell transmit power and load on theASE performance. We also look at the optimal femtocell radioparameters: transmit power and load that maximizes the ASEwhile satisfying the QoS constraints of macrocell and femtocellusers at different network conditions. From the analysis, it is seenthat in co-channel deployment mode, if femtocell radio parametersare suitably controlled according to varying network condition,the ASE gain can be increased several folds without affectingmacrocell network performance. It is also shown that, by centrallycoordinating the spectrum reuse and allocated power at eachmacro/femto tier, the overall performance can be improved.

Index Terms—Cellular, base station, macrocell, femtocell, het-erogeneous network, SINR, CCI, area spectral efficiency, cell load,interference management.

I. INTRODUCTION

R ECENT studies show that the demand for data traffic incellular networks is expected to increase several folds in

the near future [1]. Heterogeneous Network (HetNet) architec-ture with low power stations such as picocells, femtocells andrelays is one of the promising approach to support enormoustraffic demand and to provide ubiquitous Quality of Service(QoS) aware services. Particularly deployment of femtocellsalong with macro/micro cells is actively being considered bythe mobile industry since the femtocells improve the systemcapacity by offloading traffic from macrocells [2]–[4]. The

Manuscript received December 10, 2012; revised June 25, 2013 andDecember 27, 2013; accepted April 25, 2014. Date of publication May 5, 2014;date of current version July 8, 2014. A portion of this work was presented atIEEE ICC’13, Budapest, Hungary. The associate editor coordinating the reviewof this paper and approving it for publication was G. Wunder.

The authors are with the G. S. Sanyal School of Telecommunications,IIT Kharagpur, West Bengal 721302, India (e-mail: [email protected]; [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/TWC.2014.2321759

additional advantages of deployment of femtocells is that itincreases indoor coverage and reduces OPEX for operators. Themain objective of femtocell deployment is to improve the AreaSpectral Efficiency (ASE) in order to serve large number ofusers with high traffic demand. Throughout this paper, the termASE is referred for the sum of the throughput achieved by bothmacrocell and femtocell users per unit bandwidth per unit area(b/s/Hz/m2).

Deployment of femtocells in co-channel mode increasessystem capacity several folds due to full spatial reuse of totalavailable spectrum compared to dedicated deployment mode[5]. However, it is achieved at the cost of degradation in themacrocell network performance due to increased co-channelinterference (CCI) created by the randomly deployed femto-cells. Though the single frequency reuse in OFDMA basedsystems such as Long Term Evolution (LTE) and WorldwideInteroperability for Microwave Access (WiMAX) are expectedprovide enormous capacity, the CCI is the performance degra-dation factor that needs to be controlled carefully. Addinguncontrolled co-channel femtocells on top of these cellularsystems which use single frequency reuse would lead to furtherdegradation in the performance of the systems. Further, openaccess and closed access are the two main access mechanismsbeing considered for femtocell deployment [6]. Open accessmode provides an improved overall system capacity comparedto closed access mode as it allows any nearby user to accessit. Also, the impact of CCI is less significant in open accessmode. Whereas, in closed access mode, since only the usersregistered to a particular femtocell allowed to access it, theunregistered nearby users suffer due to severe CCI. Since theaccess to the femtocells depends on the interest of owner ofthe femtocell and back-haul restrictions, closed access mode ofdeployment is under active consideration by the mobile industry[6]. So, in this work, we focus on co-channel closed access fem-tocell deployment. Further, the CCI caused by the femtocellsdepends on femtocell transmit power as well as the activity ofindividual femtocell on each subchannel. Therefore, the com-bined effect of femtocell activity and transmit power should beinvestigated.

Further, the interference experienced by both macro andfemto users is not only due to femtocell parameters but alsodepends on the power configurations and load conditions at themacrocell network, due to the fact that the transmit power ofmacro BSs is much higher than that of femto BSs. The loadcondition in cellular networks varies with space and time dueto user behavior. This results in varying interference situationin the network. When the macrocell network load is higher,the users would experience heavy CCI from surrounding cells,

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CHANDHAR AND DAS: ASE OF CO-CHANNEL DEPLOYED OFDMA FEMTOCELL NETWORKS 3525

which leads to poor Signal to Interference plus Noise Ratio(SINR) and hence low throughput. Whereas, during low loadconditions in macrocells, the users would experience betterSINR and throughput because of reduced interference dueto low activity of interfering cells. Adapting femtocell radioparameters according to varying traffic conditions in macrocellnetwork would help to achieve maximum ASE. Therefore,these dynamics in the macrocell network behavior have tobe considered in the analysis of macrocell-femtocell networkperformance.

The throughput performance of co-channel deployedmacrocell-femtocell networks has been investigated throughsystem level simulations in [2], [5], [7]. The ASE analysis ofmacrocell-femtocell networks has been studied in [8]–[10]. In[8], the authors have studied the ASE performance in dedicatedchannel mode of deployment. Since, both the macrocells andfemtocells use different frequency subchannels, no analysis ofCCI is considered. In [9], the analysis of ASE of macrocell-femtocell network in dedicated channel deployment is studiedthrough simulations assuming fixed femtocell locations at theedge of a macrocell. In [10], the authors have analyzed theASE in partial co-channel two-tier networks assuming a singlemacrocell scenario which does not consider CCI from neigh-boring macrocells. The analysis on ASE performance of the co-channel deployed macrocell-femtocell networks has not beenstudied.

Further, the impact of load condition in macrocell networkhas been considered in some of the previous works [11]–[14]on femtocell networks. In [11], authors have proposed a wakeup mechanisms for open access femtocells where the activityof femtocells is controlled based on traffic load in macrocell.In [12], [13], authors have considered the activity or load ofinterfering BSs in different tiers of K-tier networks in theanalysis of coverage performance. In our previous work [14],through detailed system level simulations we have analyzedthe throughput performance of co-channel OFDMA femtocellnetworks (3GPP LTE) under different macro load conditions.In our another work [3], we studied the macrocell offloadinggain due to deployment of open access co-channel femtocellsat different macrocell load conditions. However, none of theabove mentioned works investigated the ASE performanceconsidering fractional load condition in both macrocell andclosed-access femtocell networks.

In this work, we develop an analytical framework to studythe ASE performance of OFDMA based co-channel deployedmacrocell-femtocell networks under different macrocell net-work load conditions. First, we derive the SINR distributionfor macrocell and femtocell networks as a function of femtocellparameters (transmit power, load and density) as well as macro-cell parameters (transmit power and load). Combined effect ofinterferer’s activity (binary process), slow fading (shadowing)and multi-path fading (Rayleigh) is considered in the derivationof SINR distributions. The ASE of the network is obtained fromthe derived SINR distributions. Then we investigate the impactof femtocell parameters (density, transmit power, and load) andmacrocell parameters (transmit power and load) on the ASEperformance. We also analyze the maximum achievable ASEgain with optimal transmit power and load configuration for

femtocells while satisfying QoS constraints of both macrocelland femtocell networks.

The rest of this paper is organized as follows. The systemmodel and assumptions are described in Section II. Section IIIdescribes the steps involved in the derivation of ASE. Resultsand discussions are presented in Section IV. Conclusions areprovided in Section V.

II. SYSTEM MODEL AND ASSUMPTIONS

We consider downlink of OFDMA based single frequencynetwork. The macrocell network consists of Nm number ofhexagonal cells of radius Rc, each with coverage area |A| =(3√3R2

c)/2. Omni directional antenna pattern is assumed formacro BSs. The macrocell users are assumed to be uniformlydistributed. The houses of radius Rf are assumed to be uni-formly distributed inside the macrocell network with densityρf = Nf/|A|. Here Nf denotes the average number of femto-cells per cell site and Rf denotes the boundary of the house.The femto BS is assumed to be located at the center of thehouse. The available total system bandwidth B Hz consists ofNsb number of subchannels each with bandwidth Bsb Hz. Bothmacrocell and femtocell network uses the same spectrum andclosed access mode is considered for femtocell operation. Forconvenience, the description of the symbols used in this paperare listed in Table I.

A. System Load and Interferer’s Activity Model

In OFDMA based systems, during fractional load conditions,the transmission by the base stations on each subchannel iscombination of active (ON) and inactive (OFF) states. Theactivity is related to load in the cell i.e., number of activeusers served by the BS. The higher the number of activeusers, the higher will be the activity and vice versa. Sincethe CCI received by the user terminals is a function of loadcondition in neighboring cells, in the derivation of SINR dis-tribution we consider the randomness involved in the activitystatus of individual interfering cell on each subchannel. Weassume that the subchannel assignment by the base station toits user is based on the channel condition experienced by theuser terminals which is independent and random. Therefore,i-th interferer’s activity status (ON/OFF) on subchannel k canbe considered to be binary random process vki. The processvki can be seen as a sequence of pairs of active states plusthe subsequent inactive states. The occupancy of the active andinactive states are usually modeled as exponentially distributed.To model the activity status of the interferers with transitionbehaviors of the states, we use discrete two-state homogeneousMarkov-chain stochastic model [15]. This model helps to char-acterize the transition behavior of the activity status of thesubchannels. Fig. 1 shows the state diagram of activity statusof the subchannel k in i-th cell. The transition probabilities aand b are characterizing the occupancy duration of active andinactive states. Let the first order probability mass function ofvki as

Pr[vki = 1] = βkiand Pr[vki = 0] = 1− βki

, (1)


TABLE ILIST OF SYMBOLS USED

where βkidenotes the activity factor of i-th the source. As-

sume exponentially distributed probability distribution func-tions for the duration of the ON and OFF states fon(t) =μki,on e−μki,ont, t ≥ 0 and foff(t) = μki,off e−μki,off t, t ≥ 0respectively with mean a = 1/μki,on and b = 1/μki,off . Theμki,on and μki,off are depending on the type of the traffic offeredby the BS to its users. The activity factor βki of the source i onsubchannel k can be written as

βki =a

a+ b=

μki,off

μki,on + μki,off. (2)

Fig. 1. Discrete two state Markov model.

The autocorrelation function of the process vki can be ex-pressed as [16]

Rvki(τ)=

μki,on μki,off e−(μki,on+μki,off )|τ |

(μki,on+μki,on)2+

μ2ki,off

(μki,on+μki,on)2.

(3)

The activity status of all the subchannels are considered tobe independent and active with the same probability βi. Thus,the probability that nsb subchannels are active has a binomialdistribution

Pnsb(nsb)=

(Nsb

nsb

)(βi)

nsb(1−βi)Nsb−nsb , nsb=0,1,2, . . . ,Nsb.

(4)

Therefore, the average number of active subchannels at load βi

is obtained by nsb = βi ×Nsb, where Nsb is the total numberof available subchannels. Let Nfl

ui be the number of userssupported by the i-th cell during full load condition, then thenumber of active users at load, βi, is obtained as

Nactui (βi) =

⌈βi ×Nfl

ui

⌉. (5)

B. Channel Model

Let the received signal power from the BS at the userterminal as, Pr = PtG, where Pt is BS transmit power, and G ischannel gain. The channel gain G is modeled as the product ofpathloss component (L), power of shadowing component (χ),and power of fast fading component (z):

G = Lzχ. (6)

Since, we consider the Rayleigh distribution for fast fadingh, the power of fast fading z = |h|2 follows Gamma distri-bution with unity mean. The shadowing is modeled as log-normally distributed random variable χ = exp(ξ), where ξ isa Gaussian random variable with zero mean and variance σ2

ξ

(in dB). The shadow fading is assumed to be independentof location of transmitter and receiver. The pathloss compo-nent between the user and the macro BS is modeled as [17]Lm = Km(dm/d0m)−αm , where Km = (λ/(4πd0m))2 is freespace pathloss at macrocell reference distance d0m, dm is thedistance between the user and macro BS, wavelength λ isrelated to carrier frequency fc, and αm is outdoor pathlossexponent. Similarly, the pathloss component between the userand the femto BS is modeled as Lf = Kf (df/d0f )

−αf , where


Fig. 2. Distribution of femtocell locations inside the macrocell network.

Kf = (λ/(4πd0f ))2 is free space pathloss at indoor reference

distance d0f , df is distance between the user and femto BS, andαf is indoor pathloss exponent. Further, the wall penetrationloss Lw is considered between the macrocell user and theinterfering femto BS, between the indoor user and interfer-ing macro BS, and between the indoor user and interferingfemto BS.

C. Femtocell Network Model

Previous works on femtocell networks [8], [10], [18], [19] as-sumed that the femtocell locations are distributed according tospatial point Poisson process (SPPP) and characterized the ag-gregate femtocell interference as the shot-noise process. Sincethe shot noise process has closed form expression only when thepathloss exponent is four, it makes difficult to obtain the SINRdistributions. The authors in [8], [19] obtain the lower boundson the outage probability by only considering interference fromdominant femtocells. The authors in [18] obtained the outageprobability by approximating the femtocell distribution. Inanother approach, by known statistics of individual interferingcomponents, the distribution of the cumulative interference canbe obtained using some approximation tools [30]. In this work,we follow this approach to obtain the distribution of aggre-gate femtocell interference. We consider uniform distributionfor femtocell locations. The estimated locations of interfer-ing femtocells is used to find the distribution of aggregateinterference.

Assume that the femtocells are uniformly and randomlydistributed within the macrocell network with density, ρf =Nf/|A|. The probability density function (PDF) of the dis-tance df of the femto BSs to the center of the macrocellis, fdf

(r) = 2(r −Rmf0)/(Rc−Rmf0)2, Rmf0 < r < Rc.

Consider a reference position y inside the macrocell as shown inFig. 2. In the figure, Dint denotes the radius of the interferencezone i.e. the distance within which the dominant interferersare located. Our interest is to find the distances of femto BSs

which are located around the position y within the distanceDint. Now let us order the femto BSs according to the distanceto the reference position y (i.e., df1 < df2 < df3 . . . . . .). ThePDF of the distance dfj of j-th nearest femto BS to y is givenby [20]

pdfj(r) =

2πrρf(j − 1)!

(πr2ρf )j−1

e−πr2ρf , j = 1, 2, 3, . . . (7)

The expected distance of the j-th femto BS to the referenceposition y is obtained as

dfj =Γ(j + 1/2)

√πρf (j − 1)!

. (8)

The derivation for moments of dfj is given in Appendix A.Fig. 3(a) shows the expected distance of femto BSs obtainedfrom (8) and simulations for Rc = 288 m and Nf = 40. Foranalytical tractability, we neglect the variance in the estimateddistance of femto BSs. It is observed that only with very lowfemtocell density (Nf < 10), the variation in the estimated dis-tance results in variation in the aggregate interference, whereasit is insignificant with high femtocell density.

It is possible, mainly in high femtocell density scenarios, thatthe calculated distance of the first nearest femto BS (from (8)) isless than the distance Rf (radius of the femtocell). For example,with Nf = 200, it is observed that with (i.e Nf > 180), thecalculated distance of the first nearest femto BS is 15 m whichis less than the radius of the femtocell Rf = 20 m. Further, weassume that if the user location is within Rf (boundary of thehouse in which the femtocell is deployed) distance from thefemto BS, then the user is considered to be the home user servedby the femto BS and the users located outside the radius Rf areconsidered as outdoor users attached to macro BS. Therefore,the minimum distance between the outdoor user and the femtoBS is assumed to be Rf . Therefore, in high femtocell densityscenarios, the calculated distances of femto BSs which are lessthan Rf are excluded from the interference calculation.

It is obvious that the aggregate interference power receivedat point y is mainly due to strongest femtocells. Since theinterference from the femtocells located far away is negligibledue to their distance and lower transmit power, it can beexcluded from the aggregate interference. Consider a femtoBS which transmits with maximum transmit power Ptf,max.Let Ps be the sensitivity of the receiver. The user locatedat distance d from the femto BS is considered to be withinthe interference zone of the femtocell only if the averagereceived power P (d) = KfLwPtf,max(d/d0f )

−αf is greaterthan Ps. Hence, the interference zone of the femtocell becomesthe circular area with radius D = d0f (KfLwPtf,max/Ps)

1/αf .However, due to shadowing effect, the random fluctuations inthe received signal results in varying coverage range of thefemto BS. The normalized received power P (d) = P (d)/Ps

at normalized distance, d = d/D, can be written as P (d) =

10 log10(d−αf ) + ξf , where ξf is zero mean Gaussian dis-

tributed random variable with standard deviation σξf in dB.Using log-normal model of the received power, the interfer-

ence probability (i.e. the probability that the user location is


Fig. 3. Femtocell interference model: Estimated distances of femto BSs, Interference probability, and Average aggregate interference. (a) Expected distanceof interfering femtocells for Nf = 40 and Rc = 288 m. (b) Interference probability vs normalized distance for αf = 3, Lw = 10 dB, Ps = −104 dBm/Hz,Nf = 200, Ptf,max = 20 dBm. (c) Average aggregate femto interference vs Dint for αf = 3, Lw = 10 dB, Nf = 200, Ptf,max = 20 dBm, βf = 100%,D = 63 m.

within the interference zone of the femtocell) can be obtainedas [21]

p(d) =Pr[10 log10

(P (d)

)> 0

]

=1

2

[1− erf

(10√2 ln 10

ln(d)

(σξf /αf )

)]. (9)

Note that the interference probability p(d) depends on thefollowing factors: pathloss exponent αf , and standard deviationof shadowing component σξf . Fig. 3(b) shows the interferenceprobability for varying normalized distance. It can be seenthat as the standard deviation of shadow fading componentincreases the interference probability at larger distance alsoincreases. Let Dint be the radius of the interference zone i.e.the distance at which the probability, p(d) becomes zero. Fromthe figure it can be seen that the radius of the interferencezone is Dint = 2.5D, 3.5D, and 4.5D respectively for σξf =4 dB, 6 dB, and 8 dB.

If the interference probability with respect to the j-th fem-tocell, p(dj) is non zero, then the point y is considered to beunder the interference zone of that femtocell, otherwise it willbe excluded from the calculation of cumulative interference.The expected number of interfering femtocells around thepoint y can be obtained as Nfint = πD2

intρf . The cumulativefemto interference received by the user terminal located at thereference position y is

If =

Nfint∑j=1

vkfjPtfjLw Kf (dfj/d0f )−αf

∣∣hfj

∣∣2 exp (ξfj

),

(10)

where Ptfj is transmit power of j-th femto BS, vkfj is activitystatus of j-th femto BS.

Fig. 3(c) shows the average aggregate femto interference forvarying radius of interference zone. The mean value of aggre-gate femto interference is obtained using extended Wilkinson’smoment matching method which is described in Section III-B.From the figure, it can be seen that the aggregate femto interfer-ence remains constant after 160 m (∼2.5D), 220 m (∼3.5D),and 280 m (∼4.5D) respectively for σξf = 4 dB, 6 dB, and

8 dB. This confirms the validity of the assumption i.e., theexclusion of the weak interferers in the calculation of aggregateinterference.

D. Spectral Efficiency Calculation

In order to get benchmark performance figures [22], weconsider that both macro and femto BSs schedule their usersaccording to Round-Robin (RR) scheduling policy. The BSchooses a particular Modulation and Coding Scheme (MCS) forits user based on the channel feedback provided by that user. Itis assumed that there is no power control employed by the BS.The average Spectral Efficiency (SE) of a cell is obtained fromthe area averaged SINR distribution. Let NL be the numberof MCS levels being used by the link adaptation scheme. Theprobability of utilizing l-th MCS can be obtained from the PDFof the SINR in a cell as pmcs

l =∫ γl,max

γl,minpγ(γ) dγ, where pγ(γ)

is the area averaged PDF of SINR, γl,min and γl,max are thelower and upper SINR bounds for the l-th MCS. Let bl be thenumber of bits transmitted per Hz using l-th MCS. Then theaverage SE of i-th cell can be calculated by

Ci =

NL∑l=1

pmcsl . bl (b/s/Hz). (11)

Considering identical statistics over all frequency subchannels,the long-term average cell throughput Ti achieved over band-width B by the i-th macrocell (or femtocell) at any given loadcondition can be written as, Ti = βi ×B × Ci (b/s), where βi

is the load factor.

III. AREA SPECTRAL EFFICIENCY

Let Cm(βm, βf , Ptm, Ptf , ρf) and Cf (βm, βf , Ptm, Ptf , ρf)be the spectral efficiencies (in b/s/Hz) achieved by themacrocell and femtocell network respectively in eachsubchannel with Nf number of femtocells at macrocell load,βm, and femto load, βf , for femtocell transmit power, Ptf ,and macrocell transmit power, Ptm. Let Tum,min and Tuf,min

be the minimum required throughputs of macrocell userand femtocell user respectively. The average cell throughput


(b/s) achieved by the macrocell at load condition βm canbe obtained as Tm(βm, βf , Ptm, Ptf , ρf ) = βmBCm(βm, βf ,Ptm, Ptf , ρf ). The long-term average throughput achievedby the macrocell user is Tum(βm, βf , Ptm, Ptf , ρf ) =Tm/Nact

um(βm), where Nactum(βm) is the number of users served

by the macro BS at load βm. The total throughput achieved bythe femtocell network at load condition βm can be obtainedas Tf (βm, βf , Ptm, Ptf , ρf ) = βfBCf (βm, βf , Ptm, Ptf , ρf ).The total number of femtocell users can be written asN tot

uf =∑Nf

j=1 Nufj . Here, Nufj is the number of userssupported by the j-th femtocell which is given by Nufj =βfBCfj/Tuf,min, where Cfj is the long-term spectralefficiency (in b/s/Hz) achieved by the j-th femtocell. Thelong-term average throughput achieved by the femtocell user isTuf (βm, βf , Ptf , ρf ) = Tf/N

totuf .

For a given network condition, the total throughput achievedby the macrocell and all the femtocells located within itscoverage area, |A| can be written as

TT (βm, βf , Ptm, Ptf , ρf )

= Tm(βm, βf , Ptm, Ptf , ρf )

+ Tf (βm, βf , Ptm, Ptf , ρf )(b/s)

= βmBCm(βm, βf , Ptm, Ptf , ρf )

+ βfBCf (βm, βf , Ptm, Ptf , ρf ). (12)

The derivations for Cm and Cf are given in Section III-Band C respectively. According to the definition of ASE, thetotal ASE achieved by the macrocell-femtocell network can beexpressed as

ASET (βm, βf , Ptm, Ptf , ρf )

=TT (βm, βf , Ptm, Ptf , ρf )

B.|A| (b/s/Hz/m2). (13)

A. Optimal Femtocell Radio Parameters

It can be understood that, operating femtocells at fixedtransmit power irrespective of the macrocell traffic conditionwill leads to degradation of macrocell network performance.Since the load condition in the macrocell network varies withtime, the SINR experienced by both the macrocell and fem-tocell users also varies significantly because of much highertransmit power of macro BSs. During low load conditions inmacrocell network, the femto BSs may use high transmit powerto increase femtocell network throughput, because of reducedactivity of neighboring macrocells. Conversely, during highmacro load conditions the femtocell transmit power should bekept as minimum as possible. In order to achieve the benefit offemtocell deployment i.e. to achieve maximum ASE, the CCIcaused by the femtocell network must be controlled so thatthe QoS conditions of both macrocell and femtocell networksremains unaffected.

Since the interference situation depends on the load conditionin the macrocell network as well in the femtocell networkand number of active femtocells, the femtocells should adapt

their radio parameters according to variation in the networkcondition. The CCI can be kept within the tolerable level byappropriately controlling either the transmit power (Ptf ) orthe load (βf ) of femtocells. We assume that the femto BSsallocate a set of random sub-channels to its users from the totalavailable sub-channels. This provides randomized interferenceavoidance, because the random sub-channel allocation wouldresults in less probability of sub-channel collisions between themacrocell and femtocell network [8], [23]. Further, it does notrequire any coordination between the femtocells or macrocells.

Hence, for a given network condition (macrocell load con-dition (βm = Bm), macrocell transmit power (Ptm = Ptm),number of femtocells (Nf = Nf ), the optimal combination offemtocell transmit power and load that maximizes the ASEwhile satisfying QoS constraints in both the networks can beobtained from the following optimization problem,

{P ∗tf , β

∗f

}= arg max

{Ptf ,βf }ASET (Bm, βf ,Ptm, Ptf ,Nf ),

subject to : C1 : Tum(Bm, βf ,Ptm, Ptf ,Nf ) ≥ Tum,min

C2 : Tuf (Bm, βf ,Ptm, Ptf ,Nf ) ≥ Tuf,min

C3 : Ptf,min ≤ Ptf ≤ Ptf,max.

C4 : 0 ≤ βf ≤ 1. (14)

Here the constraints C1 and C2 denote the QoS requirementof macrocell and femtocell users respectively. Constraints C3and C4 represent the range of optimization variables (femtocelltransmit power and load) respectively. Since we derive thetotal ASE, ASET semi-analytically from the SINR distribu-tions of macrocell and femtocells, it can not be explicitly de-scribed as a function of the optimization variables Ptf and βf .However, the problem can be described using oracle model(See Section 4.1.4 in [24]). The oracle model is used when theobjective function, f(x) is not known explicitly, but the func-tion and its derivatives f ′(x) (using finite difference method)can be evaluated at any x whenever they are required during theoptimization process.

As the macrocell user SINR (18) is an inverse functionof femtocell transmit power, Ptf and load, βf , the averagethroughput of macrocell users (Tum) as well as the averagemacrocell throughput (Tm) are monotonically non-increasingconvex functions. The average throughput of femtocell users(Tuf ) and average femtocell network throughput (Tf ) haveboth direct and inverse relationship with Ptf and βf (18).However, due to wall penetration loss, with increasing fem-tocell transmit power, the received power from the servingfemtocell is more dominant than the cumulative interferencepower received from the neighboring femtocells. Therefore,the SINR and the average throughput of femtocell users aremonotonically non-decreasing concave functions of Ptf andβf . Further, the increase in (Tuf ) depends on the number ofinterfering components and wall penetration loss. With lowfemtocell density (or high wall penetration loss), the femto-cell network throughput is linearly increasing function of Ptf

and βf , but the increase diminishes with increasing femtocelldensity (or decreasing wall penetration loss). Finally, since


the major part of ASE is mainly due to femtocell networkthroughput Tf (which increases with the number of femtocells),the ASE, ASET follows the behavior of Tf . Thus, the ASE ismonotonically non-decreasing concave function of Ptf and βf .

Let P(min)tf (or β

(min)f ) be the minimum transmit power

(or load) required to support minimum throughput require-ment of femtocell users (Tuf,min). Let P

(max)tf (or β

(max)f )

be the maximum allowable transmit power (or load) re-quired to satisfy minimum throughput requirement of macro-cell users (Tum,min). Let FPtf

∈ [P(min)tf , P

(max)tf ] and Fβf

∈[β

(min)f , β

(max)f ] be the feasible set of femtocell transmit power

and load that satisfy the constraints C1 and C2. The solution ofthe problem (14), [P ∗

tf , β∗f ] is a convex combination of P (min)

tf

and P(max)tf , and β

(min)f and β

(max)f i.e. for θ ∈ [0, 1], P ∗

tf =

θP(min)tf + (1− θ)P

(max)tf ∈ FPtf

. Similarly, β∗f = θβ

(min)f +

(1− θ)β(max)f ∈ Fβf

.By letting u = [Ptf , βf ], the above maximization problem

can be written in standard form as [24]

maximize f0(u)

subject to : fi(u) ≥ 0, i = 1, 2, . . . . , 6. (15)

Here, the inequality constraint functions: f0(u) = ASET (Bm,Ptm,u, ρf ); f1(u)=Tum(u)− Tum,min; f2(u)=Tuf (u)−Tuf,min; f3(u) = Ptf − Ptf,min; f4(u) = Ptf,max − Ptf ;f5(u) = βf − 0; f6(u) = 1− βf . The functions f0, −f1, f2,f3, −f4, f5, and −f6 are concave functions. The notation(15) describes the problem of finding the optimal value of uthat maximizes the concave objective function f0(u) amongall u that satisfy the constraints: fi(u), i = 1, . . . , 6. Theproblem can be solved using efficient numerical methods suchas interior-point algorithms [24]. The optimal value ASE∗

T ofthe problem (15) is obtained as

ASE∗T = sup {f0(u) | fi(u) ≥ 0, i = 1, 2, . . . , 6} . (16)

If ASE∗T = ∞, the problem is infeasible because supremum of

the empty set is ∞ i.e. none of the femtocell transmit power andload in the given range of values satisfies the constraints. Notethat the ASE can be optimized over the individual parameter(Ptf or βf ) for a given value of other parameter (Ptf = Ptf

or βf = Bf ). The optimal ASE performance results with theoptimization of femtocell transmit power with fixed femtocellload (βf = Bf ) as well as with the joint optimization of bothPtf and βf are detailed in Section IV-B.

The ASE gain, GASE is defined as the ratio of the ASEachieved by the macrocell-femtocell networks to the ASEachieved by the macrocell with no femtocell deployment.

GASE=Tm(βm, βf , Ptm, Ptf , ρf)+Tf (βm, βf , Ptm, Ptf , ρf)

Tm(βm, βf , Ptm, Ptf , ρf =0).

(17)

B. SE of Macrocell Network

We denote the SINR for a macrocell user, γm(χ, h, v) as afunction of interferer’s activity (v), shadow fading component

(χ) and small scale fading component (h). The received SINRfor a macrocell user at position rm = (rm, θm) on subchannelk can be expressed as

γkm(χ, h, v)

=Ptkm0

Gkm0

Nm−1∑i=1

Ptkmivkmi

Gkmi+

Nfint∑j=1

PtkfjvkfjGkfj+BsbN0

. (18)

By applying (6), the above SINR expression can be rewritten as

γkm(χ, h, v) =

zkm0

Ikm(χ, h, v). (19)

Where,

Ikm(χ, h, v) =

Nm−1∑i=1

PtkmiLmi

Ptkm0Lm0

vkmizkmi

e(ξmi−ξm0

)

+

Nfint∑j=1

PtkfjLfj

Ptkm0Lm0

vkfjzkfje(ξfj−ξm0

) +N0Bsb

Ptkm0Lm0

e(−ξm0)

and

Lm0=Km(dm0

/d0m)−αm , Lmi= Km(dmi

/d0m)−αm ,

Lfj =KfLw(dfj/d0f )−αf .

Where Ptkm0is the transmit power of serving macro BS

on subchannel k, Pkmiand Pkfj are the transmit power

powers of i-th interfering macro BS and j-th interfer-ing femto BS respectively on subchannel k. The Gammadistributed channel powers between the user and i-thmacro BS and j-th femto BS on subchannel k are zkmi

andzkfj respectively. The Gaussian random variables ξmi

and ξfjrepresent the powers of shadowing component between the userand i-th macro BS and j-th femto BS respectively, dmi

anddfj are the distance between the user and i-th macro BS andj-th femto BS respectively. The activity status of the i-th macroBS and j-th femto BS on subchannel k are denoted by vkmi

and vkfj respectively, and N0 is noise power spectral density in(Watts/Hz). Assuming the macrocell user location as referenceposition, the expected distances between the macrocell user andfemto BSs, dfj (j = 1, 2, 3, . . . , Nfint) are obtained from (8).

The denominator in (19) can be approximated as a log-normal random variable as Ikm(χ, h, v) ≈ exp(X), where Xis a Gaussian random variable with mean μX and variance σ2

X

[16]. The mean μX and variance σ2X are obtained using the

extended Wilkinson’s Moment matching method. The detailsof the method are given in Appendix B. The accuracy of thisapproximation is affected only for low activity factors (i.e.,β < .1) and low standard deviation of log-normal components(σ < 1.5 dB) [16].

Since, the SINR in (19) is the product of Gammarandom variable zkm0

and a log-normal random variable


exp(−X), it can be approximated as a log-normal randomvariable [25]

γkm(χ, h, v) ≈ exp(Y ), (20)

where Y is the Gaussian random variable with mean andvariance,

μY = μγm= ψ(1)− μX and σ2

Y = σ2γm

= ζ(2, 1) + σ2X

(21)

respectively. Here ψ(1) is Euler’s psi function and ζ(2, 1)is Riemann’s zeta function [25]. The accuracy of the aboveapproximation is good for σX ≥ 6 dB [26]. Note that thetypical values of standard deviation of shadowing componentin outdoor and indoor environment is greater than 6 dB and4 dB respectively [22]. Therefore, since the variance of X(interference power normalized by desired power) is additionof variances of desired and interfering components, the standarddeviation σX will always be greater than 6 dB.

The PDF of SINR γkm(χ, h, v) at position rm is given by

pγm(x|rm) =

1

xσγm(rm, θm)

√2π

e

[−(ln(x)−μγm (rm,θm))2

σ2γm

(rm,θm)

].

(22)

The above PDF expression is conditioned on the locationof the user. Since it is assumed that the user location is uni-formly distributed within a circular area (the hexagonal cellis approximated by a circle of radius Rc), the PDF of theuser location is prm(rm, θm) = (rm −Rm0)/π(Rc −Rm0)

2,Rm0 ≤ rm ≤ Rc, 0 ≤ θm ≤ 2π. Where, Rm0 represents theclosest distance of the user location from the macro BS. Thejoint distribution of the SINR and the user location is

pγm(γm, rm)) = pγm

(x|rm) prm(rm, θm). (23)

The area averaged PDF of SINR is obtained by integratingthe above expression over rm and θm as

pγm(x) =

Rc∫Rm0

2π∫0

pγm(x|rm) prm(rm, θm) drm dθm

=1

(Rc −Rm0)2√2π3

×Rc∫

Rm0

2π∫0

(rm−Rm0)e

[−(ln(x)−μγm (rm,θm))2

σ2γm

(rm,θm)

]xσγm

(rm, θm)drm dθm.

(24)

Since there is no closed form expression available for theabove integral, the PDF is obtained using numerical integra-tion. Note that the location dependent mean μγm

(rm, θm) andstandard deviation σγm

(rm, θm) in (24) are the function of fem-tocell parameters: transmit power (Ptf ), load (βf ) and density(ρf ) as well as macrocell parameters: BS transmit power (Ptm)and load condition (βm). Therefore the average SE obtainedfrom (24) will also be the function of these parameters. The

Fig. 4. Area averaged CDF of SINR of macrocell users, for Ptf = 10 dBm,Lw = 10 dB, σξm = 6 dB, σξf = 4 dB.

Cumulative Distribution Function (CDF) of SINR of macrocellusers can be easily obtained from (24) as

Pγm(Υ) = Pr[γm < Υ] =

Υ∫−∞

pγm(γ) dγ. (25)

Note that in the CDF expression the variable substitution (γ =x) has been made. Finally, the mean SE of the macrocell in eachsubchannel, (Cm) in (b/s/Hz), is obtained by using (11).

Fig. 4 shows the area averaged CDF of SINR of macrocellusers obtained through analysis (using (25)) and simulationfor different network load conditions in macrocell and femto-cell networks for Ptf = 10 dBm, Lw = 10 dB, σξm = 6 dB,σξf = 4 dB. The close agreement between simulation andanalysis results indicates the accuracy of the derived CDF ofSINR for macrocell and femtocells in co-channel deploymentconfiguration for different network load conditions. The SEobtained from the SINR distribution will be used for furtheranalysis. It can be seen that, in case of no femtocell scenario(Nf = 0), when the macro load condition βm changes from100% to 50%, the macrocell outage probability (the probabilityof SINR less than the given threshold (Υ) of 0 dB is defined asoutage probability i.e., Po = Pr(γ < Υ)) reduces from 31% to21%. This indicates an improved outage performance duringfractional load conditions due to reduced number of interferers.Therefore, the amount of bandwidth required to satisfy userthroughput requirements will be less due to improved SINRperformance when compared to peak load conditions. Further,the addition of femtocells with fixed transmit power results indecreased SINR performance for macrocell users. It can beseen from the figure that, with Ptf = 10 dBm, addition of 50femtocells increases the macrocell outage from 29% to ≈ 60%when βf = 50% and ≈ 74% when βf = 100%.

C. SE of Femtocell Network

Consider a femtocell of radius Rf located at distance dfrom the macro BS. The received SINR on subchannel k


for a femtocell user located inside the femtocell at positionrf = (rf , θf ) can be expressed as

γkf (χ, h, v)

=Ptkf0Gkf0

Nm∑i=1

Ptkmivkmi

Gkmi+

Nfint∑j=1

PtkfjvkfjGkfj+BsbN0

. (26)

By applying (6), the above SINR expression can be rewritten as

γkf (χ, h, v) =

zkf0Ikf (χ, h, v)

. (27)

Where,

Ikf (χ, h, v) =

Nm∑i=1

PtkmiLmi

Ptkf0Lf0

vkmizkmi

e(ξmi−ξf0 )

+

Nfint∑j=1

PtkfjLfj

Ptkf0Lf0

vkfjzkfje(ξfj−ξf0 ) +

N0Bsb

Ptkf0Lf0

e(−ξf0 )

and

Lf0 =Kf (df0/d0f )−αf , Lmi

= KmLw(dmi/d0m)−αm ,

Lfj =KfLw(dfj/d0f )−αf .

Assume that the femtocell user positions are uniformly dis-tributed within the circular area with radius Rf . The PDF of thefemtocell user location is prf (rf , θf ) = (rf −Rf0)/π(Rf −Rf0)

2, Rf0 ≤ rf ≤ Rf , 0 ≤ θf ≤ 2π. The area averaged PDFof SINR γk

f (χ, h, v), of the femtocell is obtained by

pγf(x) =

1

(Rf −Rf0)2√2π3

×Rf∫

Rf0

2π∫0

(rf −Rf0)e

[−(ln(x)−μγf

(rf ,θf ))2

σ2γf

(rf ,θf )

]

xσγf(rf , θf )

drf dθf , (28)

where Rf0 is the minimum distance between the user and femtoBS, μγf

(rf , θf ) and σγf(rf , θf ) are the mean and standard

deviation of the SINR of femtocell user at location rf from thefemto BS which are obtained in the same way as μγm

(rm, θm)and σγm

(rm, θm) are obtained in the macrocell PDF of SINRexpression. The CDF of SINR of femtocell users can beobtained by

Pγf(Υ) = Pr[γf < Υ] =

Υ∫−∞

pγf(γ) dγ. (29)

Fig. 5 shows the area averaged CDF of SINR of femtocellsobtained through analysis (using (29)) and simulation whenβm = 100% and βf = 100% for Ptf = 10 dBm, Lw = 10 dB,σξm = 6 dB, σξf = 4 dB. In Fig. 5, d denotes the distancebetween the femtocell and the macro BS. It can be seen that theSINR performance of femtocells located near the central macroBS (i.e., d = 50 m) is worse due to dominant interference from

Fig. 5. Area averaged CDF of SINR of femtocell users, for Ptf = 10 dBm,Lw = 10 dB, σξm = 6 dB, σξf = 4 dB, βm = 100%, βf = 100%.

Fig. 6. Macrocell-femtocell network.

the macro BS. Whereas the femtocells located at cell edge(i.e, d = 250 m) experience better SINR because of reducedmacrocell interference. This clearly shows the influence ofseparation between the macro BS and the femto BS on thefemtocell network performance.

From the Fig. 5, it can be observed that the femtocells locatedat distances d = 100 m and 110 m and d = 250 m and 260 mhave nearly the same SINR distributions. The range of distancesfrom the central macro BS over which the SINR distributionof femtocells is same can be considered as a ring. Therefore,we divide the circular disc with radius Rc into Q annularrings with inner radius Rq and outer radius Rq+1 as shownin Fig. 6. Further, since the distance from the central macroBS to each of the femto BS in q-th ring is nearly the same,the SINR distribution of all those femtocells in that ring willalso be the same. Therefore, the average SE achieved by allthe femtocells in the q-th ring is obtained by multiplying SEof a femtocell Cfq by the number of femtocells lies within thatring. The average SE achieved by the femtocells in the q-th ringCfq is obtained from the SINR distributions of femtocells in


TABLE IISYSTEM PARAMETERS

q-th ring by using (28) and (11). Since it is assumed that thefemtocells are uniformly distributed within the macrocell, thenumber of femtocells located within the q-th annular ring canbe written as NFq

= π(R2q+1 −R2

q)Nf/|A|. The cumulativeSE of all the femtocells located within the q-th annular ring iscalculated as C

(tot)fq

= NFqCfq . Finally the total SE achieved

by all the femtocells distributed within the central macrocell isobtained as

Cf =

Q∑q=1

C(tot)fq

=

Q∑q=1

R2q+1 −R2

q

R2c

Nf Cfq . (30)

Note that, here R1 is greater than the minimum distance be-tween the macro BS and femto BS Rmf0.

IV. RESULTS AND DISCUSSION

The results presented in this section are based on the systemparameters as shown in Table II. It is assumed that the macro-cells are uniformly loaded i.e. the load factor in all the macro-cells in the network is same. The same transmit power and loadis assumed for all the femtocells located within the macrocellcoverage area. For the given system parameters, the averagecell throughput of macrocell under full load condition withoutconsidering femtocell deployment is 19.5 Mbps (i.e. Cm =1.95 bits/s/Hz) i.e. the ASE achieved by the macrocell withoutfemtocell deployment is ASET (βm, βf , Ptm, Ptf , ρf = 0) =7.48× 10−6.

A. Impact of Femtocell and Macrocell Parameters on ASEWithout QoS Constraints

This section presents the results to show the impact of fem-tocell radio parameters (transmit power (Ptf ) and load (βf ))and macrocell load (βm) on the ASE and average macrocelluser throughput without considering QoS constraints. Here

femtocell user throughput performance is not shown due tospace limitations.

Fig. 7(a) and (d) show the impact of femtocell transmit poweron the ASE and average macrocell user throughput respectivelyfor Nf = 50 and βf = 100%. It can be seen that for a givennumber of femtocells and macrocell load, as the femtocelltransmit power increases, the ASE gradually increases and sat-urates at a maximum value. The ASE attains its maximum valueat nearly 8.05× 10−4 b/s/Hz/m2 at Ptf = 4 dBm, 16 dBm,19 dBm respectively when βm = 10%, 50%, and 100%. This isbecause with high femtocell transmit power the SINR of fem-tocell users improves significantly and the femtocell networkthroughput is limited by the highest MCS value. Similarly it isobserved that the ASE attains its maximum value at differentfemtocell transmit power values for different macrocell loadconditions. However, the average macrocell user throughput,Tum reduces drastically (Refer Fig. 7(d)) due to increasedfemtocell interference. Further, it can be observed that the max-imum ASE is achieved during low load conditions in macrocellnetwork. This is because as the macrocell load decreases theSINR of femtocell users increases due to reduced macrocellinterference which leads to increased SE of femtocell network.Since the major part of ASE is due to femtocell network,the ASE also increases accordingly. Similarly the macrocelluser throughput is also improved because of improved SINRduring low load conditions (Refer Fig. 4). Therefore, the max-imum ASE gain is expected at low and medium macro loadconditions.

Fig. 7(b) shows the mean ASE for varying femtocell load βf

for different number of femtocells with fixed transmit powerPtf = 0 dBm. With increasing femtocell load, the ASE in-creases monotonically because of increased bandwidth usageat the femtocell network. It can be seen that with fewer numberof femtocells, the impact of macrocell load is more significantcompared to high femtocell density. This is because with lowfemtocell density the femtocell interference is dominated bymacrocell interference. Fig. 7(e) shows the average macrocelluser throughput for varying femtocell load with Ptf = 0 dBmand 10 dBm. It can be seen that with high femtocell transmitpower, increasing femtocell load significantly degrades themacrocell user throughput irrespective of the macrocell loadcondition compared to low femtocell transmit power. Thisimplies that not only the femtocell transmit power but alsothe femtocell load has huge impact on the ASE performance.Therefore, the load of femtocell has to be configured along withthe femtocell transmit power for controlling CCI in co-channeldeployment configuration.

Fig. 7(c) and (f) show the ASE for varying number offemtocells per cell site for different macrocell load and fem-tocell load conditions with Ptf = 0 dBm. It can be seenthat, as the number of femtocells increases, the ASE sat-urates at Nf = 130, 160, and 200 respectively with βf =10%, 50%, and 100%. This is because, due to the addition ofmore number of femtocells, the SINR distribution of femtocellslocated near to the macro BS becomes worse and hence verylow throughput achieved by the femtocell network. As ex-pected, the macrocell user performance degrades significantlywith the addition of large number of femtocells.


Fig. 7. Impact of femtocell and macrocell parameters on the ASE and average macrocell user throughput without considering QoS constraints. (a) Mean ASEvs Ptf for Nf = 50, βf = 100%; (b) mean ASE vs βf for Ptf = 0 dBm; (c) mean ASE vs Nf for Ptf = 0 dBm; (d) mean macrocell user throughput vs Ptf

for Nf = 50; (e) mean macrocell user throughput vs βf for Nf = 50; (f) mean macrocell user throughput vs Nf for Ptf = 0 dBm.

B. ASE With QoS Constraints

This section presents the results of maximum achievableASE (ASE∗

T ) with the optimal femtocell transmit power P ∗tf

which is obtained from (14) with fixed femtocell load (βf =Bf ) for different macro load conditions. The required averagethroughput for macrocell users, Tum,min is set to 128 kbpsand for femtocell users, Tuf,min: 5 Mbps. The minimum andmaximum femtocell transmit power level considered for femtoBSs is −10 dBm and 20 dBm respectively [27].

The dotted lines in Fig. 7(d)–(f) indicates the through-put requirement of macrocell users, Tum,min. It can be seenfrom Fig. 7(d) that for 50 number of femtocells, whenβf = Bf = 100%, βm = 100%, 50%, and 10% the femto-cell transmit power that satisfies macrocell QoS condition(constraint C1 in (14)) is P

(max)tf = −10 dBm,−6 dBm, and

−3 dBm respectively. Similarly, when βf = Bf = 10%, βm =100%, 50% and 10% the maximum allowable femtocell trans-mit power is P

(max)tf = −8 dBm, 10.5 dBm, and 12 dBm

respectively. From Fig. 7(e) it can be seen that for 50 numberof femtocells, with Ptf = 0 dBm, when βm = 50% and 10%,

the femtocell load that satisfies constraint C1 is β(max)f =

37% and 60% respectively. From the figures it can be seen thatfor very low femtocell load values (βf < 10%) and very lowfemtocell transmit power (Ptf < 0 dBm), the macrocell userthroughput performance is unaffected even with large numberof femtocells in high macro load conditions. This is as expected,because since the femtocells use very low transmit power

Fig. 8. Mean ASE vs Number of femtocells with optimal femtocell transmitpower.

and allocates a very few suchannels randomly among largenumber of available subchannels, there is very less probabilityof subchannel collisions between the macrocell and femtocellnetworks. Therefore, the interference caused by the femtocellnetwork become insignificant.

Fig. 8 shows the mean ASE versus the number of femto-cells for different load conditions in macrocell and femtocellnetworks. The corresponding optimal femtocell transmit powervalues are shown in Fig. 9. The ASE increases with numberof femtocells, however after certain number of femtocells,


Fig. 9. Optimal femtocell transmit power vs Number of femtocells forPtm = 43 dBm.

Fig. 10. Mean ASE vs Femtocell load with optimal femtocell transmit power.

increasing number of femtocells violates the QoS constraintswhich results in limited number of supported femtocells. Withβf = 20%, 50%, and 100%, the ASE is maximized with 80,200, and 120 number of femtocells respectively for βm =50%, whereas they reduce to 60, 160, and 40 respectively forβm = 100%. This indicates that when the macrocell networkis heavily loaded the femtocell load has to be reduced inorder to maintain the QoS requirements of both macro andfemtocell users. In Fig. 9, the solid curves and dashed curvesshow the optimal femtocell transmit power level when βm =50% and 100% respectively. The optimal femtocell transmitpower, P ∗

tf decreases with increasing number of femtocells.It can be observed that the number of supportable femtocellsalso varies with femtocell load values. Another important ob-servation is that, with the combination of low transmit powerand high load of femtocells, the ASE is maximized with largenumber of femtocells. Conversely with high transmit power andlow load, the ASE is maximized with less number of femtocells.This implies that in order to support large number of femtocellsin co-channel deployment configuration, the femtocells shouldoperate at low femtocell transmit power level with high load.

Fig. 10 shows the ASE achieved with optimal transmitpower levels for varying femtocell load and macrocell loadvalues. The corresponding number of femtocells per cell siteis shown in Fig. 11. It can be seen that for higher macro load

Fig. 11. Maximum number of allowable femtocells per cell site vs Femtocellload with optimal femtocell transmit power.

Fig. 12. Mean ASE vs Macrocell Tx. power with optimal femtocell transmitpower.

values, with increasing femtocell load, the ASE and number offemtocells increase up to certain peak value and decrease withfurther increasing femtocell load. This is because, increasingfemtocell load causes severe CCI to neighboring femtocellsdue to increased activity which results in violation of QoS infemtocell network. Thus, the number of supportable femtocellsbecomes limited which results in reduced ASE. Further, itcan be observed from the results that for a given macro loadcondition, the peak ASE and the peak number of supportablefemtocells occurs at different femtocell load values. This resultclearly indicates that there is a trade-off between ASE andnumber of supportable femtocells i.e. maximization of numberof femtocells results in reduced ASE gain and vice versa.Therefore, based on the requirements one has to choose theappropriate value of femtocell transmit power and load. Further,it can be seen that for less than 15% femtocell load, thenumber of supportable femtocell is zero. This is because lowerfemtocell load does not satisfy the femtocell user throughputrequirements.

Fig. 12 shows the ASE for varying macrocell transmit power(Ptm) for different load conditions. Note that the transmitpower values are given for 10 MHz bandwidth. It can beseen that with high femtocell load (βf = 100%), increasingmacrocell transmit power increases the ASE with more number


TABLE IIIASE FOR VARIOUS MACROCELL PARAMETERS

of supportable femtocells, because the received power fromthe macro BS by the macro user is sufficient enough toovercome interference caused by large number of femtocells.Whereas, when femtocells operate with low load (βf = 20%),the improvement in ASE is insignificant. Because, with lowfemtocell load, only a few femtocells are supported due to QoSrequirements of femtocell users. Further, as explained earlier,for very low femtocell load values (βf < 20%), the macrocellnetwork performance is unaffected even with large numberof femtocells during high load conditions in the macrocellnetwork. Therefore, the ASE remains constant irrespective ofmacrocell power configurations. Further, it can be observed thateven at heavy interference situations i.e., when the macrocellnetwork is fully loaded, increasing macrocell transmit powerfrom 40 dBm to 43 dBm results in nearly a two fold increase inASE. This indicates that, in co-channel femtocell deployment,the macrocell network configuration has significant impact onthe ASE performance.

Table III shows the maximum achievable ASE gain, GASE

(obtained from (17)) and corresponding femtocell load andnumber of femtocells for different macrocell power configu-rations and load conditions. The values in Table III are ob-tained using joint optimization of femtocell transit power andload using (14). It can be observed that the maximum ASEgain is achieved during low load conditions in macrocellsfor all macrocell power configurations. As the macrocell loadincreases, the maximum ASE gain is achieved with reducedfemtocell load. It can be seen that maximum number of fem-tocells is supported during medium macro load conditionsi.e., βm = 50%. With low macrocell transmit power (Ptm =34 dBm and 37 dBm), the maximum ASE is unchanged duringmedium and full load conditions, whereas significant improve-ment is observed during low load conditions. It can be seen that,even during high macro load conditions, increasing macrocelltransmit power from 40 dBm to 43 dBm results in 20% increasein ASE gain with large number of supportable femtocells.Therefore, configuring macro BS transmit power according tofemtocell density is an another option to achieve maximum gain

in terms of large number of supportable femtocells and ASE.Considering these aspects during cell planning might be helpfulfor the operators to achieve desired performance gain.

In this work, we considered the same transmit power andload for all femtocells within the macrocell coverage area.Therefore, based on the analysis we conclude that the radioparameters of co-channel femtocells could be controlled in acentralized manner. The central controller located in the corenetwork may decide the femtocell radio parameters based onthe current network conditions such as macrocell load, numberof active femtocells, time-of-day, etc. [28]. The advantage ofemploying central power setting is that it does not requirefrequent measurement reports from the user terminals. It is tobe noted that the centralized power setting for femtocells isalso under active consideration by the mobile industry [28].Further, the framework can be easily extended to study the ASEperformance considering region wise (according to the distancefrom the macro base stations as shown in Fig. 6) power and loadsetting for femtocells.

V. CONCLUSION

In this paper, we have derived the ASE of the OFDMAbased co-channel closed access macrocell-femtocell networksfor uniformly distributed femtocell locations. The ASE is de-rived from the SINR distributions which captures the activityof interfering macrocells and femtocells under fractional loadconditions. Then, we investigated the effect of femtocell radioparameters, such as transmit power, load, and femtocell densityas well as macrocell transmit power on the ASE under differentmacrocell network load conditions.

We also analyzed the ASE performance with optimal fem-tocell radio parameters. It is seen that, in co-channel femtocelldeployment, using appropriate femtocell radio parameters, theASE gain can be achieved several folds without degradingmacrocell network performance. Depending upon the macro-cell network load condition, the peak ASE is achieved withdifferent femtocell load values. The results show that in orderto support large number of femtocells, the femtocells shouldoperate with low transmit power and high load. Whereas inorder to maximize the ASE, the femtocells should operate withhigh transmit power and low load.

It is also seen that macrocell load has significant impact onthe ASE performance. The highest ASE gain is achieved duringlow load conditions in macrocells and the maximum numberof femtocells is supported during medium load conditions. Itis observed that using optimal femtocell radio parameters anearly 160 fold and 93 fold increase in ASE can be achievedat low (10%) and high (100%) macro load condition respec-tively compared to no femtocell scenario. Further, an inverserelationship has been observed between the macrocell load andfemtocell load. It is seen the ASE performance is sensitive tothe macrocell power. From the analysis, it is found that bydoubling the macrocell transmit power, it is possible to achievea nearly 20% increase in ASE with large number of supportablefemtocells. The results suggest that the centralized controlis suitable for operating femtocells in cochannel deploymentconfiguration.


Mm1 =Eχ,h,v {Ikm(χ, h, v)} =

Nm−1∑i=1

PtkmiLmi

Ptkm0Lm0

βkmiμzkmi

e12

(σ2ξmi

+σ2ξm0

)

+

Nfint∑j=1

PtkfjLfj

Ptkm0Lm0

βkfjμzkfje

12

(σ2ξfj

+σ2ξm0

)+

N0Bsb

Ptkm0Lm0

(31)

Mm2 =Eχ,h,v

{I2km(χ, h, v)

}

= e2σ2

ξm0 ×

⎧⎪⎨⎪⎩

Nm−1∑i=1

Nm−1∑j=1j �=i

PtkmiPtkmj

LmiLmj

P 2tkm0

L2m0

βkmiβkmj

μzkmiμzkmj

e12

(σ2ξmi

+σ2ξmj

)

+

Nfint∑i=1

Nfint∑j=1j �=i

PtkfiPtkfjLfiLfj

P 2tkm0

L2m0

βkfiβkfjμzkfiμzkfj

e12

(σ2ξfi

+σ2ξfj

)

+

Nm−1∑i=1

Nfint∑j=1

PtkmiPtkfjLmi

Lfj

P 2tkm0

L2m0

βkmiβkfjμzkmi

μzkfje

12

(σ2ξmi

+σ2ξfj

)

+

Nm−1∑i=1

P 2tkmi

L2mi

P 2tkm0

L2m0

βkmiμzkmi

ρ2zkmie2σ2

ξmi +N2

0B2sb

P 2tkm0

L2m0

+

Nfint∑j=1

P 2tkfj

L2fj

P 2tkm0

L2m0

βkfjμzkfjρ2zkfj

e2σ2

ξfj

+

Nm−1∑i=1

N0BsbPtkmiLmi

P 2tkm0

L2m0

βkmiμzkmi

e12σ

2ξmi +

Nfint∑j=1

N0BsbPtkfjLfj

P 2tkm0

L2m0

βkfjμzkfje

12σ

2ξfj

⎫⎬⎭ (32)

APPENDIX A

The expected distance of the j-th femto BS to the referenceposition y is obtained as

dfj = E[dfj

]=

∞∫0

r pdfj(r) dr. (33)

By substituting (7) into (33),

dfj =Γ(j + 1/2)

√πρf (j − 1)!

, (34)

where Γ(x) =∫ ∞0 e−ttx−1dt. Similarly the second order mo-

ment of dfj is obtained as

E[d2fj

]=

∞∫0

r2 pdfj(r) dr =

Γ(j + 1)

πρf (j − 1)!. (35)

The variance of dfj is obtained by

Var[dfj

]=E

[d2fj

]−

(E

[dfj

])2=

Γ(j + 1)

πρf (j − 1)!−

(Γ(j + 1/2)

√πρf (j − 1)!

)2

=1

πρf

(j −

(Γ(j + 1/2)

Γ(j)

)2). (36)

APPENDIX B

By using the extended Wilkinson’s moment matching ap-proximation method [29], the mean μX and standard deviationσX of Ikm(χ, h, v) is obtained as

μX =2 lnMm1 − 1/2 lnMm2, (37)

σ2X = lnMm2 − 2 lnMm1, (38)

where Mm1Δ= Eχ,h,v{Ikm(χ, h, v)} and Mm2

Δ=

Eχ,h,v{I2km(χ, h, v)} are the mean and autocorrelation ofIkm(χ, h, v) respectively. Here Eχ,h,v. denotes the expectationw.r.t the distribution of shadowing component χ, small scalefading component h, and activity status v. The derivationsfor Eχ,h,v{Ikm(χ, h, v)} and Eχ,h,v{I2(χ, h, v)} are givenin (31) and (32), shown at top of the page. Note that theshadow fading, small scale fading, activity status componentsof individual link are assumed to be independent and random.In (32), μzk and ρzk denote the expectation and the correlationof power of the fading component (zk) respectively, σξmi

and σξfjare the standard deviation of shadowing component

between the user and i-th macro BS and j-th femto BSrespectively, βkmi

and βkfj are the activity factor of i-th macroBS and j-th femto BS on subchannel k. The components βkmi

and βkfj in (32) denotes the auto-correlation of vkmiand vkfj

at τ = 0 (i.e. from (3) Rvkmi(0)=βkmi

and Rvkfj(0)=βkfj ).


ACKNOWLEDGMENT

The authors would like to thank the editor and the anonymousreviewers for their valuable comments.

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Prabhu Chandhar (S’11) received the B.Eng. de-gree in electronics and communication engineeringfrom A.V. C College of Engineering, Mayiladuthurai,India, in 2007 and the M.Eng. degree in commu-nication systems from the College of Engineering,Guindy, Chennai, India, in 2009. He worked as aSenior Research Fellow—Vodafone IIT KGP Centreof Excellence in Telecommunications (VICET) withIIT Kharagpur from 2009 to 2010. He is currentlyworking toward the Ph.D. degree in the area ofmodeling and analysis of OFDMA cellular systems

at the G. S. Sanyal School of Telecommunications, IIT Kharagpur.

Suvra Sekhar Das (M’00) received the B.Eng. de-gree in electronics and communication engineer-ing from Birla Institute of Technology, Ranchi,India, in 2000 and the Ph.D. degree from AalborgUniversity, Aalborg, Denmark, in 2007. He workedas Senior Scientist with the Innovation Laboratoryof Tata Consultancy Services from 2000 to 2008.He is currently an Assistant Professor with theDepartment of Electronics and Electrical Commu-nication Engineering and with the G. S. SanyalSchool of Telecommunications, IIT Kharagpur.

His research interests include cross-layer optimization of mobile broadbandcellular networks.

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