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Distributed Interference Management in Two-TierCDMA Femtocell Networks

Duy Trong Ngo, Student Member, IEEE, Long Bao Le, Member, IEEE, Tho Le-Ngoc, Fellow, IEEE,Ekram Hossain, Senior Member, IEEE, and Dong In Kim, Senior Member, IEEE

Abstract—The current paper proposes distributed joint powerand admission control algorithms for the management of inter-ference in two-tier femtocell networks, where the newly-deployedfemtocell users (FUEs) share the same frequency band with theexisting macrocell users (MUEs) using code-division multipleaccess (CDMA). As the owner of the licensed radio spectrum,the MUEs possess strictly higher access priority over the FUEs;thus, their quality-of-service (QoS) performance, expressed interms of the prescribed minimum signal-to-interference-plus-noise ratio (SINR), must be maintained at all times. For thelower-tier FUEs, we explicitly consider two different designobjectives, namely, throughput-power tradeoff optimization andsoft QoS provisioning. With an effective dynamic pricing schemecombined with admission control to indirectly manage the cross-tier interference, the proposed schemes lend themselves to dis-tributed algorithms that mainly require local information to offermaximized net utility of individual users. The game-theoreticalapproach employed in this work is of particular attractiveness,especially in view of practical implementation under the limitedbackhaul network capacity available for femtocells. It is shownthat the proposed algorithms robustly support all the prioritizedMUEs with guaranteed QoS requirements whenever feasible,while allowing the FUEs to optimally exploit the remainingnetwork capacity. The convergence of the developed solutionsis rigorously analyzed, and extensive numerical results arepresented to illustrate their potential advantages.

Index Terms—Femtocell, macrocell, CDMA, power control,admission control, QoS protection, distributed interference man-agement.

I. INTRODUCTION

Copyright c© 2012 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

Manuscript received January 12, 2011; revised August 19, 2011; acceptedJanuary 01, 2012. The editor coordinating the review of this paper andapproving it for publication was Dr. Ananthanarayanan Chockalingam. Thiswork was supported in part by the Natural Science and Engineering ResearchCouncil of Canada (NSERC), the Alexander Graham Bell Canada GraduateScholarship for Doctoral Studies, and the McGill Engineering Doctoral Award.This paper was presented in part at the 2011 IEEE Vehicular TechnologyConference (VTC-Fall), San Francisco, CA, USA.

Duy Trong Ngo and Tho Le-Ngoc are with the Department of Electricaland Computer Engineering, McGill University, Montreal, QC, Canada H3A2A7. Email: [email protected]; [email protected].

Long Bao Le, the corresponding author, is with Centre Energie MateriauxTelecommunications, Institut National de la Recherche Scientifique (INRS-EMT), Universite du Quebec, Montreal, QC, Canada H5A 1K6. Email:[email protected].

Ekram Hossain is with the Department of Electrical and Computer Engi-neering, University of Manitoba, Winnipeg, MB, Canada R3T 5V6. Email:[email protected].

Dong In Kim is with the School of Information and CommunicationEngineering, Sungkyunkwan University, Suwon, Korea 440-746. Email:[email protected].

FEMTOCELLS have recently emerged as a promisingtechnology to increase wireless network capacity, extend

cellular coverage and introduce new services [1], [2]. Fem-tocell solution offers significant economic benefits comparedto the traditional cell-partitioning approach for which a largenumber of expensive base stations (BSs) are typically required.By deploying low-cost femtocell (home) BSs, indoor users canenjoy high-speed wireless communication due to the closeproximity between themselves and their own home BSs. Inthis new wireless solution, limited signaling data can betransmitted over the backhaul networks via residential wirelinebroadband access links, e.g., digital subscriber lines (DSL),without any further investment.

Since femtocells operate in the licensed spectrum owned bythe macrocell network, it is imperative to limit the cross-tierinterference from the femtocell users (FUEs) to the macrocell[3]. One of the central research topics is how to developautonomous interference management schemes such that (i)the quality-of-service (QoS) requirements of the existingmacrocell users (MUEs) with higher access priority are alwaysmaintained and (ii) the residual network capacity is effectivelyexploited by the newly-deployed FUEs so as to optimize theirown performance. This is the case for two-tier networks basedon either code-division multiple access (CDMA) or orthogonalfrequency-division multiple access (OFDMA) [4], [5].

The development and implementation of distributed in-terference management solutions for femtocell networks arechallenging for two main reasons [6], [7], [8], [9], [10]. First,given that the wired network infrastructure (e.g., DSL links)may only provide limited capacity for the exchange of sig-naling information, it is rather difficult to centrally coordinatefemtocell and macrocell BSs to perform such management.Second, because of the different access tariffs applicable forthese two types of users, the MUEs have strictly higher priorityover the FUEs in accessing the underlying radio spectrum.

The literature on distributed power control in traditionalCDMA wireless networks is rich. One of the most popularsolutions is the one presented in [11], which is proven toconverge to a Pareto-optimal solution whenever the minimumsignal-to-interference-plus-noise ratios (SINRs) of all the userscan be supported. In the case of infeasible SINR targets,admission-control or user-removal algorithms are introducedin [12], [13]. The works in [14], [15], [16], [17] investigateseveral other power control schemes from a game-theoreticalpoint of view. In most instances, distributed algorithms aredevised that converge to the Nash equilibrium of the corre-sponding power-control games. In addition, various pricing


schemes are developed to achieve a balance between maximiz-ing the total network utility and minimizing the power con-sumption and/or to improve the efficiency of the equilibriumsolutions [18], [19], [20], [21]. For homogeneous data-servicemulticell systems, reference [22] considers the distributedPareto-optimal joint optimization of SINR assignment andpower control. In the context of femtocell networks, references[23], [24], [25], [26] study various beamforming techniquesto mitigate the undue cross-tier interference. Joint admissioncontrol and power management has also been examined in[27] for cognitive-CDMA networks.

In this work, we present joint power and admission controlsolutions for distributed interference management in two-tierCDMA-based femtocell networks. The fundamental differencebetween the setting considered in this paper and that investi-gated in traditional CDMA wireless networks is the differenti-ated classes of users with distinct access priorities and designrequirements. The prioritized MUEs demand that their QoSrequirements be always maintained in the first place, whereasthe lower-tier FUEs attempt to optimize their performance byexploiting the remaining available system resource. Specifi-cally, we investigate the following two practical scenarios: (i)the FUEs desire to balance between their achieved throughputand the corresponding power expenditure, and (ii) the FUEsdemand certain “soft” QoS requirements, expressed in termsof the minimum attained SINRs. In lightly-loaded networks,we also propose an effective mechanism to better utilize thenetwork capacity and thereby improving the performance ofthe MUEs. Convergence properties of the proposed algorithmsare rigorously analyzed and potential extensions presented tofurther emphasize the attractiveness of the developed solutions.

It is noteworthy that whilst closest in spirit with [28], ourwork distinguishes itself in, at least, two key aspects. Firstly, inrepresenting the net utility of the FUEs, the study in [28] usesa penalty function that depends on the actual cross-tier inter-ference, and thus requires explicit information about the cross-channel gains. It is indeed quite challenging to estimate thesevalues due to the random fluctuations caused by shadowingand short-term fading. On the other hand, this paper proposesan effective dynamic pricing scheme combined with admis-sion control to indirectly manage the cross-tier interference.Together with their distributive nature, the developed schemesare more tractable in view of practical implementation underthe limited backhaul network capacity available for femtocells.Secondly, the choice of utility function for the MUEs in [28]does not always guarantee the minimum required SINRs to beachieved for these prioritized users. Instead, the joint powerand admission control algorithms devised here, through theselection of a sigmoid function to represent the macrocellutility, are capable of robustly protecting the performance ofall the active MUEs.

The rest of this paper is organized as follows: Section IIintroduces the system model under consideration and sum-marizes the assumptions applicable throughout the work. InSection III, distributed interference-management algorithmsare proposed and the corresponding analysis is presented.Section IV discusses several practical issues regarding theimplementation of the devised schemes, together with some

0 200 400 600 800 10000

100

200

300

400

500

600

700

800

900

1000Femtocell UserMacrocell UserBase Station

Fig. 1. Example of network topology and user placement in a two-tiernetwork.

possible extensions. Section V demonstrates the performanceof the developed schemes by numerical results. Finally, Sec-tion VI concludes the paper.

II. SYSTEM MODEL AND ASSUMPTIONS

Consider a two-tier wireless network with power-controlledusers. Specifically, we investigate the scenario where a macro-cell serving M macrocell users (MUEs) is underlaid with Kfemtocells using code-division multiple access (CDMA). As-sume that femtocell i has Ni users and define N =

∑Ki=1 Ni.

We further assume that the association of the femtocell users(FUEs) with their closest femtocell base stations (BSs) is fixedduring the runtime of the underlying power and admissioncontrol processes. Denote the set of all users by L, and the setof MUEs and FUEs by Lm and Lf , respectively. An exampleof such a network is illustrated in Fig. 1.

The results obtained in this work are applicable to bothdownlink and uplink scenarios. By “the transmitter of user i”we refer to the BS that serves wireless terminal i ∈ L in thedownlink case, whereas in the uplink case it is the wirelessterminal i itself. We consider a snapshot model where thechannel gains are assumed to remain unchanged during theruntime of the power and admission control algorithms. Letpi be the transmit power of user i and σi the power of additivewhite Gaussian noise measured in the spectrum bandwidth atthe receiving end of user i ∈ L. Also, denote the channel gainfrom the transmitter of user i to its receiver by g′ii, and thatfrom the transmitter of user j to the receiver of user i 6= j bygij . Then, the received SINR of user i ∈ L can be written as

γi =Gg′iipi∑

j 6=i gijpj + σi, (1)

where G is the processing gain of the system.


Note that the first term in the denominator of (1) includesboth in-cell and cross-tier interferences, i.e., aggregated inter-ference from all MUEs and FUEs except the considered useri (which can be either a MUE or a FUE). In the downlinkcase, the channel gain gij simply reduces to g′ii for the in-cell interference, while gij is termed the cross-channel gainfor the cross-tier interference. For notational convenience, letgii = Gg′ii where the processing gain G is absorbed into thechannel gain g′ii. The received SINR of user i ∈ L can thenbe expressed as

γi =giipi∑

j 6=i gijpj + σi. (2)

In cellular wireless networks such as IS-95, WCDMA andLTE networks, regardless of the traffic types, a minimumSINR is required at the receiver for a minimum data rateto be supported. While the maintenance of such minimumSINR targets is well-justified for voice users to achieve acertain desired bit error rate (BER), it is also applicable todata users, especially those with delay-sensitive applications.In our modeling framework, different SINR thresholds areassigned to different users, depending on their access priorityand service applications. Given a desired threshold Γi, weassume that the prioritized MUE i ∈ Lm requires that

γi ≥ Γi, (3)

in order to have its ongoing operation robustly protected. Onthe other hand, each FUE i ∈ Lf , which is of a lower accesspriority, is assumed to suppress transmission whenever itsattained SINR falls below a predefined threshold γ(f)

i. The

rationale behind this assumption is that a negligible levelof SINR would not help anything at all, but only createunnecessary interference to other users. Therefore, an activeFUE i ∈ Lf must have that

γi ≥ γ(f)i

. (4)

In this paper, we employ a utility function Ui(γi) and a costfunction Ci(pi) to represent the degree of satisfaction of useri ∈ L to the service quality and the cost incurred, respectively.It is the interest of user i ∈ L to maximize its own net utility,defined as

Utot,i = Ui(γi)− Ci(pi). (5)

In fact, (5) is a standard way to define the payoff functionfor network entities (i.e., wireless users and BSs). Giventhe transmit power of other users, such an optimization canbe accomplished by dynamic power adaptation performed atindividual links.

Assume that Ui(γi) is a strictly concave function withrespect to pi, whereas C(pi) is convex in that same variable.The necessary condition for the optimization of (5) can beobtained by taking the derivative of Utot,i, which is alsostrictly concave in pi, and equating to zero as follows.

dUtot,i

dpi=

dUi

dγi

dγi

dpi− dCi

dpi= 0. (6)

Upon noting that dγi/dpi = gii/Ii = γi/pi, we have

U′i (γi) =

pi

γiC′i(pi) =

Ii

giiC′i(pi), (7)

where Ii =∑

j 6=i gijpj +σi is the total noise and interferencepower at the receiving side of user i ∈ L. From (7), the optimaltarget SINR can be derived as

γi = f−1i

(Ii

giiC′i(pi)

), (8)

where fi(γi) = U′i (γi). Based on γi in (8), the following

iterative power-update rule can be applied [20]:

pi(t + 1) = γi(t)Ii(t)gii(t)

=γi(t)γi(t)

pi(t), (9)

where γi(t) is the actual SINR of user i at iteration t. In fact,(9) represents a more general power-control rule comparedwith the well-known power update:

pi(t + 1) =Γi

γi(t)pi(t), (10)

which has been extensively studied in the literature (see, e.g.,[11], [29]). Specifically, the minimum required SINR Γi onthe right-hand side of (10) is replaced by an adaptive SINRthreshold γi(t) in (8).

In what follows, we will show how to choose appropriatefunctions Ui(γi) and Ci(pi), together with their operatingparameters, to design efficient distributed power and admissioncontrol algorithms for both MUEs and FUEs. The key aspectthat makes the existing algorithms (such as those in [12],[13]) unsuitable for our current purpose is that the minimumSINRs of the prioritized MUEs should be maintained at alltimes. Accordingly, the newly-deployed FUEs must have theirtransmit powers properly controlled or, if needed, may evenbe removed for the sake of protecting the MUEs.

III. DISTRIBUTED JOINT POWER AND ADMISSIONCONTROL ALGORITHMS FOR TWO-TIER NETWORKS

A. QoS Guarantees for Macrocell Users

In the design of their power control scheme, [20] recom-mends the use of a sigmoid utility function and a linear costfunction. For our problem at hand, by employing similar utilityand cost functions for the MUEs and via properly tuning theircontrol parameters, we can develop an efficient and robustpower control algorithm that is capable of maintaining theminimum SINR requirements for these users. Specifically,we select the following utility and cost functions for MUEi ∈ Lm:

Ui(γi) =1

1 + exp[−bi(γi − ci)], (11)

Ci(pi) = a(m)i pi. (12)

Here, bi and ci respectively control the steepness and thecenter of the sigmoid function, whereas a

(m)i is the pricing

coefficient.Function Ui(γi) in (11) naturally captures the value of

the service offered to user i. Upon noting that Ui(0) = 0,Ui(∞) = 1 and that Ui(γi) is increasing with respect to γi, itis clear that user i is more and more satisfied with the offeredservice as the quality, expressed in terms of the achieved SINRγi, improves. On the other hand, power is itself a valuable


system resource. The linear cost in (12) is chosen to reflectthe expenses of power consumption to the user, while stillretaining the simplicity of subsequent analysis. As shown later,the use of dynamic values of a

(m)i may significantly affect the

resulting equilibrium of the developed algorithms.Importantly enough, the choice of sigmoid function allows

for the design of efficient schemes that guarantee the minimumSINRs imposed by the MUEs. Using (11) and (12), equation(7) can be rewritten as:

U′i (γi) = fi(γi) =

a(m)i Ii

gii. (13)

From this relationship, it is straightforward to see that theoptimal SINR target is

γi = f−1i

(a(m)i Ii

gii

). (14)

With the utility function defined in (11), an analytical form of(14) can be obtained as [20]:

γi = ci − 1bi

ln

[bigii

2a(m)i Ii

− 1−√√√√

(1− bigii

2a(m)i Ii

)2

− 1

](15)

Now, the line that goes through the origin and is tangentto the utility curve Ui(γi) can be expressed as Ui(γi) =U′i (γi) γi. At the tangent point γi,u, it is clear that

Ui(γi,u) = U′i (γi,u) γi,u. (16)

Since the cost function in (12) can also be rewritten asCi(pi) =

(a(m)i Ii/gii

)γi, it is required that a

(m)i Ii/gii ≤

U′i (γi,u) for a nonnegative total utility. On the other hand,

the necessary and sufficient condition for γi in (15) to achieveUtot,i ≥ 0 is γi ≥ γi,u; otherwise, MUE i simply suppressesits transmission and still gains zero total payoff. Therefore, bysetting

γi,u = Γi, (17)

we can ensure that any active MUE (i.e., whose transmit poweris strictly positive) will attain its minimum SINR target. Inother words, an active MUE i will eventually achieve SINRγi ≥ γi,u = Γi under this design. Some manipulations of (16)and (17) give [20]

ci = Γi − ln(biΓi − 1)bi

. (18)

Upon substituting this value of ci to (15), we finally arrive at

γi = Γi − ln(biΓi − 1)bi

− 1bi

ln

[bigii

2a(m)i Ii

− 1

−√√√√

(1− bigii

2a(m)i Ii

)2

− 1

]. (19)

In Fig. 2, we show the operating range of an active MUEi. With a sufficiently large bi, function U

′i (·) becomes very

steep; therefore, the resulting γi of user i will be very closeto its SINR threshold Γi. Also clear from Fig. 2 is that if theminimum required SINRs of all the MUEs are feasible, we

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

1.2

1.4

γi

f i(γi)

Ku

Operatingrange

aiσ

i/g

ii

Fig. 2. Illustration of the equilibrium solution for Γi = 2, bi = 5, Ku =

U′i (Γi), ai = a

(m)i .

can make them all active by setting a(m)i sufficiently small.

Specifically, given its total received interference and noisepower Ii, MUE i ∈ Lm is active if

a(m)i < giiU

′i (Γi)/Ii. (20)

B. Dynamic Pricing, Power Adaptation and Admission Con-trol of Femtocell Users

Given the MUEs’ QoS requirements already supported, thespecific choice of utility and cost functions for FUEs allowsus to achieve several practical design objectives, throughwhich certain user satisfaction metrics can be attained. Noticethat if the FUEs also wish to maintain their respective QoSrequirements, the operation of these users may cause networkcongestion, hence badly affecting the performance of theMUEs. In such cases, the FUEs should be penalized byappropriately regulating their operating parameters. Motivatedby the above observation, we will describe in the followingstwo design options for the FUEs, each with a different designobjective. Under each option, we will propose a joint poweradaptation and admission control algorithm. The convergenceof the developed solutions will be analyzed, followed by thecharacterization of their corresponding equilibrium.

1) Balancing Achieved Throughput and Power Expenditurefor Femtocell Users: We choose a utility function that capturesthe Shannon capacity for the FUEs, Ui(γi) = W ln (1 + γi)where W denotes the system bandwidth, and a linear costfunction C(pi) = a

(f)i pi with pricing coefficient a

(f)i . Alto-

gether, the net utility for FUE i is defined as

Utot,i = W ln (1 + γi)− a(f)i pi, ∀i ∈ Lf . (21)

Such choices of functions are especially relevant when theFUEs have to tradeoff between achieving the highest possibledata rates and expending as little power as necessary. Applyingthe result in (7) to these utility and cost functions gives

W

1 + γi=

a(f)i Ii

gii. (22)


Algorithm 1 POWER AND ADMISSION CONTROL ALGO-RITHM FOR MACROCELL QOS GUARANTEE AND FEMTO-CELL THROUGHPUT-POWER TRADEOFF

1: Set pi := 0, ∀i ∈ L, initialize the set of active FUEsAf := Lf , and set t := 1.

2: Each MUE i ∈ Lm measures gii(t) and Ii(t), andcalculates γi(t) by (19).

3: if γi(t) ≥ Γi then4: MUE i ∈ Lm updates its power: pi(t+1) := Ii(t)γi(t)

gii(t).

5: else if γi(t) < Γi and |Af | > 0 then6: MUE i ∈ Lm updates its power: pi(t + 1) := Ii(t)Γi

gii(t).

7: Each FUE j ∈ Af updates its pricing coefficient:a(f)j := k

(f)j a

(f)j , where k

(f)j > 1 are predetermined

scaling factors.8: end if9: Each FUE j ∈ Af measures gjj(t) and Ij(t), calculates

pj as:

pj :=W

a(f)j

− Ij(t)gjj(t)

.

10: FUE j ∈ Af updates its power: pj(t + 1) := pj .11: if pjgjj(t)/Ij(t) < γ(f)

jthen

12: If t = nT (f) then, with a small probability α, FUEj ∈ Af sets pj(t+1) := 0 and removes itself from theset of active FUEs: Af := Af\ {j}.

13: end if14: Any femtocell BS with no associated active FUE informs

the macrocell through a dedicated signaling channel.15: Set t := t + 1, go to Step 2 and repeat until convergence.

From (22) and upon noting that Utot,i is strictly concave inpi, the value of pi ≥ 0 that globally maximizes Utot,i can bederived as

p∗i = max(

W

a(f)i

− Ii

gii, 0

). (23)

We present in Algorithm 1 a joint power and admissioncontrol scheme for the interference management in bothmacrocell and femtocell networks. This algorithm lends itselfto a distributed implementation with only local informationrequired. In each iteration, each user i ∈ L simply needsto estimate (i) its received interference power Ii(t) and (ii)its own channel gain gii(t) in order to update its transmitpower. When there exists an active MUE i with its “soft”SINR target γi(t) dropping below the prescribed SINR targetΓi, we gradually increment the pricing coefficients a

(f)i of all

the active FUEs [see Step 7]. It is apparent from (23) that suchan increase in a

(f)i results in a reduction in the transmit power

of FUE i, through which the user that creates undue cross-tierinterference can be effectively penalized. Notably, this pricingmechanism is realized without acquiring the knowledge ofcross-channel gains, unlike the one proposed by [28].

The procedure of updating the pricing coefficients describedin Step 7 of Algorithm 1 impacts both the convergencespeed of that algorithm and the number of active FUEs atthe resulting equilibrium. A greater initial pricing a

(f)j and/or

a larger scaling factor k(f)j > 1 will shorten the convergence

time, albeit at the cost of being able to support a fewer numberof active FUEs at the equilibrium point. Therefore, carefulselections of k

(f)j and a

(f)j to reflect the relative amount of

interference that they induce to other users may lead to betternetwork performance. In particular, it is sensible to set largevalues of k

(f)j and a

(f)j for the FUE j that creates excessive

interference. Eventually, these “bad” users will at least seetheir transmit power reduced at equilibrium. In networks witha high load level1, they can even be removed, through whichthe built-up network congestion is relieved.

In Step 12 of Algorithm 1, if a certain FUE j has his/herSINR falling below the minimum required threshold γ(f)

j, it is

removed with probability α (where 0 < α < 1) at most oncein every T (f) iterations. Note that a smaller value of α willprevent the unnecessary elimination of too many FUEs, at theexpense of prolonging the convergence time. The same effectcan also be expected for large values of T (f).

Theorem 1: The proposed Algorithm 1 converges to anequilibrium solution if xf−1

i (x) is an increasing function,∀i ∈ Lm, and the following condition

(Mm + Nf − 1)Rmax < 1 (24)

holds, where fi(·) = U′i (·); Mm = |Am| ≤ M and Nf =

|Af | ≤ N denote the cardinality of the active macrocell andfemtocell user sets, respectively; and Rmax is defined as

Rmax = max{i∈Lf ,j∈L\{i}

}gij

gii= max{

i∈Lf ,j∈L\{i}}

gij

Gg′ii

. (25)

Moreover, for users who achieve nonzero powers at theequilibrium, it is true that

p∗i =I∗igii

f−1i

(a(m)i I∗igii

), i ∈ Am, (26)

p∗i =W

a(f)i

− I∗igii

, i ∈ Af , (27)

where I∗i =∑

j 6=i gijp∗j +σi. Further, all active MUEs i ∈ Am

have their SINR γ∗i satisfying γ∗i ≥ Γi.Proof: The proof can be found in Appendix A.

2) Soft QoS Provisioning for Femtocell Users: In thisscenario, we assume that FUE i ∈ Lf also requires a minimumSINR Γi to maintain the quality of its applications. Note thatthe meaning of Γi here is very different from that of γ(f)

idefined in (4). In practice, the value of Γi is typically greaterthan γ(f)

i. While a higher SINR at the receiving end of any

femto links implies more reliability and better services, thisusually requires more transmit power, which in turn leads toa higher cross-interference induced to the macrocell. Such an

1In this paper, the network load is defined to be “low” if ρ =ρ(diag([Γm;Γf ])G

)< 1, where ρ(·) denotes the matrix spectral radius,

G = [gij ] is the channel gain matrix, and Γm and Γf are the vectors ofminimum SINRs required by the MUEs and the FUEs, respectively. Whenρ ≥ 1, not all these minimum SINRs can be supported with a finite amount oftransmit power [30]. In such a case, the network load level is either “medium”or “high” depending on the specific value of ρ, and admission control isneeded to remove some FUEs. If ρ tends to be much larger than 1, thenetwork becomes very congested where it is even difficult to support theminimum SINR Γm of the prioritized MUEs alone.


observation motivates us to consider the following net utilityfor FUE i (similar to that in [31]):

Utot,i = − (γi − Γi)2 − a

(f)i pi, ∀i ∈ Lf . (28)

Although maximizing the first term on the right-hand sideof the above equation, i.e., the utility Ui(γi) = − (γi − Γi)

2,enforces the SINR γi of FUE i to be as close as possible tothe SINR target Γi, the resulting γ∗i at the equilibrium mayactually be less than Γi. Nevertheless, it has been shown in[31] that by allowing a reasonable deviation from the targetSINR, a significant reduction in the transmit power (and hencethe resulting interference) can be achieved. Given its loweraccess priority, this type of soft QoS provisioning is totallyacceptable for FUE i. On the other hand, the cost function,Ci(pi) = a

(f)i pi, penalizes the expenditure of transmit power,

which potentially creates undue interference to the macrocellas well as other FUEs. Here, a

(f)i is the pricing coefficient of

such penalization.Now, applying the result in (7) to these particular utility and

cost functions yields:

γi = Γi − a(f)i Ii

2gii. (29)

Because Ui(γi) is a concave function in pi, so is Utot,i, ∀i ∈Lf . The power value that globally maximizes Utot,i can thusbe computed as

p∗i = max(

IiΓi

gii− a

(f)i I2

i

2g2ii

, 0)

. (30)

Again, by setting the pricing coefficient a(f)i sufficiently

large, we can effectively shut off FUE i. Based upon the powerupdate rule in (30), a joint power adaptation and admissioncontrol algorithm is now developed that is capable of providingsoft QoS for the FUEs. This algorithm is referred to as Algo-rithm 2 in the sequel. The steps in Algorithm 2 are identicalto those in Algorithm 1 except Step 9 where pj is, instead,calculated as pj = Ij(t)Γj/gjj(t)− a

(f)j I2

j (t)/[2g2

jj(t)].

Theorem 2: Assume that xf−1i (x) is an increasing func-

tion, ∀i ∈ Lm, the proposed Algorithm 2 converges to anequilibrium, at which point

p∗i =I∗igii

f−1i

(a(m)i I∗igii

), i ∈ Am (31)

p∗i =I∗i Γi

gii− a

(f)i (I∗i )2

2g2ii

, i ∈ Af . (32)

Moreover, all active MUEs i ∈ Lm have their SINR γ∗isatisfying γ∗i ≥ Γi.

Proof: The proof can be found in Appendix B.

IV. PRACTICAL IMPLEMENTATION ISSUES AND FURTHEREXTENSIONS

A. Communication Overhead of the Proposed Algorithms

The schemes developed in this work only require a limitedamount of signaling to be exchanged among the femtocelland the macrocell. In either algorithm, the power updates

of both MUEs and FUEs can be executed in a completelydistributed manner, based on the information available at locallinks. On one hand, the receiver of each user i (i.e., eitherthe BS or the user terminal depending on uplink or downlinktransmission, respectively) can estimate g′ii by, for instance,exploiting the pilot channel. On the other hand, this receivercan also measure the total received power, and then subtractits own received power to obtain the aggregated interferenceIi, i.e., Ii =

∑j∈L gijpj − g′iipi, assuming that noise can be

ignored in interference-limited CDMA links. The receiver ofuser i then sends both values of g′ii and Ii to its correspondingtransmitter for the update of transmit power in each iteration.

In Step 7 of Algorithms 1 and 2, the FUEs are requestedto increase their pricing coefficients when certain MUEsperceive network congestion. Apparently, each MUE mayonly experience significant interference from the FUEs withinhis/her immediate neighborhood. To protect the MUEs in thedownlink case, it would therefore be sufficient that only themacrocell receivers with low SINRs request their neighboringFUEs to increase their pricing coefficients. In case of openaccess, the hand-off procedure should be established betweenthe users and the macrocell/femtocell BSs, with a controlchannel dedicated for this purpose. Hence, the “warning”message that asks for an increase in the FUEs’ prices can beincorporated into the hand-off message when the undue cross-tier interference is sensed by the victim MUEs. Other type ofcommunication overhead includes the notification made by thefemtocell BS that serves no FUEs to the macrocell in Step 14of Algorithms 1 and 2. This may take the form of a simpleflag message, to be sent over the available wired backhaulnetwork or be broadcast wirelessly.

B. Improving the Efficiency of Equilibrium Solution

It can be shown that the equilibrium solutions achieved bythe developed algorithms correspond to the Nash equilibriaof the underlying non-cooperative games [32]. In such states,no user has any incentive to unilaterally change its transmitpower level. However, Nash equilibrium in general doesnot guarantee to be either globally efficient or optimal. Wediscuss here a procedure to improve the efficiency of thisequilibrium, particularly when the system is in lightly-loadedcondition. Specifically, we attempt to make the SINRs of theactive MUEs greater than their required SINRs. In wirelessenvironments, this result implies more service reliability andmore robustness against fading for the MUEs.

From (13), the following relationship at equilibrium can beobtained for an active MUE i:

fi(γ∗i ) =a(m)i I∗igii

, (33)

where the typical shape of function fi(·) is already illustratedin Fig. 2. It is observed that a higher SINR γ∗i can berealized for a given a

(m)i I∗i /gii if fi(·) becomes flatter. This

corresponds to choosing smaller values of bi, where recallthat bi is the parameter that controls the steepness of Ui(γi).Ultimately, it is possible that the SINRs of MUEs are enhancedby reducing bi whenever possible. Nevertheless, the values of


TABLE ISIMULATION PARAMETERS

Parameter Value

Path-loss exponent, β 3

Processing gain, G 100

Noise power, σi = σ (in Watt) ∀i ∈ L 10−10

System bandwidth, W (in Hertz) 106

γ(f)i = γ(f) ∀i ∈ Lf 2

a(m)i = ai ∀i ∈ Lm 1

bi 1

Removal probability, α 0.1

T (f) 10

Tb 20

kb 0.5

bi should be updated less frequently compared with the updateof power itself.

Toward this end, the following procedure can be employedto improve the attained SINRs of the active MUEs: Wechoose in advance a particular interval Tb to periodicallyupdate bi, ∀i ∈ Lm. At the beginning of each intervalTb, MUE i ∈ Lm multiplies its bi by a factor kb < 1if its servicing macrocell BS has not been informed aboutany empty femtocell during the previous interval. The lattercondition happens if the network load is low, which also meansthat almost all the FUEs converge to the desired equilibriumwithout being removed.

C. Maximum Power Constraints

In the previous sections, we have assumed that both theMUEs and the FUEs can transmit at arbitrarily large powerlevels. We now discuss the scenarios wherein the users aresubject to power limits of the form 0 ≤ pi ≤ pmax

i , ∀i ∈L. Accordingly, the power updates of both MUEs and FUEsare performed as pi(t + 1) := min {pmax

i , pi(t + 1)}, withpi(t + 1) the power assignment in the case of no maximumpower constraint imposed. Fortunately, the convergence resultsof both Theorems 1 and 2 still hold true because (i) standardfunctions with upper power constraints remain standard [33],and (ii) inequality (38) is valid even with constrained powers.Nonetheless, as transmit power budget is limited in this case,the achieved SINRs of the MUEs at the equilibrium may dropbelow their minimum requirements. If certain MUEs achievevery low SINRs at the equilibrium while there is no activeFUE remaining in the system, we may allow these MUEs toremove themselves with a small probability. As soon as thenetwork congestion is sufficiently relieved via this removalprocess, all the remaining active MUEs will eventually meettheir SINR targets.

V. NUMERICAL RESULTS

This section presents numerical results to demonstrate theperformance of the proposed Algorithms 1 and 2. The networksetting and user placement in these examples are illustrated inFig. 1, where the MUEs and the FUEs are randomly deployed

0 10 20 30 40 500

0.02

0.04

0.06

0.08

0.1

0.12

Iteration

Pow

er (

W)

FemtocellMacrocell

Fig. 3. Algorithm 1: Power evolution for M = 10, N = 20, Γ(m)i =

8, a(f) = 109 and k(f) = 1.1.

0 10 20 30 40 500

5

10

15

20

25

30

Iteration

SIN

R

FemtocellMacrocell

Fig. 4. Algorithm 1: SINR evolution for M = 10, N = 20, Γ(m)i =

8, a(f) = 109 and k(f) = 1.1.

inside circles of radii of 500m and 100m, respectively. Down-link transmission is considered in all the simulations. We alsoassume that the number of FUEs serviced by any femtocellBS is identical. The specific numbers of MUEs and FUEsgenerated in each example are displayed in the correspondingplot. The results presented in each figure correspond to oneparticular network realization, chosen with the intention todemonstrate certain features of the developed algorithms.

The channel gain from the transmitter of user j to thereceiver of user i is calculated as d−β

ij , where dij is theirgeographical distance and β the pathloss exponent. The sameinitial pricing coefficient a

(f)i = a(f) and scaling parameter

k(f)i = k(f) are used for all the FUEs. Their values, together

with the SINR targets Γ(m)i and Γ(f)

i , can be found underneathevery plot. In each figure, a single curve corresponds toone specific user. For the ease of reference, the simulationparameters are summarized in Table I.

In Figs. 3 and 4, we show the evolutions of powers and


0 10 20 30 40 500

5

10

15

20

25

30

35

Iteration

SIN

RFemtocellMacrocell

Fig. 5. Algorithm 1: SINR evolution with FUE removal for M = 10, N =

20, Γ(m)i = 8, a(f) = 109 and k(f) = 1.1.

SINRs under Algorithm 1. As can be seen, Algorithm 1converges to an equilibrium with the target SINRs beingattained for all the MUEs. It is also clear from these figuresthat the convergence time of Algorithm 1 is relatively short,slightly larger than 10 in this case. On the other hand, Fig.5 illustrates the operation of Algorithm 1 when the networkbecomes congested. This algorithm initially converges to anequilibrium in which the SINR requirement of one FUE cannotbe satisfied, i.e., its final SINR drops below the thresholdγ(f) = 2. Then, the admission control mechanism integratedin Algorithm 1 is engaged to effectively remove this user,resulting in a noticeable growth in SINRs of several otherFUEs [see iteration 20 and beyond]. It is also evident here thatthe removal of the FUEs does not affect the transmit powersand SINRs of the MUEs. This result verifies the efficiencyand robustness of Algorithm 1 in protecting the macrocellperformance.

In Figs. 6, 7 and 8, we display the evolutions of SINRsfor all the users under Algorithm 2 when the network loadlevel is low, medium and high, respectively. In all scenarios,it is confirmed that Algorithm 2 actually converges with theSINR requirements of all MUEs being met at the equilibrium.When the network becomes more congested, the convergencespeed appears to be slower. Specifically, Fig. 6 shows thatwhen the network load is low, the achieved SINRs of theFUEs are slightly below their corresponding requirementswhile the performance of all MUEs is well protected. Thisis a desirable feature as the soft QoS for the lower-tier FUEscan only be supported to the extent that network load allows.When network congestion starts building up, Algorithm 2smoothly reduces the SINRs of the FUEs so that the MUEscan eventually reach their desired SINR targets. This featurecan best be observed in Fig. 7. Finally, when the network getsso congested that the SINRs of certain FUEs fall below theminimum required threshold γ(f) = 2, admission control isexecuted to remove such users. This operation is depicted inFig. 8, where the FUE that achieves the smallest SINR value

0 10 20 30 40 502

4

6

8

10

12

Iteration

SIN

R

FemtocellMacrocell

Fig. 6. Algorithm 2: SINR evolution in low load (i.e.,ρ(diag([Γm;Γf ])G

)= 0.9) for M = 10, N = 40, Γ

(m)i =

10, Γ(f)i = 8, a(f) = 104 and k(f) = 1.5.

0 20 40 60 80 1002

4

6

8

10

12

Iteration

SIN

RFemtocellMacrocell

Fig. 7. Algorithm 2: SINR evolution in medium load (i.e.,ρ(diag([Γm;Γf ])G

)= 1.1) for M = 10, N = 40, Γ

(m)i = 10, Γ

(f)i =

8, a(f) = 104 and k(f) = 1.5.

is eliminated from the network.

Fig. 9 illustrates how the technique presented in SectionIV-B can help improve the achieved SINRs of the MUEs inAlgorithm 1. Recall that such a mechanism, which involvesscaling down the values of bi over time, may only be activatedwhen the network load level is low. To obtain the resultspresented in this figure, we have decremented all bi’s by afactor kb = 0.5 once in every Tb = 20 iterations. Theseupdates are carried on until one FUE settles his/her SINRbelow the specified SINR threshold γ(f) = 2. Furthermore, Tb

is set to be sufficiently large so that the algorithm convergesto a new equilibrium. As shown in Fig. 9, by scaling downbi, we can enhance the attained SINRs of all the MUEs at thecost of degrading the SINRs of the FUEs.


0 20 40 60 80 1000

2

4

6

8

10

Iteration

SIN

RFemtocellMacrocell

Fig. 8. Algorithm 2: SINR evolution in high load (i.e.,ρ(diag([Γm;Γf ])G

)= 1.18) for M = 10, N = 40, Γ

(m)i =

10, Γ(f)i = 8, a(f) = 104 and k(f) = 1.5.

0 20 40 60 80 100 1200

20

40

60

80

100

Iteration

SIN

R

FemtocellMacrocell

Fig. 9. Algorithm 1: Improving SINRs of the MUEs for M = 8, N =

8, Γ(m)i = 8, a(f) = 109, k(f) = 1.1 and kb = 0.5.

VI. CONCLUSION

In this paper, we have proposed joint power adaptation andadmission control algorithms to autonomously manage theinterference in two-tier networks. Specifically, two differentdesign options for the FUEs have been considered: (i) Bal-ancing between their achieved throughput and the expendedpower, and (ii) Supporting their soft QoS. It has been shownthat the developed algorithms are able to robustly protect theMUEs by maintaining their desired SINR requirements, whilealso allowing the FUEs to flexibly share the remaining networkcapacity. Upon applying the proposed dynamic pricing schemecombined with admission control, network congestion can beeffectively alleviated whenever necessary. The convergence ofthe developed solutions has been proved analytically, and theirmerits are confirmed through extensive numerical study.

APPENDIX APROOF OF THEOREM 1

First, the power control updates for the MUEs and the FUEscan be summarized as:

p(t + 1) = [Ai (p(t))] , i ∈ L, (34)

where, specifically,

Ai (p(t)) = max

{Ii(t)Γi

gii(t),

Ii(t)gii(t)

f−1i

(a(m)i Ii(t)gii(t)

)}, (35)

for i ∈ Lm, and

Ai (p(t)) = max

{0,

W

a(f)i

− Ii(t)gii(t)

}, (36)

for i ∈ Lf .Let us define ∆pi(t) = pi(t)−p∗i with p∗i being the transmit

power of user i at the equilibrium [see (26) and (27)]. Also,denote by ‖∆p‖A the l∞-norm of vector ∆p over some setA, i.e., ‖∆p‖A = maxi∈A |∆pi|. Upon applying the resultsin (36) and (27) to a particular FUE i ∈ Af , we have thefollowing:

|∆pi(t + 1)| =∣∣∣∣I∗i − Ii(t)

gii

∣∣∣∣

≤ (1/G)

∣∣∣∣∣∣∑

j 6=i

(gij/g′ii)∆pj(t)

∣∣∣∣∣∣≤ (1/G)

∑

j 6=i

|(gij/g′ii)∆pj(t)|

≤ Rmax

∑

j 6=i

|∆pj(t)|

≤ Rmax(Mm + Nf − 1) ‖∆p(t)‖Af∪Am(37)

From this, it is clear that

‖∆p(t)‖Af≤ (Mm + Nf − 1)Rmax ‖∆p(t)‖Af∪Am

.(38)

Hence, ‖∆p(t)‖Afwill shrink over time if the condition in

(24) is satisfied and also if ‖∆p(t)‖Amshrinks over time.

The inequality (Mm + Nf − 1) Rmax < 1 in (24) is usuallymet if the network is not very congested. Here, because thedirect channel gains dominate the cross-channel gains, Rmax

typically takes small values. In the case of network congestion,the admission control in Step 12 of Algorithm 1 will removeseveral FUEs (i.e., decreasing Nf ), making it possible to fulfillsuch a condition. Even for a very dense femtocell/macrocelldeployment, (24) can still be satisfied by using a large valueof processing gain G, through which Rmax can be madesmall. As well, the integrated admission control mechanismin Algorithm 1 will autonomously remove “bad users” if thenetwork becomes congested, making (24) feasible.

On the other hand, it has been shown in [20] thatAi (p(t)) , i ∈ Lm in (35) is a standard function (i.e., itsatisfies the positivity, monotonicity, and scalability attributes[33]) if xf−1

i (x) is an increasing function. Moreover, [33]has established that a power control algorithm will converge ifsuch a standard function property is satisfied. It can be verified


that xf−1i (x) is an increasing function if bi is sufficiently

large. As discussed earlier, this can certainly be achievedby our design. Since ‖∆p(t)‖Am

shrinks over time, so does‖∆p(t)‖Af

. As a consequence, Algorithm 1 converges to anequilibrium.

Furthermore, all active MUEs i ∈ Am at that equilibriumstate must have their SINR γ∗i satisfying γ∗i ≥ Γi. This is thecase because all of the remaining users in equilibrium must beadmissible; otherwise, some of them must have been removedby the admission control mechanism integrated in Algorithm1.

APPENDIX BPROOF OF THEOREM 2

The convergence of the proposed power updates in this casecan be proven using the standard function technique [33]. Forthe MUEs, [20] maintains that Ai (p(t)) , i ∈ Lm is a standardfunction if xf−1

i (x) is an increasing function. As discussed inthe proof of Theorem 1, this is true if bi is chosen to besufficiently large.

For the FUEs, it has been shown in [31] that the powerupdates for such users [see (30)] satisfy the requirements ofa standard function if the following conditions hold for alli ∈ Lf :

Ii <giiΓi

a(f)i

, (39)

pi ≤ Γ2i

2a(f)i

. (40)

Indeed, conditions (39)-(40) can be enforced by the admis-sion control mechanism in Algorithm 2. If the network iscongested enough, the transmit powers of certain users willdiverge to some large values, creating a large amount ofinterference Ii(t) to other users. Note that the power update fori ∈ Lf satisfies γi(t+1) = Γi−a

(f)i Ii(t)/(2gii). Therefore, if

Ii(t) is sufficiently large so that γi(t + 1) < γ(f)i

, FUE i willbe removed, which in turn relieves the network congestion.Together with the proper tuning of pricing coefficient a

(f)i ,

(39) and (40) are eventually satisfied.Since the power updates of both the MUEs and the FUEs are

standard functions, Algorithm 2 converges to an equilibrium.By the similar arguments used in the proof of Theorem 1, allactive MUEs i ∈ Am at that equilibrium must also have theirSINR γ∗i ≥ Γi.

ACKNOWLEDGEMENT

The authors would like to thank the anonymous reviewers,whose comments have helped improve the presentation of thispaper.

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Duy Trong Ngo (Danny) (S’08) received the B.Eng.(with First-class Honours and the University Medal)degree in telecommunication engineering from theUniversity of New South Wales, Sydney, NSW,Australia, in 2007, and the M.Sc. degree in electricalengineering (communication) from the Universityof Alberta, Edmonton, AB, Canada, in 2009. Heis currently working toward the Ph.D. degree inelectrical engineering with the Department of Elec-trical and Computer Engineering, McGill University,Montreal, QC, Canada.

His research interest is in the area of resource allocation for wirelesscommunications systems with special emphasis on heterogeneous networks.

Mr. Ngo’s undergraduate education was sponsored by the Federal Govern-ment of Australia through the Australian Development Scholarship scheme.He received the 2006 National Information and Communication TechnologyAustralia (NICTA) Telecommunications Excellence Award. The highest stand-ing telecommunication engineering graduate, he was awarded the UniversityMedal by the University of New South Wales in 2007. From 2007 to2009, he received the Alberta Ingenuity Foundation Student Scholarship andthe Informatics Circles of Research Excellence (iCORE) Information andCommunication Technology Graduate Student Award. He is currently therecipient of the Alexander Graham Bell Canada Graduate Scholarship from theFederal Government of Canada, as well as the McGill Engineering DoctoralAward.

Long Bao Le (S’04-M’07) received the B.Eng. (withHighest Distinction) degree from Ho Chi Minh CityUniversity of Technology, Vietnam, in 1999, theM.Eng. degree from Asian Institute of Technology,Pathumthani, Thailand, in 2002, and the Ph.D. de-gree from the University of Manitoba, Winnipeg,MB, Canada, in 2007.

From 2008 to 2010, he was a postdoctoral re-search associate with Massachusetts Institute ofTechnology, Cambridge, MA. Since 2010, he hasbeen an assistant professor with the Institut National

de la Recherche Scientifique (INRS), Universite du Quebec, Montreal, QC,Canada, where he leads a research group working on cognitive radio anddynamic spectrum sharing, radio resource management, network control andoptimization.

Dr. Le is a member of the editorial board of IEEE Wireless CommunicationsLetters. He has served as technical program committee co-chairs of theWireless Networks track at IEEE VTC’2011-Fall and the Cognitive Radioand Spectrum Management track at IEEE PIMRC’2011.

Tho Le-Ngoc (F’97) received the B.Eng. degree(with Distinction) in electrical engineering in 1976,the M.Eng. degree in 1978 from McGill University,Montreal, QC, Canada, and the Ph.D. degree indigital communications in 1983 from the Universityof Ottawa, ON, Canada.

From 1977 to 1982, he was with Spar AerospaceLimited, where he was involved in the developmentand design of satellite communications systems.From 1982 to 1985, he was an Engineering Managerof the Radio Group in the Department of Develop-

ment Engineering of SRTelecom Inc., where he developed the new point-to-multipoint DA-TDMA/TDM Subscriber Radio System SR500. From 1985to 2000, he was a Professor with the Department of Electrical and ComputerEngineering, Concordia University, Montreal, QC, Canada. Since 2000, he hasbeen a Professor with the Department of Electrical and Computer Engineeringof McGill University, Montreal, QC, Canada. His research interest is in thearea of broadband digital communications.

Dr. Le-Ngoc is a Senior Member of the Ordre des ingnieurs du Quebecand a Fellow of the Institute of Electrical and Electronics Engineers, theEngineering Institute of Canada, the Canadian Academy of Engineering, andthe Royal Society of Canada. He is the recipient of the 2004 Canadian Awardin Telecommunications Research, and the 2005 IEEE Canada FessendenAward. He is the Canada Research Chair (Tier I) on Broadband AccessCommunications and the Bell Canada/NSERC Industrial Research Chair onPerformance & Resource Management in Broadband xDSL Access Networks.

Ekram Hossain (S’98-M’01-SM’06) is a full Pro-fessor in the Department of Electrical and ComputerEngineering at University of Manitoba, Winnipeg,MB, Canada. He received his Ph.D. in electricalengineering from University of Victoria, Victoria,BC, Canada, in 2001.

His current research interests include design,analysis, and optimization of wireless/mobile com-munications networks and cognitive radio systems(http://www.ee.umanitoba.ca/∼ekram).

Dr. Hossain served as the Area Editor for the IEEETransactions on Wireless Communications in the area of “Resource Manage-ment and Multiple Access” from 2010-2011. He is currently an Editor for theIEEE Transactions on Mobile Computing, IEEE Wireless Communications,and the Editor-in-Chief for the IEEE Communications Surveys and Tutorials(for the term 2012-2013). Dr. Hossain has several research awards to his creditwhich include the University of Manitoba Merit Award in 2010 (for Researchand Scholarly Activities) and the 2011 IEEE Communications Society FredEllersick Prize Paper Award. He is a registered Professional Engineer in theprovince of Manitoba, Canada.


Dong In Kim (S’89-M’91-SM’02) received the B.S.and M.S. degrees in electronics engineering fromSeoul National University, Seoul, Korea, in 1980 and1984, respectively, and the M.S. and Ph.D. degreesin electrical engineering from University of SouthernCalifornia (USC), Los Angeles, CA, in 1987 and1990, respectively.

From 1984 to 1985, he was a Researcher withKorea Telecom Research Center, Seoul. From 1986to 1988, he was a Korean Government GraduateFellow in the Department of Electrical Engineering,

USC. From 1991 to 2002, he was with the University of Seoul, Seoul, leadingthe Wireless Communications Research Group. From 2002 to 2007, he wasa tenured Full Professor in the School of Engineering Science, Simon FraserUniversity, Burnaby, BC, Canada. From 1999 to 2000, he was a Visiting

Professor at the University of Victoria, Victoria, BC. Since 2007, he hasbeen with Sungkyunkwan University (SKKU), Suwon, Korea, where he is aProfessor and SKKU Fellow in the School of Information and CommunicationEngineering. Since 1988, he is engaged in the research activities in the areasof wideband wireless transmission and access. His current research interestsinclude cooperative relaying and base station cooperation, interference man-agement for HetNet, cross-layer design and optimization.

Dr. Kim has served as an Editor and Area Editor for Cross-layer Designand Optimization for the IEEE Transactions on Wireless Communicationsfrom 2002 to 2011, and also served as Co-Editor-in-Chief for the Journal ofCommunications and Networks from 2008 to 2011. He is currently an Editorfor Spread Spectrum Transmission and Access for the IEEE Transactionson Communications and Founding Editor-in-Chief for the IEEE WirelessCommunications Letters.

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