dynamic fractional frequency reuse (d-ffr) for multicell

$: Dynamic fractional frequency reuse (D-FFR) for multicell$
RESEARCH ARTICLE

Dynamic fractional frequency reuse (D-FFR) formulticell OFDMA networks using a graph frameworkRonald Y. Chang1∗, Zhifeng Tao2, Jinyun Zhang2 and C.-C. Jay Kuo3

1 Research Center for Information Technology Innovation, Academia Sinica, Taipei, Taiwan2 Mitsubishi Electric Research Labs (MERL), Cambridge, MA 02139, U.S.A.3 Ming Hsieh Department of Electrical Engineering and Signal and Image Processing Institute, University of Southern California, Los

Angeles, CA 90089-2564, U.S.A.

ABSTRACT

A graph-based framework is proposed in this paper to implement dynamic fractional frequency reuse (D-FFR) in a multicellOrthogonal Frequency Division Multiple Access (OFDMA) network. FFR is a promising resource-allocation techniquethat can effectively mitigate intercell interference (ICI) in OFDMA networks. The proposed D-FFR scheme enhances theconventional FFR by enabling adaptive spectral sharing as per cell-load conditions. Such adaptation has significant benefitsin practical systems where traffic loads in different cells are usually unequal and time-varying. The dynamic adaptation isaccomplished via a graph framework in which the resource-allocation problem is solved in two phases: (1) constructing aninterference graph that matches the specific realization of FFR and the network topology and (2) coloring the graph by useof a heuristic algorithm. Various realizations of FFR can easily be incorporated in the framework by manipulating the firstphase. The performance improvement enabled by the proposed D-FFR scheme is demonstrated by computer simulationfor a 19-cell network with equal and unequal cell loads. In the unequal-load scenario, the proposed D-FFR scheme offerssignificant performance improvement in terms of cell throughput and service rate as compared to conventional FFR andprevious interference management schemes. Copyright © 2011 John Wiley & Sons, Ltd.

KEYWORDS

fractional frequency reuse (FFR); graph theory; intercell interference (ICI) management; Orthogonal Frequency Division Multiple Access(OFDMA); IEEE 802.16m; Long-Term Evolution Advanced (LTE-A)

*Correspondence

Ronald Y. Chang, Research Center for Information Technology Innovation, Academia Sinica, Taipei, Taiwan.E-mail: [email protected]†This work was reported in part at the IEEE International Conference on Communications (ICC), Dresden, Germany, June 14--18, 2009[1].

1. INTRODUCTION

Thanks to its effectiveness and flexibility in radioresource-allocation, as well as its capability of combatingfrequency-selective fading, Orthogonal Frequency Divi-sion Multiple Access (OFDMA) has been widely adoptedin many next-generation cellular systems such as Long-Term Evolution Advanced (LTE-A) [2] and IEEE 802.16madvanced WiMAX [3]. Since radio spectrum has long beendeemed the most scarce resource, advanced radio resourcemanagement (RRM) scheme that can increase the OFDMAnetwork capacity and reduce the deployment cost has beenin dire demand. The need for such an RRM algorithmbecomes even more acute today, as the number of sub-scribers experiences unprecedented growth globally and thevolume of traffic increases exponentially.

To improve the spectral efficiency, the same frequencyband† is often reused in multiple geographical areas orcells. However, intercell interference (ICI) will inevitablybe incurred when users or mobile stations (MSs) in adja-cent cells share the same spectrum. Since ICI is the majorperformance-limiting issue in wireless cellular networks[4], a simple interference management (IM) scheme thatcan effectively mitigate ICI is a central part of RRM.

One simple form of IM suggests the allocation of disjointbands to adjacent cells and shared bands to geographicallydistant cells. This way, the communication links in the net-work will not cause any pronounced interference to eachother. Such deployment, however, tends to lose more band-

† We use band and spectrum interchangeably in this paper.

WIRELESS COMMUNICATIONS AND MOBILE COMPUTINGWirel. Commun. Mob. Comput. 2013; :12–27Published online 18 January 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/wcm.

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1 Copyright © 2011 John Wiley & Sons, Ltd.2

width efficiency than what can be gained in signal qualityimprovement by ICI reduction. Therefore, recent researchactivities have outlined several improved IM schemes fornext-generation OFDMA systems. FFR is one such tech-nique supported in WiMAX [5]. FFR is designed withthe objective of striking a better tradeoff between spec-tral efficiency (i.e., advantage of admitting more users) andinterference mitigation (i.e., advantage of improving signal-to-interference-plus-noise ratio, or SINR) by leveraging thevery different experience of ICI in the cell center and thecell edge. In particular, since cell-edge MSs are more proneto ICI than cell-center MSs, the cell edge is granted with abigger reuse factor (e.g., 3) while the cell center is grantedwith a smaller reuse factor (e.g., 1).

FFR has drawn significant research attention due to itsefficiency and simplicity. Examples and applications of FFRwere discussed in [6--8], and variations of FFR were pro-posed and compared in [9,10]. All these schemes are offixed configuration; that is, their spectrum allocation is pre-determined and unadaptable to cell-load variations. Thisrigidity hinders the realization of FFR’s full potential andmay result in inefficient spectral usage. For example, inan unequal cell-load environment, heavy-load areas mayexperience a shortage of spectral resource while light-load areas experience a surplus of resource due to thisrigidity.

A dynamic FFR scheme was proposed in [11], whereresources are dynamically partitioned into a super groupand a regular group. This scheme demonstrates higher sys-tem throughput but lower cell-edge throughput performancecompared with a static FFR scheme. An adaptive FFRscheme was proposed in [12]. This scheme suggests thatonly cells that are dominant interferers of the cell-edge usersin service are required to employ FFR, while the remain-ing cells may still employ a reuse factor of 1. However,a practical algorithm that can systematically achieve theresource-allocation principle suggested by all these FFRschemes is missing.

Based on the above observations, we are motivated todevelop a novel multicell OFDMA channel-assignmentframework that can systematically implement dynamic FFRwhich yields superior cell-edge throughput performancecompared with fixed FFR. Our scheme, specifically termeddynamic fractional frequency reuse (D-FFR), can adaptto varying and unequal traffic loads in adjacent cells byjudiciously redistributing the radio resource among cells.This adaptation is realized by a novel graph approachin which the FFR-enabled network is first presented byan interference graph and then the resource-allocation isaccomplished by coloring the graph intelligently. Variousversions of FFR can easily be incorporated into our D-FFRframework.

The rest of the paper is organized as follows. Themulticell system model and mathematical description arepresented in Section 2. In order to establish performancebenchmarks and provide background for our proposedmethod, previous IM schemes and the graph approach toresource-allocation are introduced in Section 3. The pro-

Fig. 1. A hexagonal multicell OFDMA cellular network.

posed D-FFR framework is described in Section 4 with itsperformance demonstrated in Section 5. Finally, concludingremarks are given in Section 6.

2. SYSTEM DESCRIPTION

2.1. Multicell OFDMA networks

A hexagonal multicell OFDMA network is considered inthis paper. One example network with seven cells is shownin Figure 1. Each cell is served by a base station (BS) at thecenter of the cell, and there are a set of MSs within eachcell. Based on its physical proximity to the BS, each MS isclassified as either in the cell-center or the cell-edge area.The boundary that separates the cell center and the cell edgecan be a design parameter. In OFDMA systems, the radioresource that will be allocated to users is the subchannel. Asubchannel is a group of subcarriers that may or may not becontiguous, depending on the specific permutation schemeused. A permutation scheme determines the mapping fromphysical subcarriers to logical subchannels. For example,IEEE 802.16e standard [13] has specified partial usage ofsubchannels (PUSC) and adaptive modulation and coding(AMC) as two permutation schemes for noncontiguous andcontiguous subcarrier mapping, respectively.

2.2. The diversity set

In regular multicell operation, each MS is registered andcommunicates with a single BS, which is called the anchoror serving BS. However, in some scenarios such as soft han-dover and base station cooperation (BSC) [14], an MS maycommunicate with multiple BSs simultaneously. To keep

R. Y. Chang et al. D-FFR for multicell OFDMA networks

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track of both the anchor BS and neighbor BSs‡ that arewithin the communication range of each MS, a diversity setis defined in the IEEE 802.16e standard [13]. The diversityset of MS m is denoted as Dm = Am∪Bm, where Am is theanchor BS set that has only one element (i.e., anchor BSAm) and Bm is the neighbor BS set that may contain 0, 1, ormultiple elements (i.e., nearby BSs). Note that the numberof elements in setBm depends on the geographic location ofMS m in relation to its neighboring BSs and on some path-loss threshold. Specifically, to form the diversity set, MSm monitors the signal from different BSs, and determineswhether or not to add each BS to its diversity setDm depend-ing on whether the corresponding measured signal strengthis above a predetermined path-loss threshold. The diversityset information is maintained at both the MS and the BS, andcan readily be used by the radio network controller (RNC)to perform centralized ICI-aware resource-allocation. Notethat when defining the SINR at the MS, we consider allBSs in the network (rather than only those in the diversityset of the MS) as the potential interfering source. This con-sideration will be presented in Section 2.3 and used in thesimulation in Section 5.

2.3. System model and performancemetrics

We consider a downlink hexagonal cellular network asdescribed in Section 2.1. In our network, there are L BSs,each with NT antennas. Meanwhile, in the area of cell l,there are Ml MSs, each with NR antennas, that have pend-ing traffic. Idle MSs are neglected as they will not affectOFDMA resource-allocation. The total number of MSs inthe entire network is therefore M = ∑L

l=1 Ml. Among theMl MSs, a subset of them, denoted by Sl and |Sl| ≤ Ml isserved by BS l at a given time, where |·| is the cardinalityof a set. Each MS, depending on its proximity to the BS,is labeled as either a cell-center or a cell-edge user. Let Sc

l

be the set of cell-center MSs served in cell l, and Mcl be

the number of total cell-center MSs (served or unserved) incell l. Likewise, Se

l is the set of cell-edge MSs served in celll, and Me

l is the number of total cell-edge MSs (served orunserved) in cell l. Thus, Sl = Sc

l ∪Sel and Ml = Mc

l + Mel .

Assume a set of N subchannels is available for resource-allocation in the network. Depending on the specificresource-allocation method used, an entire or partial set ofthe subchannels may be available to each cell. Let Ol, Oc

l ,andOe

l be the set of subchannels allocated to cell l, the cellcenter of cell l, and the cell edge of cell l, respectively. Dueto the intracell allocation constraint in OFDMA networks,which restricts the use of a subchannel by at most one MS

‡ It is worthwhile to make a distinction between neighbor and adjacentwhen designating cells or BSs. Adjacency refers strictly to the physicalproximity of cells, and in a typical hexagonal deployment each cell hassix adjacent cells. Neighbors refer generally to nearby cells which maybe nonadjacent but have the potential to interfere with the center cell.

within the same cell,Ocl ∩Oe

l = φ andOl = Ocl ∪Oe

l . For thesame reason, the number of served MSs must be less thanor equal to the number of subchannels available,§ that is,|Sc

l | ≤ |Ocl |, |Se

l | ≤ |Oel |, and |Sl| ≤ |Ol| ≤ N for all ls.

Signal transmission in the multicell OFDMA system ismodeled as follows. We consider an arbitrary symbol in anOFDMA frame for the interference study in the ensuingdiscussion. An arbitrary MS m, m∈{1, 2, . . ., M}, that haspending traffic and will be served in the network is consid-ered. Let the NR × NT matrix H (l)

mn represent the channelfrom BS l to MS m in the subchannel n, which has com-plex Gaussian elements. Let the Lmn × 1 vector smn bethe data intended for MS m transmitted using subchan-nel n, which has zero mean and normalized power, thatis, E[smns

Hmn] = ILmn

. The data vector smn is precoded byan NT × Lmn precoding matrix,‖ Tmn, which also has nor-malized power, that is, ||Tmn||2F = 1, where || · ||2F is theFrobenius norm of a matrix.

Suppose that downlink power control is employed toreduce the ICI caused to neighbor cells. That is, the down-link signal for MS m is sent with power Pm, depending onits proximity to the BS. In particular, we have

Pm ={

P0, if MS mis in the cell centerP1, if MS mis in the cell edge

(1)

where P0 < P1.In the typical operation, each MS communicates with

one BS.¶ Thus, the received baseband discrete-time signalat MS m that uses subchannel n after matched filtering andsampling, rmn, comprises useful signal from the serving BSAm, and the interference from neighbor BS Av serving MSv plus noise, that is,

rmn =√

PmH(Am)mn Tmnsmn +

∑v∈Im

√PvH

(Av)mn Tvnsvn + nmn

(2)

Im is the set of MSs whose serving BS will cause inter-ference to MS m’s reception from its serving BS Am. nmn

is the additive white Gaussian noise with noise powerE[nH

mnnmn] = N0W , where N0 is the thermal noise densityand W is the subchannel bandwidth. Based on (2), the SINR(in the linear scale) of the received signal at MS m that uses

§ Here, we assume no space-division multiple-access (SDMA) [15] isused in the network.‖ The precoding matrix design is beyond the scope of this paper. Werefer interested readers to [16] and references therein.¶ The IEEE 802.16 standard allows the use of Macro Diversity Han-dOver (MDHO) and BSC in which an MS may communicate withmore than one BS simultaneously. The interference management forsuch scenarios is studied in [17].

D-FFR for multicell OFDMA networks R. Y. Chang et al.

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subchannel n is given by

SINRmn = Pm||H (Am)mn Tmn||2F∑

v∈ImPv||H (Av)

mn Tvn||2F + N0W(3)

Note that the SINR corresponds to the measured signalstrength used to create the diversity set of each MS. Thus, theSINR information is implicitly used in the proposed frame-work presented in Section 4, which leverages the diversityset information.

Several key performance metrics are considered for net-work performance evaluation. Specifically, we consider cellthroughput and service rate. Cell throughput is used to quan-tify the aggregate network performance of IM schemes withdifferent reuse factors. To model it mathematically, considera served MS m in cell l, m∈Sl, using a set of subchannel(s)Nm∈Ol. Then, the theoretical cell throughput for cell l (bps)is given by the Shannon capacity:

Tl =∑m∈Sl

∑n∈Nm

W log2(1 + SINRmn) (4)

Likewise, the cell-center and cell-edge throughput forcell l are T c

l = ∑m∈Sc

l

∑n∈Nc

mW log2(1 + SINRmn)

and T el = ∑

m∈Sel

∑n∈Ne

mW log2(1 + SINRmn), where

Ncm∈Oc

l (Nem∈Oe

l ) represents the set of subchannel(s) usedby a served MS m in the cell center (edge) of cell l. Tofacilitate the study of theoretical throughput performance,it is assumed that all served MSs have infinite backloggeddata to receive.

Service rate is used to study the service capacity of reuse-n and FFR systems where typically only a fraction of totalMSs are granted service at a given time. The service ratein cell l (%) is defined by the ratio between the number ofserved MSs and the total number of MSs that have pendingtraffic in cell l, that is,

Gl = |Sl|Ml

× 100 (5)

3. RELATED WORK

In this Section, we present several IM schemes that arerelated to our work and introduce the graph approach toresource-allocation, which will lay the foundation for thediscussion of our proposed schemes in Section 4.

3.1. Previous IM schemes

3.1.1. Reuse-3.

The simplest IM scheme is a reuse-n (n > 1) system[18]. A reuse-n system partitions a geographical area inton regions, each of which is exclusively allocated a band insuch a way that cells adjacent to each other are assigned withdifferent bands and cells sufficiently distant from each other

may use the same band. The rate at which the same band isreused is dictated by the reuse factor n. A reuse-3 (n = 3)scheme is depicted in Figure 2a, wherein each of the threeadjacent cells uses one-third of the total bandwidth. Thethree-cell scheme shown here constitutes the basic build-ing block for an arbitrary-sized geographical area, so theprinciple can generalize to more cells. In a typical reuse-3network, each cell is surrounded by six adjacent cells thatoccupy a band different from that of the center cell. Due toaggravated loss of spectral efficiency, reuse-n schemes withn > 3 (e.g., 4, 7, and 9) are not considered in this work.

3.1.2. Reuse-1.

A reuse-1 system, also known as the universal reuse, allo-cates the total bandwidth to every cell in the network. Areuse-1 scheme is used in many modern cellular OFDMAsystems due to its effectiveness in relieving loss of spec-tral efficiency in reuse-n (n > 1) systems [18]. Nevertheless,users of the reuse-1 system, especially those in the cell edge,admittedly suffer more severe ICI compared with users ofthe reuse-n (n > 1) system. Thus, an IM scheme is oftenembedded into the reuse-1 system to address this problem[17,19,20]. In [19], beamforming antennas in combinationwith interference coordination between cells were used toachieve ICI reduction. ICI coordination (ICIC) enhancedreuse-1 schemes were proposed in [17], where the overallICI is reduced by judiciously coordinating the channel allo-cation for strong ICI-prone MSs in adjacent cells. In [20],a two-level algorithm that performs dynamic interferenceavoidance was used to achieve higher network throughputin the reuse-1 system.

3.1.3. FFR.

FFR is developed as a flexible frequency reuse scheme tostrike a better tradeoff between spectral efficiency and inter-ference mitigation than the generic frequency reuse. FFRcan be realized in many different fashions [8,10,11,20,21],which are variations of the two representative realizationsas described in the following.

• FFR-A: One realization, termed FFR-A in this paper,follows the principle that all adjacent cells’ cell centershare the same band while their cell edge use orthog-onal bands. In addition, the cell-center band of onecell and the cell-edge band of an adjacent cell arenonoverlapping. An FFR-A scheme with an exemplarybandwidth partitioning is shown in Figure 2b. A fixedFFR-A scheme is such that the bandwidth partitioningis determined initially and remains fixed regardless ofchanges in the cell load.

• FFR-B: Another realization, termed FFR-B, followsthe principle that all adjacent cells’ cell edge useorthogonal bands. Different from FFR-A, FFR-Ballows partial overlapping between the cell-centerband of one cell and the cell-edge band of an adjacentcell. An example is shown in Figure 2c. A fixed FFR-B



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scheme, similar to fixed FFR-A, is one in which thebandwidth partitioning is performed only initially andoblivious of any subsequent change in the cell load.

3.2. The Graph Approach toResource-Allocation

Graph multi-coloring method has been used extensively toaddress the channel assignment problem in cellular andmesh networks (e.g., [22--24]). In the traditional formu-lation, each node in a graph corresponds to a BS or anaccess point (AP) in the network to which channels areassigned. The edge that connects two nodes represents thepotential co-channel interference between the two BSs/APs,and, typically, the severity of this co-channel interferenceis related to the geographical proximity between the twoBSs/APs represented by the two nodes. Once the graph isconstructed, the channel-assignment problem is formulatedas a node-coloring problem. The objective is to find theminimal number of colors necessary for coloring the entiregraph (i.e., the chromatic number of the graph) providedthat no two interfering nodes have colors in common, orequivalently, are assigned with the same channel.

Recently, this graph approach finds its application inreuse-1 OFDMA networks [17]. In this new application,a node in the graph represents an MS rather than a BS,and the edge is assigned an integer rather than a binaryweight to represent different interference levels. A new col-oring approach is also devised in [17], incorporating anICI-mitigation mechanism that selectively assigns the samecolor to two interfering nodes. This method, however, can-not be directly applied to nonreuse-1 systems, includingFFR-enabled OFDMA networks. The reason is that FFR

presents a new resource-allocation problem as summarizedbelow:

• Unlike the systems investigated in [22--24], wheregraph coloring aims at minimizing the use of colors(subchannels), an OFDMA network has a fixed andpredetermined number of colors (subchannels) avail-able to use.

• Different from the coloring approach in [17], wherenodes are always colored, the coloring algorithm inthe nonreuse-1 setting should accommodate the factthat some MSs may be suspended from service andtherefore the corresponding nodes are uncolored.

Motivated by the above observations, we have developeda new graph framework to achieve efficient resource-allocation in FFR-enabled OFDMA networks, which ispresented next.

4. PROPOSED DYNAMIC FFR(D-FFR) FRAMEWORK

4.1. Graph Construction

The first phase of our proposed graph approach to FFRresource-allocation is to construct an interference graphaccording to the OFDMA network topology. Consider anillustrative example with three BSs and five MSs as shownin Figure 3. Our objective is to construct an undirectedinterference graph, denoted by G = (V, E), based on thetopology and the bandwidth-assignment requirement ofFFR-A or FFR-B. In this graph, set V contains nodes that

Fig. 2. The frequency planning for different interference management schemes, where the bandwidth assignment for a geographicalarea is shown by a matching color on the total available spectrum.



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Table I. The diversity set of MSs in Figure 3.

Anchor BS set Neighbor BS set

MS 1 A1 = {3} B1 = {2}MS 2 A2 = {2} B2 = �

MS 3 A3 = {1} B3 = �

MS 4 A4 = {2} B4 = {3}MS 5 A5 = {1} B5 = {2, 3}

are labeled to represent MSs in the multicell network, thatis, V = {1, 2, . . ., M}. Set E contains two-element subsetsof V, and induces a symmetric binary relation on V thatis called the adjacency relation of G. Specifically, node aand node b are said to be adjacent to each other if they areconnected by an edge, or equivalently, if {a, b}∈E.

To determine the edge set, E, a practical method basedon the diversity set is used. The basic idea is to infer theMS’s geographic location, and consequently the adjacencyrelation, from both the diversity set and the site deploymentinformation available at RNC. To provide an example, thediversity set for the scenario in Figure 3 is shown in TableI, where each row indicates the diversity set maintainedfor the corresponding MS. Each MS has an anchor BS andpossibly several neighbor BSs if it is located at the celledge. For instance, MS 5 belongs to BS 1, but since MS 5also detects signals from BS 2 and BS 3 it includes themin the neighbor BS set. As a result, we have A5 = {1} andB5 = {2, 3} for MS 5. Given the diversity set in Table I, thefollowing information can be obtained:

• MS a is a cell-center (or cell-edge) user if its neighborBS set,Ba, is an empty (or nonempty) set. For example,MS 2 is a cell-center user and MS 4 is a cell-edgeuser.

• MS a and MS b are users of the same cell if they havethe same anchor BS (i.e., Aa = Ab). For example, MS2 and MS 4 are users of the same cell.

• MS a and MS b are users of two adjacent cells if theiranchor BSs, according to the site deployment informa-tion maintained at RNC, serve two adjacent cells. For

example, MS 2 and MS 3 are users of two adjacentcells.

The analysis is performed for every pair of MSs todetermine the pairwise relation between them. Then,this information is used in the edge construction fordynamic FFR-A (D-FFR-A) and dynamic FFR-B (D-FFR-B) schemes, as described as follows.

4.1.1. D-FFR-A.

The edge-construction algorithm for D-FFR-A isdescribed in Table II. Two nodes are connected by an edgeif they satisfy specific pairwise relations. Specifically, a pairof nodes will be connected by an edge if the correspondingMSs have intracell relation (A1) or some intercell relations(A2 and A3), which, according to the FFR-A principle, posechannel-assignment constraints. Since two cell-center MSsof adjacent cells are permitted to use overlapping bands inFFR-A, corresponding nodes are not connected by an edge.

After running the edge-construction algorithm for allpairs of nodes, the interference graph can be constructedfor D-FFR-A. The resulting interference graph that corre-sponds to the scenario in Figure 3 is drawn in Figure 4. It isseen that all pairs of nodes, except for nodes 2 and 3, satisfysome relation in A1--A3 and therefore are connected by anedge.

4.1.2. D-FFR-B.

The edge-construction algorithm for D-FFR-B isdescribed in Table III. Again, a pair of nodes will have anedge if the corresponding MSs have intracell relation (B1)or particular intercell relation (B2). Different from FFR-A,however, the intercell constraints posed by the FFR-B prin-ciple include only the use of nonoverlapping bands for twocell-edge MSs of adjacent cells.

The interference graph constructed for D-FFR-B that cor-responds to the scenario in Figure 3 is drawn in Figure 5.Note that the graph for D-FFR-B has fewer edges comparedwith the graph for D-FFR-A. This is due to fewer intercell

Table II. Edge construction algorithm for D-FFR-A.



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Fig. 3. Example of a multicell multiuser scenario.

constraints presented by the FFR-B principle, as discussedpreviously.

4.2. Graph coloring

The second phase of the graph approach to OFDMAresource-allocation is to color the nodes in the interferencegraph. A color represents a subchannel, and coloring thenodes corresponds to the physical meaning of allocatingsubchannels to the MSs. A coloring of a graph is calledproper if the coloring constraint is met; that is, no twoadjacent nodes in the graph have colors in common.

Many heuristic coloring algorithms have been proposedto color a graph efficiently. Most of the algorithms (e.g.,the methods compared in [25]) were proposed to color agraph given that the graph is colorable, that is, the numberof available colors is no less than the best-known chromaticnumber of the graph. These algorithms aim at improvingthe execution time and/or the percentage of arriving at thebest-known result upon termination of the algorithm.

In the graph for OFDMA networks, the number of col-ors (i.e., subchannels) is constant while the size of thegraph is variable to different network load. As a result,

Fig. 4. The interference graph constructed for D-FFR-A for thescenario given in Figure 3.

when the network is heavily loaded, colors become under-provided and coloring the entire graph becomes infeasible.Therefore, a mechanism to color only selective nodes mustbe incorporated, which will serve as an admission con-trol mechanism in the network. On the other hand, whenthe network is lightly loaded, or equivalently, when col-ors are over-provided, diversifying colors is desired toavoid unnecessary color collisions. These considerationsare incorporated in the new graph coloring problem thatextends the original formulation [22] as follows.

P. Given an interference graph G = (V,E) with |V| = Mnodes, an augmented set of colors Caug containing a regularcolor set C = {1, 2, . . ., N} and a blank color set {0}, anda function f that assigns to each v∈V a subset f(v) of Caug,find a coloring of the graph such that

1. C1: ∀v, |f (v)| = 1, that is, each node is assigned a singlecolor.

2. C2: ∀(u, v)∈E, f (u)∩f (v) = φ or {0}, that is, no twoadjacent nodes have regular colors in common.

3. C3: With C1 and C2 met, |{v|f (v) = {0}}| is minimizedand the use of colors is balanced.

Constraints C1--C2 are the coloring constraints thatguarantee a proper coloring. Note that constraint C2 hasaccommodated the possibility that a node may be uncolored,

Table III. Edge construction algorithm for D-FFR-B.



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Table IV. Modified Dsatur algorithm for solving graph coloring for D-FFR schemes.

that is, assigned the blank color. Without violating con-straints C1--C2, however, an uninteresting solution whereall nodes are uncolored may be yielded. Constraint C3 istherefore added, which states that the number of uncolorednodes should be minimized and the use of colors should bebalanced (‘balancing’ here follows the same concept as in[25]). Note that C3 is a soft constraint in the sense that vio-lating it will not invalidate a coloring but fulfilling it willimprove the performance of a coloring. This is achievedby maximizing the service potential of the network andreducing channel collision, as suggested by constraint C3.

A heuristic algorithm is proposed to solve Problem P.Since many considerations in Problem P are new and notaddressed in any existing coloring algorithm, we proposeto modify an efficient coloring algorithm, that is, the Dsaturalgorithm [25], to meet these needs in OFDMA networks.The modified Dsatur algorithm is presented in Table IV,with the interference graph G as its input. Note that twomodifications are made to the original Dsatur algorithm inStep 2. First, the selected node is given a randomly selected(instead of the least possible or lowest numbered) colorfrom the available color set of this node. Second, when anode’s available color set is empty, the node is allowed toremain uncolored. The first modification helps achieve colorbalancing when colors are over-provided, and the secondmodification accommodates the case of under-provided col-ors. The algorithm terminates when all nodes are examined,that is, either colored or, by decision, uncolored.

4.3. Further discussion on the proposedframework

Some discussions on the complexity issues, mechanics, andapplications of the proposed framework are presented here.

4.3.1. Complexity.

We evaluate the computational complexity of the pro-posed method in terms of the total number of MSs in thenetwork, M, to understand the scalability of the proposedmethod to the size of the network. The proposed frame-work consists of two phases: graph construction and graphcoloring. The complexity of graph construction comes fromexamining the pairwise relations between nodes, as in edge-construction algorithms in Tables II and III, and thereforedepends on the number of all possible two-element subsetsof V. Since |V | = M, the complexity of graph constructionis on the order of O(M2). The complexity of graph coloringcan be understood by studying the three steps in the coloringalgorithm in Table IV. The algorithm iterates M times, eachtime with a node examined and then excluded from the set U.As a result, each iteration of the algorithm requires dimin-ishing computational efforts as more nodes are excludedfrom U. To get an idea of the approximate complexity, how-ever, we approximate the complexity involved in subsequentiterations by the first one. To realize Step 1, a sorting pro-cedure where nodes in U are sorted in ascending order ofthe size of their available color set is needed. Sorting algo-rithms that require operations on the order of M log M exist[26], and thus after M iterations the complexity requirementfor Step 1 is approximately O(M2 log M). The operation inStep 2 is independent of M and does not grow with the sizeof the network. The complexity of Step 3 arises from updat-ing the available color set for all nodes in U. Since in eachiteration nodes in U need only to look at the selected nodeto update their available color set, the complexity of Step3 is O(M). The overall complexity requirement for Step 3is therefore O(M2). In sum, the complexity of graph con-struction is O(M2) and the complexity of graph coloring isdominated by O(M2 log M). Thus, the proposed method isof polynomial-time complexity in terms of the size of thenetwork, making it practical even for expansive networks.



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Fig. 5. The interference graph constructed for D-FFR-B for thescenario given in Figure 3.

4.3.2. Sectorized FFR systems.

While the discussion in this paper has focused on thenonsectorized cell structure, the concept of FFR can alsobe applied to sectorized systems [11]. With simple mod-ification, the proposed D-FFR framework can be adaptedto sectorized scenarios. Specifically, an edge-constructionalgorithm similar to the ones in Tables II and III canstill be used, however with new pairwise relations, thatis, intra-sector and inter-sector relations. The same col-oring algorithm in Table IV is then used to complete theresource-allocation.

4.3.3. The mechanics of adaptation.

The proposed dynamic allocation method can be appliedin practical OFDMA networks on either a periodic oron-demand basis. A periodic approach is explained byFigure 6, which shows the grouping of IEEE 802.16eOFDMA frames into periods. In the first frame of eachperiod, the dynamic FFR allocation is triggered and theallocation result, conveyed to MSs using downlink signal-ing (e.g., DL-MAP message), remains unchanged until thenext period. The period T can be chosen by considering thenetwork-load variability as well as the mobility of users. Inan on-demand approach, instead of periodically reassigningchannel resources, the RNC will perform channel allocationwhen the system performance (e.g., network throughput)drops below a predetermined performance threshold. Thisfashion gives the on-demand approach a potential edge inyielding the best performance.

4.3.4. Quality of service.

The proposed D-FFR framework is performed in a‘best-effort’ fashion and cannot guarantee the quality ofservice demanded by each individual MS. That is, whena user requests a priority service or extra resource (orequivalently, a node in the graph requests preemptivecoloring or multiple colors), the algorithm in Table IVwill not guarantee the requested resource. The algorithmcan however be augmented by an initialization process

Table V. Simulation setup.

Cell parametersNumber of cells, L 19Cell (cell-center) radius 750 (500) mAntennas NT , NR 1, 1Frequency reuse factor 1, 3, or FFR

OFDMA parametersTotal bandwidth 30 MHzNumber of subchannels, N 30DL Permutation type PUSC

Channel modelPath loss (dB) 130.62 + 37.6 × log10(d), (d in km)Fast fading ITU pedestrian B

Power control parametersCell-center trans. power, P0 40 dBmCell-edge trans. power, P1 46 dBmThermal noise density, N0 −174 dBm/Hz

where the demands from the priority MSs are first fulfilled(provided that this is within the network capacity), followedby same steps in Table IV to allocate the residual resourceto other nonpriority/best-effort MSs in the network. Exten-sion of this primitive scheme to take into account fairnessand prioritization across MSs is a worthwhile futurework.

5. SIMULATION RESULTS

Here, we study the performance of the proposed schemesby computer simulation. The performance of the pro-posed D-FFR schemes is compared with some previousIM schemes described in Section 3. The proposed schemesand the benchmarks are summarized in Figure 7. By con-sidering these benchmarks with various frequency reusefactors and comparing their performance side-by-side, athorough understanding of cellular network planning, fre-quency reuse, and particularly the proposed D-FFR schemescan be gained. Note that in this Section, we will use the par-ent scheme in the taxonomy tree (Figure 7a) to represent allits children schemes and their shared properties. For exam-ple, ‘FFR’ is used to refer to FFR-A and FFR-B combined,and ‘FFR-A’ is used to refer to both F-FFR-A and D-FFR-A,etc.

5.1. Simulation setup

The simulation setup closely follows the IEEE 802.16mevaluation methodology [27] and is summarized in Table V.Note that although a single-input single-output (SISO)system is considered in the throughput evaluation, the com-parison result is readily extensible to a simple multiple-inputmultiple-output (MIMO) system (i.e., no BSC or SDMA isused) with increased throughput capacity.

To fairly evaluate the performance of different schemes,the total bandwidth is properly apportioned among cells. For



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Fig. 6. The periodic operation of dynamic channel allocation for 802.16e OFDMA systems.

Reuse-3, without prior knowledge of the traffic load in dif-ferent cells, it is reasonable to allocate one-third of the totalbandwidth for each cell; that is, |Ol| = 10 for all cell ls. Sim-ilarly, for F-FFR-B it is reasonable to have a cell edge thatoccupies one-third of the total bandwidth; that is, |Oe

l | = 10and |Oc

l | = 20 for all cell ls. To fairly evaluate F-FFR-A,we need to carefully partition the total bandwidth such thatthe band allocated to the cell center and the cell edge isroughly proportional to their traffic/user loads. Under theuniform traffic model, it can be shown that with the sizeof the cell-center area defined in Table V# the traffic ratiobetween the cell center and the cell edge is roughly 1:1.Thus, we adopt |Oc

l | = 15, which leads to |Oel | = 5, for all

cell ls. Furthermore, to conduct fair comparison betweenF-FFR-A and D-FFR-A, we consider a common size of thecell-center band to equalize the ‘white spectrum’ in F-FFR-A and D-FFR-A; that is, |Oc

l | = 15 for both schemes. Notethat the above bandwidth allocation corresponds roughly tothe illustration in Figure 2a--c.

# In practice, the size of the cell center is determined by the diversityset and further by the path-loss threshold used in creating the diver-sity set. To ease implementation, however, we adopt a definitive-sizedcell center, which can be considered as the result of properly settingthe path-loss threshold such that the diversity set would give the sameinformation about the size of the cell center, as discussed in Section 4.1.

5.2. Results and discussion

5.2.1. Equal cell-load scenarios.

First, we simulate the equal cell-load scenario, whereeach cell has the same number of uniformly distributed MSs.Figure 8a shows the cell throughput performance, obtainedby (4) and averaged over all cells, for different IM schemesin comparison. It is seen that in low-load conditions (i.e., nomore than 10 MSs per cell), Reuse-3 outperforms all oth-ers. This is because in low-load conditions Reuse-3 achievescomplete nullification of ICI from all interferers in the adja-cent cells and has 100% service rate, as shown in Figure 8b.As the traffic load increases, Reuse-3 becomes increas-ingly inefficient as more users are rejected from service,as revealed by the diminishing service rate in Figure 8b andthe stagnant cell throughput in Figure 8a. This inefficiencyis remedied by FFR. As shown in Figure 8b, in medium-load conditions, FFR-A and FFR-B have much improvedservice rates, which contribute to the higher cell through-put in Figure 8a. It is also seen that D-FFR-A (D-FFR-B)achieves slight but consistent improvement in throughputand service-rate performance compared with F-FFR-A (F-FFR-B). The advantage of the dynamic method is not verynoticeable in the equal cell-load scenario because its capa-bility of redistributing the channel resource among cellsis not fully exploited. The slight improvement observed isdue to the flexible use of the spectrum which is unavail-able in the fixed counterpart. In medium-load conditions,



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Fig. 7. Test schemes. (a) Taxonomy. (b) Description.

Reuse-1-ICIC achieves very good performance, yet largelycomparable with FFR-A.

In heavy-load conditions, the throughput of Reuse-1-ICIC decays because of the aggravated ICI and the fact thatit always serves all MSs. The throughput of FFR schemes,however, increases consistently at the cost of more MSs

being rejected from service. The Reuse-1-BL scheme per-forms poorly regardless of the load, because no IM schemeis employed.

Comparing FFR-A and FFR-B, it is seen that FFR-Aoutperforms FFR-B in throughput despite the lower ser-vice rate (Figure 8b). The reason is that while fewer MSs

Fig. 8. Average cell throughput and service rate under different traffic loads: equal cell-load scenarios.



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Fig. 9. Average cell-edge and cell-center throughput for FFR schemes under different traffic loads: equal cell-load scenarios.

are served, a served MS experiences better SINR (i.e., per-user throughput) for FFR-A. Furthermore, while FFR-Ayields higher aggregate cell throughput, it achieves lowercell-edge throughput compared to FFR-B, as illustrated inFigure 9. The higher aggregate cell throughput of FFR-A islargely contributed by its higher cell-center throughput. Theabove observation introduces tradeoffs in choosing FFR-Aor FFR-B as an IM scheme.

5.2.2. Unequal cell-load scenarios.

Second, we simulate the unequal cell-load scenario. Wedefine the traffic load ratio as the load proportion of heavy-to light-load cells. For every three adjacent cells, we con-sider two light-load cells (with two MSs each) and oneheavy-load cell (with a varying load controlled by the trafficload ratio). We plot the same performance measures against

different traffic load ratios in Figure 10. It is seen, in sharpcontrast to the equal cell-load scenario, that D-FFR-A (D-FFR-B) achieves substantially better performance in termsof cell throughput (Figure 10a) and service rate (Figure 10b)than F-FFR-A (F-FFR-B). Specifically, when the traffic loadratio is equal to 15, D-FFR-A outperforms F-FFR-A by 12%in cell throughput and 33% in service rate, and outperformsReuse-3 by 70% in cell throughput and 107% in servicerate. This is due to the flexibility in borrowing light-loadcells’ resource for the use of heavy-load cells in the dynamicscheme.

In Figure 10, we also observe that the performance gapbetween D-FFR-A and F-FFR-A is bigger than that betweenD-FFR-B and F-FFR-B. This is because the dynamic mech-anism in D-FFR-B benefits the cell edge significantly butnot the cell center; in fact, D-FFR-B performs worse than F-FFR-B in the cell center, as shown in Figure 11. This results

Fig. 10. Average cell throughput and service rate under different traffic loads: unequal cell-load scenarios.



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Fig. 11. Average cell-edge and cell-center throughput for FFR schemes under different traffic loads: unequal cell-load scenarios.

from the band-allocation structure of FFR-B, which, whileyields higher throughput in the cell edge, causes more inter-ference to the cell center due to band overlapping betweenone cell’s cell center and adjacent cells’ cell edge. Com-paring FFR-A and FFR-B, FFR-A yields lower cell-edgethroughput but higher cell-center throughput than FFR-B,as shown in Figure 11. This is similar to the equal-load case.

Note that in this unequal-load scenario, Reuse-1-ICICachieves the best throughput performance. This is becausethe scenario concerned has a fairly light overall load, aseach of the light-load cells has only two MSs. As a result,Reuse-1-ICIC can leverage its full flexibility in utilizingall the available band as well as performing ICI mitigationthrough a pure algorithmic approach without any constrainton the band allocation as exhibited in FFR-A and FFR-B.

More specifically, in the heavy-load condition in Figure 8,Reuse-1-ICIC trades its throughput for its service rate; herein Figure 10, due to the lighter load, the perfect service rateis achieved without much compromise in throughput. It isexpected, however, that a similar degradation in throughputwill be observed for Reuse-1-ICIC when the light-load cellsstart to increase their load in this unequal-load scenario.

Figure 12 shows the snapshot of channel-assignmentresults yielded by FFR-A for a specific topology and anunequal cell-load scenario with two cells of two MSs andone cell of 20 MSs. Each square node in the figure repre-sents an MS, and the color and the number shown on eachsquare indicate the band and the subchannel assigned to theMS. The colors shown here match those in Figure 2 (e.g.,a ‘dark-red 16’ node represents an MS in the cell edge of

Fig. 12. Snapshot of the FFR-A channel allocation for an unequal cell-load scenario (i.e., cell1 of 20 MSs, cell2 and cell3 of 2 MSs),where each square node represents an MS, and the color and the number shown on each square indicate the band and the subchannel

assigned to the MS.



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cell 1 that is assigned subchannel 16). MSs not served areuncolored and marked by ‘N.’ It is seen in Figure 12 thatD-FFR-A can serve much more MSs in the cell edge ascompared with F-FFR-A (in fact, no more than five cell-edge MSs can be served by F-FFR-A because |Oe

l | = 5).The reason is that D-FFR-A can borrow bandwidth fromadjacent light-load cells so that the cell-edge band of theheavy-load cell essentially expands. FFR-B presents simi-lar results when it comes to the comparison shown in Figure12. The snapshot confirms the superior performance of thedynamic scheme shown in Figure 10.

6. CONCLUSION

A D-FFR framework for multicell OFDMA networks wasproposed in this work. The dynamic feature is charac-terized by the capability of redistributing the spectralresource according to the varying cell load. The adapta-tion is accomplished via a graph approach in which theresource-allocation problem is translated to a graph coloringproblem. Different versions of FFR can be easily realizedin this framework by customizing the graph to match thespecific FFR principle. The proposed dynamic scheme isshown to yield better cell throughput and service rate per-formance, especially in unequal cell-load scenarios. Theproposed method is simple yet effective, and can be used innext-generation cellular systems such as LTE-A and IEEE802.16m.

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AUTHORS’ BIOGRAPHIES

Ronald Y. Chang received the B.S.degree in electrical engineering fromthe National Tsing Hua University,Hsinchu, Taiwan, in 2000, the M.S.degree in electronics engineering fromthe National Chiao Tung University,Hsinchu, in 2002, and the Ph.D. degreein electrical engineering from the Uni-versity of Southern California (USC),

Los Angeles, in 2008. From 2002 to 2003, he was with theIndustrial Technology Research Institute, Hsinchu. Since2004, he has conducted research with USC as well as withthe Mitsubishi Electric Research Laboratories, Cambridge,MA. Since 2010, he has been with the Research Centerfor Information Technology Innovation at Academia Sinica,Taipei, Taiwan. His research interests include resource allo-cation, MIMO detection, and cooperative spectrum sharingfor wireless communications and networking. He has pub-lished more than ten papers and is the holder of five awardedor pending U.S. patents. He is a recipient of the AcademiaSinica postdoctoral research fellowship.

Zhifeng Tao obtained his B.S. fromXian Jiaotong University, P.R. China.He received the M.S. and Ph.D.degrees in Electrical Engineering fromPolytechnic Institute of New York Uni-versity at Brooklyn, NY. He joinedMitsubishi Electric Research Labora-tories (MERL) in September 2006 andmost recently holds the position of

principal member of technical staff. His research interestsinclude electric vehicles network, smart grid, cooperativecommunications, resource allocation, interference manage-ment and wireless routing. He has published over 40 papers,filed over 60 US patents, written several book chaptersand made over 70 technical contributions to IEEE stan-dards. He has played a key role in the development ofsuch standards as IEEE 802.16j, IEEE P2030 (smart gridinteroperability guideline), and received IEEE StandardAssociation’s recognition for Outstanding Contribution tothe Development of IEEE Std 802.16j -- 2009 (Multihop

Relay) Specification. He is a co-editor of IEEE Communi-cations Magazine special issue on Green Communications,and EURASIP Journal on Advances in Signal Processingspecial issue on Cooperative MIMO Multicell Networks. Heis the founding chair of the 1st IEEE International Work-shop on Smart Grid Communications (affiliated with IEEEICC 2010), and a symposium chair of the 1st IEEE Interna-tional Conference on Smart Grid Communications. He hasserved as TPC chair of Frontier on Communications andNetworking Symposium of ChinaCom 2008, tutorial chairof ChinaCom 2009 and publication chair of InternationalConference on Ambient Media and Systems (Ambi-sys)2008. He has also been a TPC member for numerous confer-ences, including IEEE Globecom, ICC, VTC and PIMRC.He has delivered tutorials on next generation wireless sys-tem in IEEE Globecom and ICC, and served as a paneliston Green Communications Panel in ICC 2009. He is also aco-recipient of IEEE Globecom 2009 Best Paper Award.

Jinyun Zhang received her Ph.D.degree in electrical engineering fromUniversity of Ottawa, Canada in 1991.Dr. Zhang then joined Nortel Net-works, where she held various man-agement positions and engineeringpositions of increasing responsibilityin the areas of digital signal pro-cessing, wireless communication and

optical networks. Since 2001, Dr. Zhang has been theManager of the Digital Communications & Network-ing Group at Mitsubishi Electric Research Laboratories(MERL), Cambridge, MA, USA. She is a MERL Fellowand leading various new research projects on broadbandwireless communications, optical communications, smartgrid technologies and standardization activities. Dr. Zhanghas authored and co-authored more than 140 publica-tions, invented and co-invented more than 130 patentsand patent applications, and made numerous contribu-tions to international wireless communications standards.Dr. Zhang is a Fellow of the IEEE and a member ofthe IEEE BT, COMM, IT, ITS, Photonics, SP, and VTSocieites. She is an Associate Editor of IEEE Transactionson Broadcasting, an AdCom member of IEEE BroadcastingTechnology Society, and has served as a Technical Pro-gram Committee member for various IEEE internationalconferences.

C.-C. Jay Kuo received the B.S. degreefrom the National Taiwan University,Taipei, in 1980 and the M.S. andPh.D. degrees from the MassachusettsInstitute of Technology, Cambridge,in 1985 and 1987, respectively, all inElectrical Engineering. From October1987 to December 1988, he was Com-putational and Applied Mathematics

Research Assistant Professor in the Department of Mathe-matics at the University of California, Los Angeles. Since



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January 1989, he has been with the University of South-ern California (USC). He is presently Director of the Signaland Image Processing Institute (SIPI) and Professor of Elec-trical Engineering and Computer Science at the USC. Hisresearch interests are in the areas of digital image/videoanalysis and modeling, multimedia data compression, com-munication and networking, and biological signal/imageprocessing. Dr. Kuo has guided 105 students to their Ph.D.degrees and supervised 21 postdoctoral research fellows.He is co-author of about 185 journal papers, 800 confer-ence papers and 10 books. He delivered over 450 invitedlectures in conferences, research institutes, universities andcompanies. Dr. Kuo is a Fellow of IEEE and SPIE. Dr. Kuoreceived the National Science Foundation Young Investi-

gator Award (NYI) and Presidential Faculty Fellow (PFF)Award in 1992 and 1993, respectively. He received the bestpaper awards from the multimedia communication Tech-nical Committee of the IEEE Communication Society in2005, from the IEEE Vehicular Technology Fall Conference(VTC-Fall) in 2006, and from IEEE Conference on Intelli-gent Information Hiding and Multimedia Signal Processing(IIH-MSP) in 2006. He was an IEEE Signal ProcessingSociety Distinguished Lecturer in 2006, a recipient of theOkawa Foundation Research Award in 2007, the recipientof the Electronic Imaging Scientist of the Year Award in2010, and the holder of the 2010-2011 Fulbright-NokiaDistinguished Chair in Information and CommunicationsTechnologies.



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dynamic fractional frequency reuse (d-ffr) for multicell

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