Universität StuttgartINSTITUT FÜR

KOMMUNIKATIONSNETZEUND RECHNERSYSTEME

Prof. Dr.-Ing. Dr. h. c. mult. P. J. Kühn

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c©ACM, (2007). This is the author’s version of the work. It is posted here by permission of ACM for your personal use. Not forredistribution. The definitive version was published in Proc. ACM MSWiM, Chania, Crete Island, Greece (October 2007)

http://doi.acm.org/10.1145/1298126.1298178

Institute of Communication Networks and Computer EngineeringUniversity of Stuttgart

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Coordinated Fractional Frequency Reuse

Marc C. NeckerInstitute of Communication Networks and Computer Engineering

University of Stuttgart, Pfaffenwaldring 47, D-70569 Stuttgart, GermanyEmail: marc.necker@ikr.uni-stuttgart.de

ABSTRACTIn recent years, Orthogonal Frequency Division MultipleAccess (OFDMA) has become an attractive transmissiontechnology, which is part of various emerging system stan-dards for broadband cellular communications. Examples in-clude the 3GPP Long Term Evolution (LTE) and 802.16eWiMAX. In OFDMA, mobile terminals are multiplexed intime and frequency. A major problem in these systems is theinter-cell interference, which is caused by neighboring cellswhen transmitting on the same time and frequency slots.This problem can be solved by using beamforming anten-nas and coordinating the transmissions among base stations.This is known as interference coordination. In this paper,we present a distributed algorithm for interference coordina-tion, which enhances the cell edge performance with globalinformation provided by a central coordinator. The signal-ing delay during the communication with the central coor-dinator can be on the order of seconds, while an additionallocal interference coordination in each base station ensuresa high performance even in dynamic environments. Thiscombination of global and local coordination enhances theoverall spectral efficiency as well as the cell edge performancecompared to a Reuse 3 system.

Categories and Subject DescriptorsH.m [Information Systems]: Miscellaneous

General TermsAlgorithms, Performance

KeywordsWiMAX, 802.16e, interference coordination, FDM, TDM,OFDMA, Fractional Frequency Reuse, beamforming anten-nas

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1. INTRODUCTIONOrthogonal Frequency Division Multiple Access

(OFDMA) is the basis for several emerging standardsfor wireless broadband communication. In particular,it is the underlying transmission technology for 802.16e(WiMAX) and the future 3GPP Long Term Evolution(LTE). In OFDMA, the different users are multiplexed intime and frequency based on an underlying OFDM system.Therefore, OFDMA is basically a combination of Frequencyand Time Division Multiple Access (FDMA and TDMA). Amajor problem in these systems is the inter-cell interference,which is caused by neighboring cells when transmitting inthe same frequency/time slots. This eventually leads tosevere performance degradation or even connection loss.

There exist several approaches to mitigate inter-cell in-terference. The most common approach is to employ a fre-quency reuse pattern and avoid the usage of the same fre-quency bands in adjacent cells. The disadvantage of thisscheme is the waste of precious frequency resources. In-stead, it is desirable to reuse the whole available frequencyspectrum in every cell. Another possibility to lower inter-cell interference is to use beamforming antennas, which di-rect their transmission power towards the currently servedmobile terminal. This minimizes interference towards othermobile terminals. Last but not least, the transmissions indifferent cells can be coordinated to optimize the interferencesituation in all cells. This is referred to as interference coor-dination (IFCO). All these approaches can be combined tooptimize the system performance in a dynamic fashion [13].

In [11] we introduced an interference coordination algo-rithm which is based on an interference graph. This graphrepresents critical interference relations among mobile termi-nals. If two mobile terminals in different cells have a criticalrelation, they may not be served on the same frequency/timeresource. This scheme requires a central omniscient entitywhich is capable to acquire the system state instantly andperform scheduling decisions in all cells on a per-frame basis.Naturally, such a scheme is not implementable. However, itprovides important information about the key performanceparameters and also delivers an estimate of the upper per-formance bound.

In [13], we limited this interference graph based schemeto the coordination of the cell sectors served by the samebase station. This was combined with Fractional FrequencyReuse (FFR), which applies a frequency reuse of 1 in the in-ner portions of the cell and a frequency reuse of 3 in the outerportions. This combination can achieve the same aggregate

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cell throughput as the global scheme from [11], but it fallsshort with respect to the throughput at the cell borders.

This paper has two main contributions. First, we con-siderably enhance the global scheme of [11] by an optimizedgeneration of the interference graph. Second, based on theseoptimizations, we present a novel interference coordinationscheme named Coordinated Fractional Frequency Reuse,which achieves a high aggregate and cell border performanceat the same time. This scheme does not require an om-niscient device which performs scheduling decisions everyframe. Instead, it relies on the communication of the basestations with a central entity on a much longer time scale,e.g., on the order of seconds. Therefore, the proposed schemeis well implementable in a real system.

This paper is structured as follows. Section 2 introducesthe considered 802.16e system and its simulation model.Section 3 rehearses the global scheme from [11] and presentsan optimized generation of the interference graph. Subse-quently, section 4 briefly introduces the concept of FFR andderives the proposed coordinated FFR scheme. Finally, sec-tion 5 presents a thorough performance evaluation of thecoordinated FFR scheme, and section 6 concludes the pa-per.

2. SYSTEM MODEL

2.1 Overview of transmission systemWe consider an 802.16e-system [10] with a total available

system bandwidth of 10 MHz and a MAC-frame-length of5 ms. This results in a total number of 49 OFDM-symbolsper MAC-frame and 768 data subcarriers per OFDM-symbol.Each MAC-frame is subdivided into an uplink and a down-link subframe. Both subframes are further divided intozones, allowing for different operational modes. In this pa-per, we focus on the Adaptive Modulation and Coding(AMC) zone in the downlink subframe. In particular, weconsider the AMC 2x3 mode, which defines subchannels of16 data subcarriers by 3 OFDM-symbols. This is illustratedin the left part of Fig. 1. A subchannel corresponds to the re-source assignment granularity for a particular mobile termi-nal. The AMC zone can therefore be abstracted by the two-dimensional resource field shown in the right part of Fig. 1.

We assume the AMC zone to consist of 9 OFDM-symbols,corresponding to a total number of 48 · 3 available subchan-

nels. Adaptive Modulation and Coding was applied rangingfrom QPSK 1/2 up to 64QAM 3/4. This results in a the-oretical maximum data rate of about 6.2 Mbps within theAMC zone. The burst profile management is based on theexponential average of the terminal’s SINR conditions withchannel feedback delay of one MAC-frame.

2.2 Simulation model and metricsWe consider a hexagonal cell layout comprising 19 base

stations at a distance of dBS = 1400 m with 120◦ cell sec-tors as shown in Fig. 2. The scenario is simulated withwrap-around, making all cells equal with no distinct centercell. All cells were assumed to be synchronized on a framelevel. Throughout our paper, we evaluate the shaded ob-servation area when investigating the cell coverage, and theaverage of all cell sectors when considering throughput met-rics. Besides the total sector throughput, we evaluate the5% throughput quantile, which is a good indication for theachievable throughput in the cell border areas [3]. It is cap-tured by measuring the average short-term throughput ofeach terminal within 4-second periods and calculating thequantile over all measurements. All throughput measureswere taken on the IP-layer, capturing all overhead causedby fragmentation, padding, and retransmissions.

Every base station has 3 transceivers, each serving onecell sector. The transceivers are equipped with linear arraybeamforming antennas with 4 elements and gain patternsaccording to [11]. They can be steered towards each termi-nal with an accuracy of 1◦ degree, and all terminals can betracked ideally.

2.3 Scenario and simulation parametersThe system model was implemented as a frame-level sim-

ulator using the event-driven simulation library IKR Sim-Lib [1] with all relevant MAC protocols, such as ARQ andHARQ with chase combining. The path loss was modeledaccording to [8], terrain category B. Slow fading was con-sidered using a log-normal shadowing model with a stan-dard deviation of 8 dB. Frame errors were modeled basedon BLER-curves obtained from physical layer simulations.

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Figure 4: Mean vertex degree of a mobile terminal in the interference graph. Left: two-tier coordination,DS = 10 dB. Middle: two-tier coordination, DS = 0 dB. Right: zero-tier coordination, DS = 20 dB. Note thedifferent scales.

Each sector contains N mobile terminals moving at a ve-locity of v = 30 km/h. The underlying mobility model isa random direction model with a mean free path length of50 m and a maximum turning angle of 25◦. All mobile ter-minals are bound to their respective cell sector in order toavoid handovers. A greedy traffic source is transmitting datatowards each terminal, i.e., there is always data available tobe transmitted for a terminal (see also [11]).

3. INTERFERENCE GRAPH BASEDINTERFERENCE COORDINATION

3.1 Basic ConceptIn [11], a scheme for global interference coordination in

a cellular OFDMA network was proposed. It is based onan interference graph whose nodes represent the mobile ter-minals, and whose edges represent critical interference re-lations in-between the terminals. Terminals which are con-

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nected must not be served using the same set of resources.For each terminal, the interference from base stations withina certain diameter dic of the serving base station is calcu-lated. Afterwards, the largest interferers are blocked fromusing the same set of resources by establishing a relation inthe interference graph. This is done such that a desired min-imum SIR DS is achieved for each terminal. For a detaileddescription, please refer to [11].

The original scheme in [11] assumed a central omniscientdevice which is capable of acquiring the system state in-stantly and perform scheduling decisions on a per-frame ba-sis. Naturally, such a scheme is not implementable. How-ever, it provides important information about the key per-formance parameters and also delivers an estimate of theupper performance bound.

3.2 PerformanceThe two major configurable parameters of the interfer-

ence graph based scheme are the desired minimum SIR DS

and the coordination diameter dic. We refer to dic = 0 aszero-tier coordination, indicating a coordination only amongsectors of the same base station. Alike, a one-tier coordina-tion means a coordination of neighboring base station sites,i.e., dic = dBS, and a two-tier coordination implies a globalcoordination of all cells in our scenario.

Figure 3 plots the 5% throughput quantile over the aggre-gate throughput per cell [13]. The zero-tier coordination,which can be implemented locally within a base station,achieves a significant improvement compared to the Reuse 3scenario with respect to the overall cell sector throughput,but falls short with respect to the throughput quantile, i.e.,with respect to the cell edge performance. As the number ofcoordinated tiers increases, the performance with respect toboth the aggregate throughput and the throughput quantileincreases.

3.3 Relation to graph coloring problemGlobal interference coordination based on the interference

graph is directly related to the graph coloring problem [12].In the graph coloring problem, each node in a graph needsto be assigned one color such that no connected nodes areassigned the same color. If the colors correspond to non-overlapping resources on the air interface, then the solution

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of the graph coloring problem corresponds to the assignmentof disjoint resources on the air interface to nodes which havea relation in the interference graph. In general, the graphcoloring has to be recomputed whenever the interferencegraph changes, i.e., every frame.

Let M be the chromatic number of the interference graph,i.e., M is the number of colors which are required to solve thegraph coloring problem. Then, for each scheduling round,the air interface resources need to be divided into M disjointpartitions. Each of these partitions is then assigned to amobile terminal based on its assigned color. Note that asolution of the problem requires at least N colors, whereN is the number of mobile terminals in each cell sector.In general, M will be larger than N , making more disjointresource partitions necessary than there are mobile terminalsto serve. Consequently, the resource utilization in a cellsector will drop and in general be ρ = N/M < 1.

Graph coloring is an NP-hard problem. Various heuristicshave been proposed to find near-optimal solutions. In thispaper, we use the heuristic Dsatur [7] and a Tabu searchtechnique [9] to obtain colorings. While Dsatur is quite fast,Tabu search obtains much better solutions, though at thecost of a highly increased computational complexity.

In contrast to these heuristics for the classical coloringproblem, the resource assignment heuristic from [11], whichwas also used to generate the results of section 3.2, solvesa variant of the graph coloring problem. It differs from thejust described original graph coloring problem in that only acertain number NF < N of mobile terminals is served withineach scheduling round. In other words, only NF colors areused, and only NF mobile terminals need to be assigned acolor. This leads to a much better resource utilization ρ ascompared to when using a full coloring as described in thissection, and consequently to a better system performance.

In both cases, the resource utilization ρ depends on thestructure of the interference graph. In particular, it dependson the vertex degree of all nodes. For the full coloringas described above, a higher vertex degree will lead to alarger chromatic number M and a lower resource utilization

ρ. Likewise, the performance of the coloring heuristic from[11] will suffer from a larger vertex degree. The most im-portant parameters having an impact on the vertex degreeare the coordination diameter dic and the minimum desiredSIR DS . If dic or DS are increased, the vertex degree andhence the chromatic number M increases, leading to a lowerresource utilization ρ. This is illustrated in Fig. 4, whichplots the mean vertex degree of a node in the interferencegraph depending on the position of the corresponding mo-bile terminal. The figure illustrates the increase in the vertexdegree for an increase of dic or DS .

In the following section, we will evaluate ways to constructthe interference graph in such a way that the vertex degreeand hence M is reduced, eventually leading to a better re-source utilization.

3.4 Performance OptimizationThe results from [13], which were rehearsed in the previ-

ous sections, show that a one-tier or two-tier coordinationwith a fairly low desired SIR DS achieves an excellent celledge performance while falling short with respect to the ag-gregate throughput. On the other hand, a zero-tier coor-dination provides an increased aggregate performance whilefalling short with respect to the throughput quantile. Bothconfigurations feature an interference graph with a relativelysmall vertex degree compared to the optimum case of a two-tier coordination with DS = 10 dB, as can be seen fromFig. 4. This suggests that a separate generation of zero-tier and one/two-tier interference graphs and a subsequentmerging of both graphs will lead to a lower vertex degree asin the two-tier case while providing an optimized SIR withinthe area. As discussed before, a lower vertex degree will leadto a lower chromatic number of the interference graph andhence potentially increase the system performance. Merg-ing of the two graphs is done simply by including an edge inthe merged graph whenever one of the two original graphscontains an edge.

The performance of a system with a global coordinationbased on the combination of interference graphs is plotted in

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Figure 7: Throughput in kBit/s depending on po-sition for optimized global zero-tier/two-tier co-ordination with DS,o = 10 dB and DS,i = 20 dB.

Fig. 5 for a combination of a zero-tier interference graph witha one-tier (left) and a two-tier (right) interference graph. Wedenote the zero-tier graph as inner graph, which is generatedfor a desired minimum SIR DS,i, and the one/two-tier graphas outer graph, generated for a desired minimum SIR DS,o.

Figure 5 shows a strong dependence of the system per-formance on DS,o. As we increase DS,o from −5 dB inthe one-tier case, we first observe a performance increaseat DS,o = 0 dB, while it decreases for DS,o = 5 dB. ForDS,o = 10 dB the performance significantly improves again,and finally decreases for DS,o = 15 dB and larger values.The two separate maxima can be explained by the super-position of the curves in Fig. 3, which show maxima fordifferent values of DS . This superposition is caused by themerging of the interference graphs.

The combination of zero-tier and one-tier interferencegraphs (Fig. 5 left) has two optimal configurations. ForDS,o = 0 dB, the cell border performance is maximized,while for DS,o = 10 dB the aggregate throughput is maxi-mized. In contrast, the combination of zero-tier and two-tierinterference graphs (Fig. 5 right) shows an optimal operatingpoint for DS,o = 10 dB which maximizes both the aggregatethroughput and the cell border performance. This raisesthe spectral efficiency of the global scheme by more thanone third to over 1.1 Bit/Hz and can be explained with thebetter control of the two-tier scheme over the interference inthe cell border areas.

Figure 6 plots the throughput depending on the mobileterminal’s position for the global two-tier coordination ac-cording to section 3.1 and [11]. Figure 7 plots the same met-ric for the optimized coordination mechanism with combinedzero-tier and two-tier coordination. We can observe an in-creased throughput at the cell borders but also a substantialperformance increase in the central parts of the cell sectors.

4. COORDINATEDFRACTIONAL FREQUENCY REUSE

In this section, we first give an overview over state-of-the-art fractional frequency reuse techniques. Subsequently, weintroduce the concept of Coordinated Fractional FrequencyReuse.

4.1 Classical Fractional Frequency ReuseA system with a frequency reuse factor of 1 achieves a

high resource utilization of 100%, while suffering from heavyinter-cell interference in the cell border areas. On the otherhand, a frequency reuse 3 system achieves acceptable inter-ference conditions at the cell border, but has a resource uti-lization of only 1/3. One possibility to resolve this dilemmais Fractional Frequency Reuse (FFR). With FFR, a fre-quency reuse of one is applied in areas close to the basestation, and a higher reuse factor in areas closer to thecell border. This idea was proposed for GSM networks (seefor example [6]) and has consequently been adopted in theWiMAX forum [2], but also in the course of the 3GPP LongTerm Evolution (LTE) standardization, e.g., in [5] and [4].

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Figure 8: Schematic illustration of FFR with thesame (top) and disjoint (bottom) resources for reuse1 and reuse 3 areas.

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Figure 8 schematically illustrates the division of air in-terface resources. Basically, there exist two options. [14]proposed that the reuse 1 and reuse 3 areas be on disjointfrequency bands (Fig. 8 bottom), while [5] and [4] use thefull set of available resources in the reuse 1 areas and onethird of the same resources in the reuse 3 areas (Fig. 8 top).In the remainder of this paper, we will base our work on thelatter option. We will refer to mobile terminals in the reuse1 area as reuse 1 terminals, and to mobile terminals in thereuse 3 area as reuse 3 terminals.

[14] proposes to combine FFR with a coordination of thetransmissions among the sectors of one base station site.This lowers the interference between sectors belonging to thesame base station. However, it is not possible to lower theinterference caused by other base stations, which is why sucha system still suffers from a rather low throughput at the cellborder to neighboring base stations (see [13] for an exten-sive performance evaluation). In the following section, wewill develop an IFCO scheme which overcomes this problem,and which eventually could be implemented under realisticsignaling delays.

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Figure 9: Illustration of system concept with centralcoordinator

4.2 Coordinated Fractional Frequency ReuseWhile the aggregate throughput in an FFR system can

be increased by performing an additional local interferencecoordination among the sectors served by one base station(zero-tier coordination), the interference from other basestations cannot be controlled. Coordinated Fractional Fre-quency Reuse overcomes this drawback by introducing a gen-eralized frequency reuse pattern for mobile terminals at thecell border which is coordinated by a central entity. Thisconcept is illustrated in Fig. 9.

Every cell communicates all data which is necessary togenerate an interference graph as described in section 3 tothe central FFR coordinator. This includes measured inter-ference and pathloss components for all mobile terminals.The coordinator then performs a complete graph coloringas detailed in section 3.3. The result of the coloring processis a color index for every mobile terminal, which is trans-mitted back to the base stations. If NC is the number ofcolors in the coloring (where NC ≤ M in general due to thesub-optimality of the graph coloring heuristics), the AMC-zone of a MAC frame is then divided into NC parts, eachcorresponding to a reuse partition. This is illustrated inFig. 10 on the right side. The Reuse 3 terminals at thecell border are then assigned to a partition depending ontheir color, while Reuse 1 terminals in the inner cell areascan still utilize the full AMC-zone. Alternatively, in orderto avoid a fragmentation of the AMC-zone into very smallpartitions, the reuse partitions can be spread over severalMAC-frames, as it is illustrated in Fig. 11 on the right side.In the following, the number of AMC-zones (i.e., the numberof MAC-frames) which are required will be called a virtualframe duration. In our example of Fig. 11, the AMC-zoneof a single frame is divided into NF = 4 partitions, and thevirtual frame duration is ⌈NC/NF ⌉ = ⌈NC/4⌉.

In order for this scheme to be practical, the communica-tion with the FFR coordinator needs to be limited. Fig-ure 12 shows a signaling-time diagram of the communica-tion with the FFR coordinator. The base stations reportthe data which is required to build the interference graphwith an update period of TC,period. After a certain delayTC,delay, the coloring of the FFR coordinator arrives at thebase stations and is then valid until the arrival of the nextcoloring. The delay TC,delay includes all signaling delays,

the processing delay in the FFR coordinator, and also allnecessary synchronization delays.

Coordinated FFR ensures a coordinated allocation of re-sources to Reuse 3 terminals, i.e., to mobile terminals atthe cell border. This global coordination is done on a largertime-scale due to the signaling delays described above. Inorder to make the system more agile, we perform an addi-tional local coordination in every base station (zero-tier co-ordination), which coordinates the transmission of all Reuse1 terminals. This local coordination can operate on up-to-date system state information of all cell sectors served bythe respective base station.

The procedure is summarized as follows. First, all Reuse3 terminals are reserved resources in their respective reusepartition (cmp. Fig. 11). Second, in every frame, the reg-ular zero-tier coordination scheme is applied in every basestation, obeying all conflicts in the inner interference graph.This is repeated periodically. Note that the scheduling andresource assignment is still done on a per-frame basis. Ifa Reuse 3 terminal does not need to be scheduled in itsreserved reuse partition, the idle resources can be used byReuse 1 terminals if allowed by the local interference coor-dination. This allows for a high resource utilization whileat the same time ensuring good interference conditions formobile terminals at the cell border.

4.3 Degrees of freedomThe described coordinated fractional frequency reuse has

several degrees of freedom. Besides the desired SIR DS,o andDS,i and the coordination diameter dic for the outer graph,the SINR-thresholds thup and thlow for the assignment of

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mobile terminals to Reuse 1 or Reuse 3 areas in the FFRscheme are configurable parameters (see [13]). Moreover, itis possible to perform the graph coloring based on the com-bined inner and outer graphs, or purely on the outer graph(i.e., based on a classical one/two-tier graph as describedin [11]), while the local interference coordination is alwaysbased on the locally generated zero-tier graph.

5. PERFORMANCE EVALUATIONThis section evaluates the performance of the proposed

Coordinated FFR. Section 5.1 first investigates the perfor-mance of Coordinated FFR under ideal signaling conditions.Next, section 5.2 assesses the performance with realistic sig-naling delays. Finally, section 5.3 shows the impact of themobility scenario, and section 5.4 demonstrates the impactof the graph coloring heuristic.

5.1 Performance under ideal signalingconditions

In this section, we will first evaluate the performance ofCoordinated FFR under ideal signaling conditions, i.e.,TC,delay = 0, and TC,period is equal to the virtual frame du-ration. Figure 13 plots the 5% throughput quantile over theaggregate throughput for different values of DS,o and DS,i

for a coloring based on the combined inner and outer graphs.thup and thlow were set to 25dB and 15dB, respectively. Theleft chart shows the performance if the outer coordinationby the FFR coordinator is based on a one-tier coordination,whereas the right chart shows the results with an outer two-tier coordination. The coloring heuristic applied in the FFRcoordinator was Dsatur [7].

In general, the performance with a one-tier coordinationis slightly better when it comes to the throughput quan-tile, and the two-tier coordination is slightly better when itcomes to the aggregate throughput. When comparing theseresults to a system with global coordination as described insection 3, the performance is significantly worse. However,we should mention once more that a globally coordinatedsystem is not implementable and only serves as a perfor-mance reference. We therefore have to compare the perfor-mance of Coordinated FFR to the Reuse 3 system and to asystem with classical FFR, which are both state-of-the-art.For DS,o = 0 dB and DS,i = 20 dB, the cell border perfor-mance of Coordinated FFR is comparable to the cell borderperformance of the Reuse 3 system, and significantly betterthan the cell border performance of the system with classi-cal FFR. With respect to the aggregate throughput, we canachieve an improvement of about 45—55% over the Reuse 3system at the same cell border performance.

To look deeper into the difference between coordinatedFFR with outer one-tier and outer two-tier coordination,Fig. 14 plots the average number of colors NC over DS,o

for both cases. In accordance with section 3.4, the num-ber of required colors NC increases as the coordination di-ameter increases. This leads to an increase of the virtualframe duration. As Reuse 3 terminals are served only oncein every virtual frame, the throughput for these terminalsdecreases significantly as DS,o and hence NC increases. Onthe other hand, this effect yields more available resourcesfor the Reuse 1 terminals, which accounts for the higheraggregate throughput in the two-tier case.

Figure 15 shows a scatter plot of the system performancefor different choices in the various degrees of freedom. It

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Figure 13: 5% throughput quantile over aggregate sector throughput for differnt values of DS,o and DS,i ={15; 20; 25} dB. Coordinated FFR with ideal signaling conditions. Left: one-tier centrally coordinated by FFRCoordinator, Right: two-tier centrally coordinated by FFR Coordinator.

becomes obvious that the aggregate throughput and the celledge throughput can be traded off against each other withthe appropriate parameter choice. In the following, we willlimit our further studies to the parameter set which wasalready used in the previous paragraphs, which maximizesthe aggregate throughput for dic = 1 while keeping the celledge throughput at the same level as in the Reuse 3 system.

5.2 Impact of signaling delay andupdate period

This section considers the impact of the signaling delayand the update period on the system performance. Fig-ure 16 plots the aggregate sector throughput (left) and the5% throughput quantile (right) for different update periodsTC,period and signaling delays TC,delay.

In general, the impact of TC,period and TC,delay influencesthe throughput quantile much more than it does the ag-gregate throughput. This is expected, since the coloringinformation is used to coordinate mobiles at the cell bor-der, while the aggregate performance is dominated by thelocal zero-tier coordination, which is not degraded by anysignaling delays.

An increase of the delay TC,delay leads to a worse per-formance compared to an identical increase of the updateperiod TC,period, in particular for the throughput quantile.This is logical, since an increase of the update period impliesoutdated coloring information only for the later time pointsof the update period, while an increase of the signaling delayleads to outdated coloring information all the time.

In general, the throughput quantile and the aggregatethroughput continuously decrease as TC,delay and TC,period

increase to large values. However, for relatively small val-ues of TC,period around 500 to 1000 ms, we note a slightincrease in the aggregate throughput and the throughputquantile. This slight increase is a side effect, which resultsfrom the burst profile management. As described in section2.1, the burst profile management is based on the exponen-tial average of the terminal’s SINR conditions with channel

feedback delay of one MAC-frame. If TC,period = 0 ms, themobile terminals will be assigned new colors in every virtualframe. In contrast, if TC,period > 0 ms, new colors will beassigned less frequently, which means that mobile terminalsare served in the same resource partition for a number of vir-tual frames. This leads to more stable SINR conditions anda better SINR estimation, and consequently to a better se-lection of the appropriate burst profile. As TC,period > 0 msincreases further, the effect of obsolete color information be-comes dominant and the performance decreases.

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Figure 16: Aggregate sector throughput (left) and 5% throughput quantile (right) over update period TC,period

for different delays TC,delay. One-tier centrally coordinated, of DS,o = 0 dB, DS,i = 20 dB.

Figure 17 plots the throughput depending on the termi-nal position. Shown is the result for TC,delay = 1000 ms,TC,period = 2000 ms, and for a combined zero-tier/one-tiercoordination with DS,o = 0 dB and DS,i = 20 dB. Comparedto Fig. 6 and 7, it shows a less distinct throughput increasein the cell center areas, which is typical for FFR systems[13]. The graph also shows a smooth and rather symmetricdegradation of the system performance from the cell centerto the cell edge, with large well-to-medium covered areas.

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Figure 15: Scatter plot for the performance achievedby various combinations of DS,i, DS,o, thup, thlow, anddic. Shown are the results for a graph coloring basedon purely the outer graph, and based on a combinedinner and outer graph. Error bars are omitted forclarity.

5.3 Impact of terminal mobilityAll results presented so far have been obtained in a high

mobility scenario with mobile terminals moving at a speed ofv = 30 km/h. When mobile terminals move at high speeds,the coloring information provided by the FFR coordinatorbecomes outdated relatively quickly. Hence, the signalingdelay TC,delay and the update period TC,period have a bigimpact on system performance.

A major use case for 802.16e are slowly moving terminals,for example carried by pedestrians, or nomadic terminal us-age, where users are stationary and occasionally relocate toa new position. For these scenarios it is directly obviousthat the information provided by the FFR coordinator willbecome obsolete much slower. Therefore, the performanceof the system will be much less sensitive to larger values ofTC,delay and TC,period.

5.4 Impact of graph coloring heuristicIn the previous sections, the coloring heuristic Dsatur [7]

was applied. It is known that more sophisticated heuristicslike Tabu search [9] deliver results where the number of re-quired colors NC is much closer to the chromatic numberM of the graph. For our scenario, the coloring heuristic hasonly a minor impact. For the case of TC,delay = 1000 msand TC,period = 2000 ms, the throughput performance withTabu search is only slightly better than the performancewith Dsatur. In particular, the 5% throughput quantile re-mains almost unchanged, while the aggregate performanceincreases by about 1%. The average number of colors NC

decreases from 15.8 to 14.7, which means that the averagevirtual frame duration remains identical at ⌈NC/4⌉ = 4.Since Reuse 3 terminals are served only once every virtualframe duration, this points out why the throughput quantiledoes not increase.

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6. CONCLUSIONIn this paper, we have first presented an optimized al-

gorithm for global interference coordination in a cellularOFDMA network. Even though such an approach is notimplementable since it requires almost instant communica-tion among base stations, it delivers important performancevalues which can serve as an estimate for an upper per-formance bound of an interference coordinated system. Inour example, the 802.16e system achieves an overall spectralefficiency of more than 1.1 Bit/Hz/s while maintaining anexcellent cell edge throughput which is twice as large as ina classical Reuse 3 system with beamforming antennas.

In the second part of this paper, we proposed the conceptof Coordinated Fractional Frequency Reuse, which bases theresource assignment in the outer areas of the cell on informa-tion from a central FFR coordinator. This scheme does notrequire a global omniscient device and can be implementedin a distributed way. The communication with the centralcoordinator can take place with realistic signaling delays onthe order of seconds, while still maintaining a competitivesystem performance even in scenarios with a high terminalmobility. In particular, the cell edge performance of a clas-sical system with Fractional Frequency Reuse can greatlybe improved to match or exceed the cell edge performanceof a Reuse 3 system. At the same time, the spectral ef-ficiency reaches more than 0.72 Bits/hz/s, which is a 50%improvement over the Reuse 3 system. Finally, we arguedthat the system performance will be even better when mov-ing to more static scenarios, since signaling delays will haveless impact.

7. ACKNOWLEDGMENTSThis research was done in cooperation with Alcatel-Lucent

Research and Innovation Department, Stuttgart.1

1Alcatel-Lucent Deutschland AG, Research & Innovation,Holderackerstr. 35, 70435 Stuttgart, Germany. Con-tact: Michael Tangemann (Michael.Tangemann@alcatel-lucent.de).

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