Fractional Frequency Reuse in Optical Wireless CellularNetworks

Cheng Chen∗, Nikola Serafimovski∗ and Harald Haas∗∗Institute for Digital Communications Joint Research Institute for Signal and Image Processing

The University of Edinburgh EH9 3JL, Edinburgh, UK{cheng.chen, n.serafimovski, h.haas}@ed.ac.uk

Abstract—Interference coordination in optical wireless cellularnetworks using different frequency reuse techniques are discussedand compared in this paper. On the one hand, full frequencyreuse maximises the system throughput at the cost of poor cell-edge user performance. On the other hand, cluster-based staticresource partitioning offers good cell-edge user performanceat the cost of low system throughput. Fractional frequencyreuse (FFR) is introduced as a compromise between cell-edgeuser performance and the system throughput with low systemcomplexity. Simulation results show that a guaranteed userthroughput of 5.6 Mbps and an average area spectral efficiency(ASE) of 0.3389 bps/Hz/m2 are achieved by the FFR opticalwireless system with appropriate power control factors. Theseresults show considerable throughput improvement compared toboth benchmark systems. It is also shown that by adjusting theLED transmission optical power of a system using visible lightspectrum, the illumination requirement for an office room canbe satisfied without extra lighting facilities.

Index Terms—optical wireless communications, fractional fre-quency reuse, co-channel interference and orthogonal frequencydivision multiple access.

I. INTRODUCTION

Recent work has shown many advantages of optical wireless(OW) technology [1]. These advantages make OW a suitablecandidate for improving the performance of heterogeneousnetworks. OW uses visible light or infrared light which areunregulated. Furthermore, inexpensive incoherent light emit-ting diodes (LED) and photo diodes (PD) can be applied at thetransceiver, which lower the cost of the OW systems. In par-ticular, OW system can be used in safety critical environmentswhere radio frequency (RF) transmissions are restricted. In ad-dition, optical signals cannot penetrate opaque objects, whichmeans that the optical signal is confined to a single room or aspecific area. This makes OW particularly suitable for securitycritical applications. In addition to security, this mitigates theinterference to adjacent rooms. In the multi-user OW system,optical orthogonal frequency division multiplexing (O-OFDM)based on optical intensity modulation (IM) and direct detection(DD) can be used to realise an orthogonal frequency divisionmultiple access (OFDMA) cellular network [2].The limited bandwidth of the IM/DD systems makes it

essential to reuse the finite available bandwidth to meetthe high throughput requirements. However, full frequencyreuse and ubiquitous system coverage result in co-channelinterference (CCI) between users in adjacent cells. Therefore,cellular interference coordination must be considered. Several

interference coordination techniques have been investigated inthe literature. On the one hand, the simplest method is toapply traditional cluster-based resource partitioning [3]. Thistechnique assigns different sub-bands to neighbouring cells toavoid CCI. However, this technique significantly reduces theavailable bandwidth in each cell and restricts the achievablepeak data rates in the cell [4]. On the other hand, a self-organising interference mitigation technique is proposed in [5].It uses busy burst (BB) signalling and channel reciprocity ofthe time division duplex (TDD) technique to define a dynamicinterference aware resource allocation solution for interfer-ence coordination. However, its dynamic decision relies onchannel information feedback, which increases the overheadof the transmission. A method that strikes a reasonable trade-off between the overall spectral efficiency and the cell-edgeuser throughput is fractional frequency reuse (FFR) [6]. Itpartitions the available bandwidth for the cell-edge users toavoid CCI and uses the full system bandwidth for the cellcentre users in an attempt to maximise the system throughput.Once the system is established, users can simply choosetheir transmission modes by comparing the received signalto interference plus noise ratio (SINR) with a pre-determinedthreshold. The system employing the BB protocol requiresextra mini time slots to feedback the channel information. Incontrast, FFR system exploits regular feedback to transmit themode decision. Therefore, FFR has the potential to achieveeffective interference coordination with low complexity andbetter quality of service for the cell-edge users, thereby makingit a fairer system than full frequency reuse system.

To the best of our knowledge, this paper introduces FFR asan interference coordination technique in an optical cellularnetwork for the first time. The corresponding simulationsdemonstrate that FFR effectively improves the cell-edge userthroughput and the overall system throughput, relative to thesystems applying full frequency reuse and standard cluster-based resource partitioning schemes.

The remainder of the paper is organised as follows. Sec-tion II introduces the system model including LED arraydeployment, transmission model and metrics. Section III in-troduces the FFR applied to the OW system. Simulationresults and discussions are presented in Section IV. Finally,we conclude the paper in Section V.

2013 IEEE 24th International Symposium on Personal, Indoor and Mobile Radio Communications: Special Sessions

978-1-4577-1348-4/13/$31.00 ©2013 IEEE 3594

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Fig. 1. The inlay figure at the left top corner illustrates the arrangement ofthe LED array. The main figure illustrates the coverage arrangement in a cell.Each LED cluster in the LED array covers a different region of a cell.

II. SYSTEM MODEL

A. LED array deployment

Multiple LED arrays are used as APs serving the usersunderneath them. They are distributed on the ceiling usingthe hexagonal grid model to form a cellular network. AnLED array is composed of multiple LEDs with different beamdirections. Accordingly, the coverage area in the room isdivided into multiple cells. Each cell is divided into multiplesub-cells to enable the discrete cell region division that will bediscussed in Section III. In addition, several low power LEDsare integrated with the same beam direction to form a higherpower LED cluster to guarantee enough signal strength. AnLED cluster provides coverage for a single sub-cell. The spa-tial alignment of all the beams of the LED clusters establishesthe cell coverage. Furthermore, the half-power angle shouldbe small (typically 10◦) to confine most of the signal powerwithin each sub-cell [7]. An example LED array deploymentand the sub-cell coverage arrangement are illustrated in Fig. 1.There are several advantages that result from using this

LED array deployment: 1) a small half-power angle resultsin less CCI, 2) the received optical power distribution in thecell is relatively uniform compared to an AP composed of asingle LED with wide half-power angle, 3) the deployment ofmultiple sub-cells leads to a more accurate approximation ofthe hexagonal cell shape.

B. Optical channel DC gain

The free space channel model between a transmitter at theAP side and a receiver at the user side is introduced. Since thesignal at the receiver is dominated by the line-of-sight (LOS)component, only the LOS path is considered while any multi-path effects are disregarded. The optical channel DC gain fromthe transmitter to the receiver is given by [7]

G =(m+ 1)A

2πd2cosm(φ)Ts(ψ)gc(ψ) cos(ψ), (1)

Fig. 2. Deployment of fractional frequency reuse in an optical wirelesssystem.

where m denotes the Lambertian emission order which isgiven by m = − ln(2)/ ln(cos(Φ1/2)), where Φ1/2 is the half-power angle of the LED; A is the area of the PD; d is thedistance between the transmitter and receiver; φ is the radiantangle; ψ is the incident angle; Ts(ψ) is the optical filter gainand gc(ψ) is the concentrator gain which is given by

gc(ψ) =

{n2

sin2 Ψc

0 ≤ ψ ≤ Ψc,

0 ψ > Ψc,(2)

where Ψc is the concentrator FOV and n denotes the internalrefractive index.

C. Metrics

The OFDMA system is assumed to experience a flat-fadingchannel. This is valid for intensity modulated OW systemswhich do not suffer from fading effects as the informationcarrying signal is encoded in the intensity of the signal asopposed to the in-phase and quadrature electric fields inRF systems. The received SINR on each sub-carrier can beexpressed as [5]

γu =

( ∑i∈L(n)

RpdGn,i,uPn,i,u

)2

Foe

∑n̂�=n

( ∑i∈I(n̂)

RpdGn̂,i,uPn̂,i,u

)2

Foe + σ2

, (3)

where Rpd is the PD responsitivity; Pn,i,u is the LED opticaltransmission power per sub-carrier from LED cluster i of LEDarray n to the user u; Gn,i,u is the channel DC gain from LEDcluster i of LED array n to the user u; Foe denotes the opticalto electrical conversion factor; L(n) is the set containing theLED clusters contributing to the desired signal of LED arrayn; I(n) is the set of the LED clusters contributing to theinterfering signal in LED array n and σ2 denotes the powerof the noise which is dominated by ambient light shot noise.Modulation schemes are not considered in this paper. Instead,we use the Shannon capacity formula to establish an upper

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Fig. 3. The cellular network arrangement in the simulated room.

bound on the downlink capacity. The achievable data rate persub-carrier is given by

Rsc = Bsc log2(1 + γ), (4)

where Bsc denotes the bandwidth of a sub-carrier. The consid-ered data rate metrics are the user throughput and the systemthroughput that refers to the aggregate throughput of all usersin a cell. To account for the average spectral efficiency in thewhole network and to highlight the short reuse distance in theroom, area spectral efficiency (ASE) is also considered as oneof the data rate metrics which is calculated by using [8] asfollows:

η =

∑u∈S

Ruser(u)

BsysAroom, (5)

where Ruser(u) is the data rate achieved by user u, S is theset of all the users within the room, Bsys denotes the totalsystem bandwidth and Aroom is the area of the room.

III. FRACTIONAL FREQUENCY REUSE IN OPTICAL

WIRELESS

The considered FFR technique is similar to the soft fre-quency reuse (SFR) applied in an RF system. The entirebandwidth is partitioned into several sub-bands, depending onthe reuse factor. In this case, the deployment with a reusefactor of 3 for the cell-edge users is illustrated in Fig. 2. Onepractical and simple method to partition a cell region is tocompare the received SINR of the user using full frequencyreuse with a pre-determined threshold [6]. The same approachis applied in an OW system to achieve frequency reuse.However, in an OW system the allocation of the sub-bandsis performed in a discrete manner rather than a continuousone. In particular, the transmission of users in each sub-cellis dominated by a single LED cluster. If any section of thesub-cell experiences an SINR that is less than the threshold,then the sub-cell is included in the exterior region and thedominating LED cluster transmits on one of the available sub-bands. Otherwise, the sub-cell is included in the interior regionand the corresponding LED cluster is permitted to use theentire bandwidth for transmission. In this manner, each cellis partitioned into an interior region and an exterior region.Indeed, the interior/exterior user partitioning is a discreteapproximation of the continuous process when compared tothe FFR technique in RF systems. Since the centre users in

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Fig. 4. The spatial distribution of the received horizontal illuminance on themeasurement plane in the room.

one cell share sub-band with edge users in adjacent cells,the transmission power for edge users should be higher thanthat for the centre users. Therefore, a coarse power control isneeded. The power control factor β is defined as

β =Pn,i,u

Pn,j,u, (6)

where the LED cluster i belongs to the set that dominatesthe coverage of the exterior sub-cells while the LED cluster jbelongs to the set that dominates the coverage of the interiorsub-cells.

IV. RESULTS AND DISCUSSIONS

A cellular network is assumed in a 15.6 m × 9.0 m × 3 mlarge office. The coverage area in the room is divided into 13hexagonal cells and served by 13 LED arrays, as shown inFig. 3. The optical receivers are placed at a height of 0.85 m.This is a typical desk height and defines the measurementplane. The PD receiver is facing upward toward the ceiling.The system uses OFDMA based on DC-biased optical OFDM(DCO-OFDM) [2]. To achieve the lighting function concur-rently, visible light is used. The system bandwidth is dividedinto 512 sub-carriers. However, only 255 sub-carriers areused for information data transmission due to the Hermitiansymmetry constraint. The performance of the system applyingFFR with a reuse factor of 3 for edge users is compared tothe benchmark systems which use full frequency reuse andtraditional resource partitioning with a static reuse factor of 3.For simplicity, the downlink transmission power of each LEDis equally distributed among the sub-carriers that are used. Forthe benchmark systems, this transmission power is fixed. Forthe FFR system, the transmission power of the LEDs servingthe interior and exterior users are adjusted to maintain thevalue of β. The SINR threshold for FFR is set to 10 dB which,after some initial investigations, was found to achieve a goodcompromise between the edge user throughput and the overallsystem throughput. To guarantee a fair comparison, the totaldownlink transmission power of all systems is normalised. Thesystem parameters are listed in Table I.

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TABLE ISIMULATION PARAMETERS

Parameters ValuesOptical transmitter radiant power for transmission 63 mW

Transmitter semi-angle 10◦

PD responsitivity 0.28 A/WPD area 1.5 cm2

Optical filter gain 1.0Concentrator refractive index 1.5

System bandwidth 20 MHzNumber of sub-carriers 512

Number of users 40Noise power spectral density 1 × 10−21A2/Hz

A. Illuminance requirement

Aside from data transmission, the system should also guar-antee the required illumination levels, which are 400 lx forreading purposes [9]. The spatial distribution of the horizontalilluminance on the measurement plane is depicted in Fig. 4.Above 90% of the area in the room receives illuminance ofabove 400 lx, which indicates that the illumination requirementis mostly satisfied.

B. SINR performance

The SINR distributions in the room with full frequencyreuse and FFR are illustrated in Fig. 5 and Fig. 6, respectively.As previously mentioned, the bandwidth is equally partitionedinto sub-band A, B and C for interference coordination in theexterior region of the cell in the FFR technique. The first threeSINR spatial distributions depicted in Fig. 6 correspond to thedistributions of SINR on the sub-carriers in sub-bands A, Band C, respectively. The last distribution D shown in Fig. 6 isthe average SINR distribution over all three sub-bands. In thefull frequency reuse system, the cell-edge user SINR falls inthe range of -2.6 dB to 9 dB. In contrast, in the FFR system,since interference is mitigated for the exterior sub-cells byapplying traditional resource partitioning, there is an increasein the SINR. Consequently, the SINR for the exterior regionof the cell is within the range of 26 dB to 36 dB. On the onehand, in the full frequency reuse system, the cell-centre SINRis within the range of 10 dB to 29 dB. On the other hand,in the FFR system, the interference mitigation also improvesthe cell-centre average SINR to the range of 24 dB to 32 dB,as shown in Fig. 6.D. Therefore, significant improvement interms of overall SINR is achieved by using FFR relative tothe full frequency reuse system.

C. Throughput performance

It is assumed that 40 users are uniformly distributed in thenetwork. A proportional fair scheduler is used to allocate thesub-carriers to multiple users in each cell. This achieves a goodtrade-off between fairness and system throughput performance[10]. Table II shows the average ASE of the entire network andthe guaranteed user throughput (measured at the first percentileof the user throughput) achieved by the systems with differ-ent techniques and parameters. Fig. 7 shows the cumulativedistribution function (CDF) of the downlink user throughput.Fig. 8 shows the CDF of the downlink system throughput.

Fig. 5. The spatial distributions of the received SINR on the whole frequencyband in the room for the system applying full frequency reuse with a receiverFOV of 70◦ .

Fig. 6. Plot A, B and C correspond to the spatial distributions of thereceived SINR on the sub-band A, B and C for the system using FFR,respectively. The receiver FOV is 70◦ and the value of β is 4, which providesa balanced performance in terms of overall system throughput and cell-edgeuser throughput. The black region indicates the sub-band is unavailable to theusers in that region. Plot D correspond to the average SINR distribution overall three sub-bands

In each figure, “FR” denotes the full frequency reuse system,“RP” denotes the traditional resource partitioning system and“FFR” denotes fractional frequency reuse system. In particular,the curves corresponding to the FFR systems with β values

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Fig. 7. The CDF curves of the user throughput. “FR” denotes the fullfrequency reuse system, “RP” denotes the traditional resource partitioningsystem and “FFR” denotes the fractional frequency reuse system.

TABLE IIAREA SPECTRAL EFFICIENCY AND GUARANTEED USER THROUGHPUT

Frequency partitioning ASE Guaranteed user throughputtechnique [bps/Hz/m2] [Mbps]

FR 0.2607 0.6RP 0.1776 4.1

FFR, β = 2 0.3389 4.3FFR, β = 4 0.3211 5.2FFR, β = 8 0.2937 5.6

of 2, 4 and 8 are presented in each figure. For the exteriorusers in the system applying FFR, a power gain of β increasesthe signal quality further. This results in a better performancefor the exterior sub-cells in the FFR system relative to asystem applying only traditional resource partitioning. Theimprovement in terms of guaranteed user throughput is in therange of 5% to 37%. All three sub-bands are available fortransmission for the interior users in the system applying FFR.In addition, due to the interference mitigation, the averageSINR in the FFR scenario is higher than the SINR in the fullfrequency reuse scenario as discussed in Section IV-B. Thisimproves the performance of the FFR system relative to thetwo benchmark systems in terms of both the user throughputand system throughput, as shown in Fig. 7 and Fig. 8. Theimprovement relative to the full frequency reuse system interms of average ASE is in the range of 13% to 30%. Onthe one hand, when β = 8, the cell-edge user throughput isenhanced at the cost of cell-centre user throughput. In thiscase, a guaranteed user throughput of 5.6 Mbps is achieved.However, the average ASE is only 0.2937 bps/Hz/m2. On theother hand, when β is decreased to 2, the SINR of the cell-centre users is improved. This results in a higher average ASEof 0.3389 bps/Hz/m2 and a lower guaranteed user throughputof 4.3 Mbps. In Fig. 8, it is shown that there is a smallproportion of the cells which have a relatively lower systemthroughput of about 35 Mbps. This occurs when all users inthese cells are in the exterior sub-cells, which is reasonable dueto the low user density in each cell. In this case, the interiorsub-bands are idle which wastes bandwidth and results in alower system throughput. In future work, we will address thisissue.

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Fig. 8. The CDF curves of the system throughput.

V. CONCLUSIONS

This paper addressed the issue of interference coordinationin an optical wireless OFDMA cellular network deployed inan office environment by using FFR. The performance of thesystem applying FFR was compared to systems that used fullfrequency reuse and cluster-based resource partitioning witha reuse factor of 3. The results showed that FFR improvesthe system in terms of cell-edge users throughput and overallsystem throughput relative to the two benchmark systems. Inaddition, by adjusting the power control factor β, the perfor-mances of cell-centre and cell-edge users can be balanced tomeet the design requirements.

ACKNOWLEDGEMENT

Prof. Haas acknowledges the Engineering and Physical Sci-ences Research Council (EPSRC) for the support of this workunder Established Career Fellowship grant EP/K008757/1.

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