Distributed Spectral Efficiency Optimization AtHotspots Through Self Organisation of BS Tilts

Ali Imran, Muhammed Ali Imran, Atta-ul-Quddus and Rahim TafazolliCentre for Communication and Systems Research

University of Surrey, Guildford, United Kingdom. GU2 7XH.email: {A.Imran, M.Imran, R.Tafazolli}@surrey.ac.uk

Abstract— Pop up traffic hotspots i.e. geographically concen-trated user pockets are a time persistent reason behind pooruser experience in wireless cellular system. Spatio temporalunpredictability of such pop up hotspots renders them difficultto be designed out in the planning phase of the cellular systemhence dynamic and adaptive solutions are required to cope withthem in an impromptu manner. In this paper we present a novelsolution that addresses this problem by dynamically enhancingspectral efficiency in hotspot regions through optimisation ofsystem wide BS antenna tilts in distributed fashion. Unlike mostof the existing works that provide solutions for hotspot relief,our solution does not rely on load transferring to neighbour cells;rather it dynamically enhances the overall spectral efficiency andthus capacity of the system by jointly optimising antenna tiltsof multiple adjacent cells with respect to hotspot locations inthose cells. Furthermore, being designed on the principles of selforganization in biological system, our solution is self organisingand can improve the user spectral efficiency in a system by upto1b/s/Hz in presence of hotspots with no significant overheads.

I. INTRODUCTION

User distribution in real world is not uniform as often con-sidered during Wireless Cellular System (WCS) planning anddesign phase as well as in simulation based evaluations. In realworld, high user densities intermittently occur near points ofattractions e.g. theaters, shopping malls, event venues, beachesand office complexes etc. These concentrated pockets of usermanifest themselves as traffichotspotsthat pop up at randomtimes and at random locations in the coverage area. Thesehotspots become a source of low user satisfaction because ofthe congestion they might cause. Furthermore, pop up hotspotsalso can have adverse effect on overall performance of thesystem when they occur in the in areas where interference orshadowing is high. In such scenario only low order modulationand coding schemes can be used by the system to provideservice to the users in these hotspots. Therefore, such hotspotscan cause a significant proportion of user population to beserved with low spectral efficiency. This in turn deterioratesthe QoS and system wide throughput in WCS.

The pop up hotspots, in general, are hard to be designedfor, during the WCS deployment phase because of theirunpredictability both in time and space. An over safe designto accommodate potential pop up hotspots is not feasibleoption either, as it can be expensive and may result in underutilization of resources itself. To this end, in this paper weprovide a novel Self Organising (SO) solution that resolveshot hotspot problem by dynamically maximising the user link

spectral efficiency for users in hotspot. The basic idea is toenhance the average user Signal to Interference ratio (SIR)by focusing better antenna gains dynamically at locations ofpop up hotspots, through optimization ofsystem wide antennatilts but in distributed and self organising manner. Numericalresults show that in addition to improving spectral efficiencyof hotspot user, this solution can can also improve the overallspectral efficiency of the system in face of hotspots.

There have been several studies on tilt optimization [1]1

most of which focused on improving the coverage and capacityin general for GSM [2], CDMA [3]–[5], HSDPA [6] and LTE[7]–[11] based WCS. The approaches taken in all these workscan be divided in two main categories.

In first category fall the schemes that use antenna tiltbasically as aninterferencereduction tool. Such schemes adaptantenna tilt to minimise interference and thus improve overallthroughput of the system. These type of schemes are mostlyinvestigated in context of CDMA based WCS to control intercell interference [2], [4] with no consideration for hotspots.

Second category consist of schemes that exploit antenna tiltas a tool to control effectivecoverageand thus control the loadin the cell to achieveload balancingeither in the CDMA basedWCS [3], [5], [6] or OFDMA based WCS [8]. Out of these themost relevant to the scope of this paper are works presented in[3] and [5]. Both [3] and [5] deal with hotspot through antennatilting but for CDMA and HSDPA respectively unlike our workwhere we address this problem for OFDMA based WCS. Themost important difference between the two systems in thiscontext lies in the fact that unlike the soft handover in CDMAbased WCS, in OFDMA based WCS the handover is hardhandover i.e. this may involve a change of carrier frequency.This change of carrier frequency increases the complexityand overheads associated with handovers compared to thesoft handovers in CDMA based WCS. Since pop up hotspotsare acutely dynamic in both time and space, therefore, thecompensating mechanisms for them, that require excessivehandover among cells do not remain a attractive solutionfor OFDMA based WCS. The tilting mechanism proposed inboth [3] and [5] are based on the basic idea of tilting downthe overloaded cell antenna to reduce its effective coveragearea in order to shift its load to neighbouring cells. Suchtilting mechanisms are shown to rely on excessive handovers

1A detailed survey on tilt optimization can be found in our work in [1].

from overloaded cell to adjacent cells [3]. As discussed above,such handovers can be manageable softly in CDMA, but inOFDMA based networks like LTE and LTE-A they are hardhandovers and undermine the practicality of this approach.

To the best of our knowledge, the tilt optimisation basedsolution for hotspot based user distribution presented inthis paper is novel and essentially different from the twoapproaches taken for tilt optimisation explained above andgenerally used in literature. Although we use antenna tilts todeal with hotspot , but unlike both of the works [3] and [5] ,our work does not seek hotspot relief through load balancingachieved by antenna down tilting of over loaded sectors andthereby triggering handovers from that cells to neighbourcells. Neither we present a scheme to tilt down antennas forinterference minimization in the system in general. Rather weintroduce a novel concept of traffic’s Center of Gravity (CG) torepresent hotspot based user geographical distribution in a cell.By building on this concept we then develop a unique adaptiveand yet scalable and agile mechanism where a pre-determinedset of neighbouring cells jointly optimize their tilts to focustheir antenna gains at the CG’s e.g hot spots in those cells. Thisantenna tilt optimization is performed in distributed mannerbut on system wide scale by using another novel concept oftriplet of most interdependent sectors. Thus, this mechanismcan improve the overall spectral efficiency of WCS in faceof a realistic non homogenous spatio temporarily varyinguser distribution. Since, unlike the hotspot relief approachesused in [3], [5] our approach does not achieve hotspot reliefby transferring load to nearby under loaded cells, rather itrelieves congestion by enhancing the spectral efficiency athotspots, therefore, it does not necessitate handovers. The SOnature of this solution enabled by distributed nature and lowcomplexity; and the fact that solution can be implementedthrough electronic antenna tilting based on local feed backonly, makes it pragmatic solution for pop up hotspots.

The rest of this paper is organised as follows. In sec-tion II we present system model, assumptions and problemformulation. In order to achieve a SO solution, in section IIIwe propose a way to decompose the system wide probleminto local subproblems as inspired by SO systems in nature.Solution methodology for local subproblems is also presentedin this section. Section IV presents numerical results andsection IV concludes this paper with remarks on pragmaticimplementation aspects and future work directions.

II. SYSTEM MODEL AND PROBLEM FORMULATION

We consider a multicellular network with each base stationhaving three sectors as shown in figure 1. LetN denote the setof points corresponding to the transmission antenna locationof all sectors andK denote the set of points representingthe locations of users in the system. The geometric Signalto Interference Ratio i.e. SIR perceived on the downlink at alocationk being served bynth sector can be given as:

γnk =PnGnkα (d

nk )−β

∑∀m∈N\n

(PmGmk α (d

mk )−β) m,n ∈ N , k ∈ K (1)

Fig. 1. System model for problem formulation. Red circles show locationof hot spots in some sectors while others have uniform user distribution.

whereP is transmission power,d is distance between transm-mitng sector and receiving user location.α andβ are pathlossmodel coefficient and exponents respectively.G is antennagain and for 3GPP and LTE and LTE-A, it can be modelledas in [8] and written in dB as:

Gnk = λv

(

Gmax −min

(

12

(θnk − θ

ntilt

Bv

)2, Amax

))

+

λh

(

Gmax −min

(

12

(φnk − φ

na

Bh

)2, Amax

))

(2)

whereθnk is the vertical angle in degrees fromkth location ofuser tonth sector andθntilt is the tilt angle of thenth sectoras shown in figure 1. Theφnk is horizontal angle in degreeswith similar meanings of subscript and postscript. Subscriptsh, a andv denote horizontal, azimuth and vertical respectively.ThusBh andBv represents horizontal and vertical beamwidthsof the antenna respectively, andλh andλv represent weightingfactors for the horizontal and vertical beam pattern of theantenna in 3D antenna model [8], respectively.Gmax andAmax denote the maximum antenna gain at the boresight ofthe antenna and maximum antenna attenuation at the sides andback of the boresight of the antenna respectively, in dB. Forsake of simplicity we can neglect the the maximum attenuationfactorAmax in (2). Without loss of generality we can assumemaximum gain of0 dB. Thus by puttingGmax = 0dB in (2),converting it fromdB to linear form it can be simplified as:

Gnk = 10−1.2

(λv

(θnk−θ

ntilt

Bv

)2+λh

(φnk−φ

na

Bh

)2)

(3)

For ease of expression we use following substitutions:

cnk =B2vλh

λv

(φnk − φ

na

Bh

)2;hnk = α (d

nk )−β;μ =

−1.2λvB2v

(4)We assume that all the BS antennas transmit with same power.For such scenario, by using (3) in (1) and applying thesubstitutions in (??), the SIR in (1) can be written as:

γnk =hnk10

μ((θnk−θntilt)

2+cnk)

∑∀m∈N\n

(

hmk 10μ((θmk −θmtilt)

2+cmk

)) (5)

Since our objective is to maximise hotspot user throughputwithout sacrificing non hotspot user throughput, so our prob-lem statement becomesoptimize system wide antenna tilts tomaximize the aggregate bandwidth normalised throughputforall users in the system. Mathematically:

maxθNtilt

∑

∀s∈K

log2 (1 + γnk

(θNtilt

)) (6)

Note thatγnk is a function of vector of tilt angles ofall sectorsin WCS i.e.θNtilt whereN = |N |. FurthermoreK can also beanticipated to be a large set. This indicates (6) is large scalenonlinear optimization problem. In next section we show howthe paradigms of SO can be exploited to reduce to complexityof this solution to achieve a distributed near optimal solution.

III. D ESIGNING A SO SOLUTION

In nature many systems can be observed to manifest perfectself organization. A detailed discussion on designing selforganisation can be found in our work in [1] as well asin [12]. Here it would suffice to say that, for perfectly selforganising solution, perfect objective may not be aimed forat system-wide level [12]. Rather,anapproximation of theobjectivecan be aimed for, given that it can bedecomposedinto local subproblems that can be solved at local level bythe local entities of system. This phenomenon, in turn canapproximately achieve the original system wide objectiveresulting into emergence of self organising behaviour [1], [12].

This design principle of self organisation when appliedto our problem in (6) means, given the complexity of thisproblem, we need to 1)find anapproximation that can bethen 2)decomposeddown into locally solvable independentproblems. And then we need to 3)determine the solution ofthat local problem. In following subsection we follow thesethree steps to achieve a novel self organising solution.

A. Approximating the Complex Problem with Simpler Problem

In order to simplify the problem in (6) such that it canbe decomposed into local subproblems, we propose a novelconcept of CG to effectively represent user geographicaldistribution in this context of tilt optimization. i.e. We proposeto use hotspot’s central locations as CG’s of user distributionin a sector with respect which the antenna tilts of the systemcan be optimised. Since in case of hotspots based demographymajority of user are in close vicinity of that central location ofhotspot, so such optimization is bound to improve the overallsystem performance compared to arbitrary tilting, or the tiltingdoes not aim at any particular point e.g. the one done forinterference reduction [3] and [5] or no tilting. (This pointwill be further clarified in numerical results). The locationsof of pop up hotspots can be easily determined by number ofmechanisms including CCTV’s surveillance cameras, throughGPS or plethora of alternative location estimation algorithms,to be supplied to WCS as CG in an online manner.

If S denotes the set of all CG’s in the system i.e. set ofpoints representing geographical center of hotspots as shownin figure 2 with small circles, and we assume that each sector

Fig. 2. A pictorial illustration of how hotspot based user distribution in WCScan be represented by single points called center of Gravity (shown by redcircles)i.e. Figure also shows how system-wide optimization of tilts can bedecomposed into optimization of tilts within each triplet independently.

has one hotspot, our problem in (6) can be approximated as:optimize system wide antenna tilts to maximize the aggregatebandwidth normalised throughput at CG’s in whole system.i.e.

maxθNtilt

∑

∀s∈S

log2(1 + γns

(θNtilt

))(7)

B. Decomposing System-wide Problem into Local Subproblem

As discussed above, decomposition of (7) is necessary for aself organising solution [1], [12]. To enable this decompositionor localisation, we propose the concept oftriplet as illustratedin figure 2. The reason to exploit triplet as a local monolithicentity for self organisation, is that it isfixed cluster of threeadjacent and hence mutuallymost interferingsectors as shownin figure 2. Thus, firstly it will not require system-wide co-operations as suggested by some works, thereby avoiding theneed for heavy signalling; and secondly, yet it incorporates thedominant interferer cells in the optimization process, thirdlyit converts the large scale optimization problem in (7) to asmall scale optimization problem that is solvable with state ofthe art optimization techniques as we show in the following.Let θTitilt denote vector of tilt angle of sectors withinith triplet,now the local optimization problem to be solved and executedwithin a triplet is given as:

maxθTitilt

∑

∀s∈Si

log2

(1 + γns

(θTitilt

))(8)

Whereasγ shows that SIR here is an approximate SIR as itconsiders interference from the two most interfering adjacentsectors only. It can be written as:

γnp(θTtilt

)=

hnp10μ((θnp−θ

ntilt)

2+cnp

)

∑∀t∈T \n

(

htp10μ((θtp−θttilt)

2+ctp

)) (9)

The pros and cons of this localisation of problem in (7) arehighlighted in III-D. In next section we present methodologyto solve this local problem.

C. Solving Local Problem

If C is the total achievable bandwidth normalised throughputin a given triplet at the three CG’s within (subscript droppedfor simplicity of expression) then:

C = log2(1 + γ11

)+ log2

(1 + γ22

)+ log2

(1 + γ33

)(10)

where postscript denote sector number and subscripts denoteCG within a triplet, as shown in figure 2. Since number ofoptimization parameters is only three now and their range isalso finite i.e.0 < θ < 90, so the solution of (8) can be easilydetermined using a non linear optimization technique thatcan tackle a small scale non convex optimization problem.2

Observing that (10) is twice differentiable, we solve this subproblem using sequential quadratic programming (SQP). Forsake of clarity, we drop the subscript tilt. Instead we usesubscript to present the association with sector in the triplet.Then the problem in (8) can be written in the standard form:

minθ

−C (θ) (11)

subject to: gj (θj ) < 0 , j = 1, 2, 3whereθ = [θ1, θ2, θ3] and gj(θj) = θj − π

2 . The Lagrangianof constrained optimization problem in (11) can be written as:

L (θ ,λ) = C (θ)− λTg (12)

L (θ ,λ) = C (θ)−3∑

j=1

λj(θj −π

2) (13)

If H denotes the approximate of the Hessian matrixH,then we can define quadratic subproblem to be solved atrth

iteration of SQP as follows:

minw∈RJ

1

2wT H (L (θ ,λ) )rw +5C(θ)rw (14)

subject to: wj + θjr −π2 < 0 j = 1, 2, 3

At each iteration the value ofH can be updated using theBroyden-Fletcher -Goldfarb -Shanno (BFGS) approximationmethod. Once the Hessian is known the problem in (14) isa quadratic programming problem that can be solved usingstandard methods e.g. gradient projection method in [13].

Through the above steps of SQP, the problem in (8) canbe solved within each triplet independently to determine theoptimal tilt angle to be adapted and maintained by eachtriplet for given locations of hotspots within that triplet. Theexecution of these solutions in each triplet in the whole WCSindependently, results in achievement of the system wideobjective in (6),approximately. We call this framework SOT-HR i.e. SO of Tilts for Hotspot Relief

2Non convexity of C can be observed by plotting C againstθ. See in figure 3

TABLE I

SYSTEM LEVEL SIMULATION PARAMETERS

Parameters ValuesSystemtopology 19 BS×3 sector, Frequency Reuse1

BS Transmission Power 39dBmCell Radius,BS and userheight 600, 32 and 1.5 meters respectively

User antenna gain 0 dB (Ominidirectional)Bh,Bv 700,100λv = λh 0.5Gmax,Amax 18, 20dB

Frequency 2 GHzPathlossmodel 3GPP UrbanMacro

Bandwidth 5MHzShadowing standard deviation 8 dB

Scheduling RoundRobinTotal userpopulation 10000users

Hot SpotsRadius 10% of cell radius ( locatedrandomly)% of users in hotspots 50%

D. Implications of SOT-HR

It can be seen that the subproblem in (8) does not aim tooptimise system wide antenna tilts. This feature has one majoradvantage i.e. this subproblem can be solved independently inwithin each triplet without requiring coordination with rest ofthe antennas in other triplets. The cost of this advantage is thatthe system-wide globally optimal performance is neither aimedfor nor achieved through SOT-HR; however, it is just like thecase that in nature SO systems do aim for perfectly optimalobjectives. For instance, common cranes never fly in perfectV-shape, but even maintaining a near V-shape increases theirgroup flight efficiency by 70% [14]. Furthermore, as postulatedin [12], one of the four main paradigms for designing SO intosystem is that, for perfect SO perfect objectives need not beaimed for. So here the SO nature of the proposed solution isperfect but at cost ofsub-optimal global objective.

IV. PERFORMANCEEVALUATION

In order to demonstrate the potential of SOT-HR we evaluateits performance for a stand alone triplet (figure 3) as well atsystem level (figure 4) by implementing it in a system levelsimulator that models an OFDMA based generic WCS. TableI shows key simulation parameters used.

Figure 3 plotsC/3 in (10) for a stand alone triplet fortwo different set of locations of CG i.e. hotspot centres. Twokey observations can be made from this result. Firstly, SOT-HR can improve spectral efficiency of users at hotspots byupto 1b/s/Hz (2 to 3 and 3 to 4 b/s/Hz in bottom and topleft of figure 3, receptively). Secondly, the optimal value oftilt angles are strongly dependent on the location of hotspots.This observation highlights the need for SO of tilts to copewith spatio temporally dynamic pop hotspots; and SOT-HRactually enable this SO of tilts in a pragmatic way. This alsois demonstrated by system level performance of SOT-HR infigure 4.

For a comparative analysis of SOT-HR performance is alsoevaluated for four other fixed tilting options with arbitrary tiltvalues of00, 50, 200 or 250 . Unlike these tilting options whereall sectors in system have fixed tilts, SOT-HR optimally setsvalue of each sector independently in each triplet based on lo-cation of hotspots. A significant gain in throughput achievable

0

50

0

50

3

3.5

4

θtilt2

X: 15Y: 10Z: 3.845

θtilt1

(b/s

)/H

z

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

-1000 -500 0 500 1000

-1000

-500

0

500

Distance(m)

Dis

tanc

e(m

)

0

50

0

50

2

2.5

3

θtilt2

X: 5Y: 7Z: 2.821

θtilt1

(b/s

)/H

z

2.3

2.4

2.5

2.6

2.7

2.8

-1000 -500 0 500 1000

-1000

-500

0

500

Distance(m)

Dis

tanc

e(m

)

BS locationCG location

For given hotspot locations optimal tilt angles are: θ1tilt

=100, θ2tilt

=150

For given hotspot locations optimal tilt angles are: θ1tilt

=70, θ2tilt

=50

Fig. 3. Bandwidth normalised average throughput per linkC3

plotted for astand alone triplet against tilts of two sectors while third is fixed at00 degree.

0 2 4 6 8 10 12 14 16 180

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Bandwidth Normalised User Theoratical Throughput (b/s/Hz)

CD

F

Tilt=0, SO=OFFTilt=5, SO=OFFTilt=20, SO=OFFTilt=25, SO=OFFTilt=auto, SO=ONTilt=0, SO=OFF(Hot Spot Users)Tilt=5, SO=OFF(Hot Spot Users)Tilt=20, SO=OFF(Hot Spot Users)Tilt=25, SO=OFF(Hot Spot Users)Tilt=auto, SO=ON(Hot Spot Users)

Fig. 4. Throughput for all users and users in the hotspot. Results for fixedtilts are denoted by legend ‘Tilt=x,SO=OFF’. Where x denotesθtilt . Theresults with SOT-HR in place are denoted with legend ‘Tilt=auto,SO=ON’

with SOT-HR can be observed in figure 4 compared to otherfixed tilt configurations. Another important observation is thatfor all other fixed tilt configurations throughput for hotspotonly and all users are almost same. But SOT-HR provides arelatively higher throughput to hotspot users. This is becausethe SOT-HR optimises the antennas with respect to hotspotcenters i.e. C.Gs in the sectors. CDF’s also show that SOT-HR does not degrade the overall average user throughput.

V. CONCLUSION AND FUTURE WORK

A novel framework SOT-HR for spectral efficiency opti-mization in presence of hotspots through self organisation ofantenna tilts in distributed and dynamic manner is presented.Both numerical and system level simulations results presentedshow that a significant gain in spectral efficiency of up

to 1b/s/Hz achievable with the proposed framework. Frompractical implementation point of view, the main advantage ofSOT-HR is that it requires a negligible amount of only localsignalling i.e. among the sectors within triplet to determinethe location of hotspot. This signaling can be done throughX2 interface and most importantly it can be done only whenlocation of whole hotspot changes i.e. tracking of individualuser location is not required. In future this framework wouldbe extended for interference avoidance at Femto cells insteadof hotspots.

ACKNOWLEDGMENT

This work has been performed in the framework of the ICTproject ICT-4-248523 BeFEMTO, which is partly funded bythe European Union. The authors would like to acknowledgethe contributions of their colleagues from the BeFEMTOconsortium.

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