AGeometricMethodforEstimatingtheNominalCellRangein ...downloads.hindawi.com/journals/misy/2018/3479246.pdf · closest neighbor sites, the CR of cell clocated in site sis ... planning

Research ArticleA Geometric Method for Estimating the Nominal Cell Range inCellular Networks

A J Garcıa 1 V Buenestado 2 M Toril 1 S Luna-Ramırez 1 and J M Ruiz2

1Departamento de Ingenierıa de Comunicaciones Universidad de Malaga Malaga Spain2Ericsson Malaga Spain

Correspondence should be addressed to A J Garcıa ajgpicumaes

Received 4 January 2018 Revised 13 March 2018 Accepted 26 March 2018 Published 2 May 2018

Academic Editor Ioannis D Moscholios

Copyright copy 2018 A J Garcıa et al is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In cellular networks cell range is a key parameter for network planning and optimization With the advent of new radio accesstechnologies it is not easy to obtain a good estimate of the nominal cell range on a cell-by-cell basis due to the complexity ofphysical layout in a real network In this work a novel geometrical method for estimating the cell range based on Voronoitessellation is presented e inputs of the method are site locations antenna azimuths and antenna horizontal beamwidths emethod is tested with a real dataset taken from a live LTE network During assessment the proposed method is compared withtraditional approaches of estimating cell range Results show that the proposed method improves the accuracy of previousapproaches while still maintaining a low computational complexity

1 Introduction

With the increasing complexity of mobile networks radionetwork planning has become a challenging task for mobileoperators e aim of planning is to find a cost-effectivedeployment solution to offer subscribers the best networkperformance in terms of coverage capacity and connectionquality [1ndash3] For this purpose in the initial preplanningstage the required site density is estimated based on linkbudgets en in the nominal planning stage optimal sitelocations are determined in terms of network coverage andcapacity In the final detailed planning stage the best siteconfiguration is selected In all these processes estimatingthe nominal (ie planned) Cell Range (CR) is a critical tasksince it influences the number of required base stations theirgeographical location and the optimal antenna settings(eg transmit power or tilt angle) [1 2 4 5]

An improper network modeling during the planningstage can lead to suboptimal system performance duringnetwork operation is problem can be solved by im-proving network models with live measurements (akameasurement-based replanning) or counteracted by tuningradio network parameters (aka network optimization) In

both cases an accurate estimation of the nominal cellservice areas is critical to obtain good results [4 6] Anexample of such a need is the automatic method proposedin [7] to detect cells with overshooting problems In thatmethod the actual (ie measured) cell range obtainedfrom Time Advance (TA) statistics [8] is compared withthe nominal cell range In such a comparison any deviationof the nominal cell range causes that a cell is classified as anovershooter or not Similarly the planning methods pro-posed in [9 10] for selecting the best antenna tilt anglebased on geometric considerations strongly depend on thenominal CR

Traditionally operators use two different approaches toestimate the nominal cell range in mobile networks efirst approach consists of using commercial cellular net-work planning tools [11] mainly based on static system-level simulators that allow analyzing coverage capacityand quality of service related issues One of the key pro-cesses performed during a step simulation is the dominancearea calculation and thus nominal cell range In this processthe link losses from each base station to each position inits calculation area are estimated by using network config-uration parameters for base stations mobiles stations and the

HindawiMobile Information SystemsVolume 2018 Article ID 3479246 8 pageshttpsdoiorg10115520183479246

network area and different propagation models that allow tosimulate path losses in a real environment [12] Static sim-ulators obtain an accurate estimation of network parametersbut assuming a high computational load especially for high-density scenarios us cellular network planning tools areused generally in the initial preplanning stage where timerequirements are not so restrictive Alternatively a geometriccalculation of nominal cell range is also commonly used foroperators Geometric calculation is uniquely based on physicalinformation of base stations (eg location of base stations)is approach consists of a simple method that allows toobtain with a considerable grade of accuracy an estimate ofcell range with a very low computational load by avoiding touse complex tools in its process us it is an efficient al-ternative used by operator to be integrated in their networkmanagement systems for optimization processes since it isable to be executed over large geographical areas in seconds

In an ideal cellular network with regular geometry thegeometric CR (ie the distance to cell edge) can be estimatedanalytically by using the inter-site distance (ISD) [13]Specifically the CR in a hexagonal grid scenario is ISD

3

radic

with omnidirectional antennas and ISD3 with trisectorizedantennas However in a live scenario sites are unevenlydistributed to deal with factors such as topography cost oravailability causing that cell shapes are irregular [14]Moreover new radio access technologies (4G5G) will resultin the deployment of a higher number of small cells in-creasing the complexity of physical layout [15] us the CRcannot be calculated by using the distance to the nearest site

Current operator practice is to compute the nominal CRof a site by averaging the distance to some of the nearest sitesen the number of nearest sites selected is limited in anattempt to avoid considering several rings of adjacent cellsUnfortunately the best number of nearest sites is difficult todefine as it depends on the specific scenario [16] Forsimplicity such a parameter is set to a fixed value leading toinaccurate CR estimates in many cases To solve theselimitations some authors use Voronoi tessellation [17 18] todefine the polygon representing the service (or dominance)area for every site [14 19ndash22] Such a diagram can then beused to choose the nearest sites more accurately and con-sequently to estimate the ISD [21] Once the nominal ISD isobtained CR is estimated as half of the ISD value e mainlimitation of this method is that the CR assigned to all cells ina site (ie cosited cells) is the same which is seldom true inthe live network Such inaccuracies can jeopardize thebenefits of network planning and optimization methods thatrely on CR estimates (eg [7])

In this work a geometric method to calculate the CRbased on Voronoi tessellation is presented e main nov-elties are that (a) CR is calculated on a cell (and not on a site)basis (b) CR depends on the antenna pointing direction ofeach cell (ie azimuth) and (c) the antenna beamwidthvalue is used to define the cell border (ie side of the servicearea)us a more accurate estimation of the CR is obtainedwith a low computational cost e analysis is extended bychecking the impact of the proposed method on the per-formance of the cell overshooting detection algorithm de-scribed in [7]

e main contributions of this work are (a) a novel andcomputationally efficient method to estimate the CR on a per-cell basis suitable for radio network optimization processes(b) a comprehensive analysis of the proposedmethod in a realscenario showing the limitations of current practice and howthese can be solved by the new approach and (c) an eval-uation of the impact of CR estimates on the performance ofa classical cell overshooting detection algorithm in a live LTEnetwork

e rest of the work is organized as follows Section 2reviews the current method used to calculate the CR on a sitebasis Section 3 describes the method proposed to calculatethe CR on a cell basis Section 4 shows the results obtained bythe method in a real scenario Finally Section 5 presents themain conclusions of the study

2 Calculation of Cell Range on a Site Basis

In a network consisting of n sites an estimate of CR can beobtained by calculating the average distance to the k nearestsites where klt n [21] us the average ISD from site s tothe k nearest sites is defined as

ISDsk 1k

1113944

k

m1dist(s m) (1)

where dist(s m) is the Euclidean distance from site s to sitem Once the average ISD of site s is calculated with the k

closest neighbor sites the CR of cell c located in site s iscalculated as

CRsite(c)

ISDsk

2 (2)

where ISDsk is the ISD of site s calculated by using the k

nearest sites Note that CRsite(ci) CRsite(cj) forall ci cj isin sFigure 1 shows an example of how the current method

works CRsite is represented by a dashed circumference andthe pointing direction of cell by a solid arrow In this exampleit is assumed that the number of nearest sites used for ISDcalculation (represented by crosses with dotted circles) is 6and the solid arrow represents the pointing direction of thecell From the figure it is clear that the previous method hasseveral limitations the foremost of which is the calculation ofthe ISD at a site level causing that all cells in the same site areassigned the same CR value (represented by a dashed arrow)Moreover the CR of a cell is only based on the distancebetween the site where the cell is located and surroundingsites However in a real network the service area of a cell withdirectional antennas is mainly determined by the sites that arein the pointing direction of (ie in front of) the cell

3 Calculation of Cell Range on a Cell Basis

To solve the above-described problems the CR should becomputed in a cell level making the most of geometricconsiderations is is done in the method described nexte method consists of three stages Voronoi tessellationcell border definition and computation of average distanceto cell border

2 Mobile Information Systems

31 Voronoi Tessellation A Voronoi diagram is dened asa partitioning of a plane into regions based on the distance topoints in a specic subset of the plane [23] LetP p1 p2 pn be a set of points in the plane callednodes ν(pi) is dened as the Voronoi cell of pi formed bythe set of points q in the plane that are closer to pi than toother nodes us the Voronoi cell of node pi is dened as

ν pi( ) q | dist pi q( )lt dist pj q( ) foralljne i (3)

where dist(pi q) is the Euclidean distance from node pi topoint q and dist(pj q) is the Euclidean distance from nodepj to point qν(pi) can also be dened as an intersection of planes

Given two nodes pi and pj the set of points that are strictlycloser to pi than pj is the open half plane whose line thatseparates the two half planes is the perpendicular bisectorbetween pi and pj formed by those points equidistant fromthese two nodesis half plane is denoted as h(pi pj)usthe Voronoi cell of pi is dened as

ν pi( ) capjne ih pi pj( ) (4)

Figure 2 shows an example of Voronoi diagram for a setof nodes taken from a real cellular scenario Nodes (rep-resented by crosses) in the gure represent the sites of thenetwork It is observed that each Voronoi cell contains all thenearest points to each node representing the dominancearea of the site

ere are several algorithms to compute the Voronoidiagram e computational complexity of most of them isO(n2) where n is the number of nodes However somealgorithms use more ecient methods that reduce thecomputational complexity to O(n log n) [23] An exampleof the latter is Fortunersquos algorithm [23] used in this work

32 Cell Border Denition Once the Voronoi diagram isconstructed for the whole scenario the next step is to denethe cell border from the Voronoi cell generated for each siteSuch a cell border is later used to compute the CR(ie distance to cell edge)

e process to estimate the cell border is shown inFigure 3 e inputs to the methods are site locations(represented by crosses) polygons dening the Voronoicells (solid lines) antenna pointing direction in the hori-zontal plane (arrows) and beamwidth (θ) All the requireddata (except Voronoi polygons) are included in networkplanning les used by the operator e cell border can beobtained graphically by the intersection between thestraight lines dened by the beamwidth (dashed lines) andthe outline of the Voronoi cell (solid lines)

0 5 10 15 20 25 30 350

5

10

15

20

25

x (km)

y (km

)

Figure 2 Voronoi diagram for a set of sites in a real cellularscenario

0 05 1 15 2 25 3 35 40

05

1

15

2

25

3

35

L2L1

θ

L3

A B

CD

s

Cell

y (km

)

x (km)

Figure 3 Cell border denition

0 5 10 15 200

5

10

15

20

x (km)

y (km

)

CRsite

Figure 1 Computation of the average inter-site distance on a sitebasis

Mobile Information Systems 3

To automate the method it is necessary to nd the lineequation of each line segment dening the cell shape (labeledas L1 L2 and L3 in the gure) For this purpose the co-ordinates (x y) of all intersection points (A B C and D inthe gure) can be obtained by matching the equations of theVoronoi cell segments and those dened by the beamwidthen intersection points that are not located in the pointingdirection (arrow) are discarded (C and D in Figure 3) Fi-nally cell border consists of the line segments dened by thenondiscarded intersection points (A and B) and the Voronoicell (solid lines) Note that depending on the beamwidthvalue and the shape of the Voronoi cell the cell border isdened by dierent line segments

33 Computation of Average Distance to Cell Border enal step is to obtain the CR value from the cell border Forthis purpose the average distance from the site to all seg-ments dening the cell border is calculated analytically Asthe cell border can consist of more than one segment it isnecessary to calculate the average distance from the sitewhere cell is located to each of those segments

e average distance from a point P to a line segment Lcan be calculated by a simple transformation in the co-ordinate system Figure 4 illustrates that change In the newcoordinate system (XprimeYprime) the line segment under calcu-lation must be located in the positive x-axis In the newcoordinate system the average distance between the pointand the line segment dist(P L) is dened as

dist(P L) 1lLintlL

0

xprime minusxpprime( )

2 + ypprime2

radicdxprime (5)

where (xpprime ypprime) is the point location in the new coordinatessystem and lL is the length of the line segment L

e integral shown in (5) can be solved analytically as

int(xminus a)2 + b2radic

dx 1

2a2 + b2 minus 2ax + x2

radic (minusa + x) a2 + b2 minus 2ax + x2( )minus b2a2 + b2 minus 2ax + x2

radic

middot log 2 a +b2 +(aminus x)2( )

radicminusx( )[ ] (6)

where a and b are xpprime and ypprime respectivelyOnce the average distance between the site and each

segment of the cell border is known by using (6) a weightedaverage distance is obtained based on the length of eachsegment Such a weighting operation ensures that the av-erage distance is dominated by longer segments us theCR of cell c is computed as

CRcell(c) sumnseg(c)

i1 dist s Li( ) middot lLisumnseg(c)

i1 lLi

(7)

where nseg(c) is the number of segments in the border of cellc and dist(s Li) is the average distance from site s to linesegment Li

e proposed geometric method has a limitation for cellsin sites located at the border of the scenario when there is noother cell in their pointing direction As observed in Figure2 the Voronoi cell in these cases is not bounded and extendsto innity in the pointing direction of the cell us it isimpossible to calculate the CR by using the geometricmethod as the segments dening the cell border cannot be

identied In the absence of a better estimate the CR mightbe set to the maximum cell radius given by the link budgetin that scenario [4] Note that such an estimate would stillbe more accurate than assigning the CR of the other cells inthe same site as the service area of border cells tends to belarge

4 Performance Assessment

In this section the above-described methods of computingthe CR on a site and cell basis are compared based on theresults obtained in a real LTE network e analysis is rstfocused on the CR values obtained by each method enthe analysis is extended by checking the impact of theproposed methods on the performance of the cell over-shooting detection algorithm proposed in [7] Finally thecomputational load of both methods is evaluated

41Analysis Set-Up Most of the analysis is done in an urbanscenario consisting of 160 LTE cells distributed in 54 sitesIn this area only a single carrier is deployed e dataset

Y

X

Yprime

Xprime

P

xp

yp

yprimep

xprimep

L

Figure 4 Point translation


includes (a) the geographical location of all sites in the areaas well as sites in the surroundings to avoid border eects(b) the pointing direction of each cell (ie azimuth) and (c)the number of cells in each site used to dene the antennabeamwidth (eg if there are three cells in the same site thebeamwidth value is 3603 120deg)

To compare methods the following indicators arecalculated

(1) CR at cell level CRcell which is the indicator pro-posed in this work computed as in (7)

(2) CR at site level CRsite which is the indicator used inprior works computed as in (2) with the k 6nearest sites e value of 6 sites intends to take intoaccount the rst tier of neighbors

Comparison is done by computing CR relative dier-ences as

εsitecell(c) CRsite(c)minusCRcell(c)

CRcell(c) (8)

e cell overshooting detection algorithm presented in [7]is used to check the impact of estimating CRs by dierentmethods (ie site level or cell level) In the algorithm can-didate cells for downtilting are ranked based on the com-parison of the nominal (planned) and real (measured) celledge e actual maximum serving distance of each cellhereafter referred to as measured cell range can be derivedfrom TA measurements collected by the base station (eNo-deB) [24] e TA procedure adjusts uplink transmissions toensure that the downlink and uplink subframes are syn-chronized at the base station us the TA value can bedirectly mapped to the distance between the user and the basestation (ie eNodeB in LTE) In LTE TA resolution is 052 micros(78m) A statistical TA distribution for each cell can begenerated by collecting TA measurements over long timeperiods (eg one day) From this data the measured CRCRmeas is dened as the 95th percentile of the TA distribution(ie the distance exceeded only by 5 of the users served bythe cell) Once the measured and nominal CRs are known theratio between both indicators can be used as an indicator ofcell overshooting Specically the overshooting ratio (OVSR)is dened as the ratio between the measured and the nominalCRs A large value of OVSR in a cell indicates that the cell iscapturing users farther than planned us the higher theratio the higher the need to increase antenna tilt of the cell

To measure the computational load both methods areimplemented in Matlabcopy e Voronoi tessellation is com-puted by the Voronoi routine [25] en the methods aretested in two scenarios consisting of 160 and 12500 LTE cellsdistributed in 54 and 2966 sites respectively All methods areexecuted in an IntelcopyCore i5 dual-core computer with26GHz clock frequency and 8GB of RAM In this casemethod assessment is done based on the execution time

5 Results

A comparison of methods is rst carried out by checking thecorrelation between the indicators CRsite and CRcell From

this analysis two abnormal cases are identied and discussedin more detail

Figure 5 shows the comparison of CR values obtained bythe methodse x-axis represents CRsite values whereas they-axis represents CRcell values Each point in the gurerepresents a cell in the scenario To ease the comparisonregression line is superimposed It is observed that even ifsite-level and cell-level CRs are related correlation is notstrong which is clear from the modest value of the de-termination coecient (ie R2 045)

In some cells the dierences between site- and cell-levelestimates are noticeable Specically relative dierencesrange from εsitecell minus61 (outlier 2) up to 128 (outlier1) with minus186 as the average value e following analysisis restricted to abnormal cases as the rest of cases showsimilar results for CRcell and CRsite deduced from the lowaverage value of the relative dierence (minus186) To nd thecause of such dierences a closer analysis is carried out onthe two extreme cases highlighted in Figure 5

e rst abnormal case (outlier 1) corresponds to a cellwith CR in a cell level much smaller than CR in a site level(ie CRcell≪CRsite) Figure 6 depicts the local environmentof this cell in more detail showing site locations (crosses)the Voronoi diagram (polygons) the cell azimuth (arrow)the 6 neighbor site locations (crosses with dotted circles) theCR in a site level (dashed arc) and the CR in a cell level (solidarc) As observed in the gure the analyzed cell has a nearbysite just in front of it but the other 5 nearest sites used tocalculate the CRsite are farther us CRsite (dashed circle) ismuch larger than CRcell (solid line)

e other abnormal case (outlier 2) corresponds toa cell where the CR estimated in a cell level is much largerthan in a site level (ie CRsite≪CRcell) Figure 7 shows thesituation where the closest site in front of a cell is muchfarther than the 6 nearest sites used to compute CRsite iscauses that the CR obtained by averaging ISDs CRsite

(dashed arc) is smaller than the one obtained from polygonsin the Voronoi diagram CRcell (solid arc)

Note that in both abnormal cases the correct solution isgiven by the proposed method as it can adapt to the localdierences between cells of the same site

Table 1 presents the numerical values of CR obtained inboth cases to quantify the dierence betweenmethods From

0500

10001500200025003000350040004500

700 900 1100 1300 1500 1700 1900

Outlier 2

Outlier 1

y = 145x ndash 44561R2 = 045

CRsite (m)

CRce

ll (m

)

Figure 5 Comparison of cell ranges obtained by the site-level andcell-level methods


the values it can be veried that CR relative dierence ina real environment can be of up to 128

Having detected large dierences in the CRs obtained byboth methods the following experiment checks the impact

of each method on the cell overshooting detection algorithmpresented in [7] For brevity the analysis is restricted to thetwo cases presented above e analysis is carried out bycomputing the overshooting indicator with the nominal CRobtained in a site and a cell level

Figure 8 represents the case of a nearby site located infront of the cell under study It is observed that CRmeas (grayll) is much larger than both CR estimates (CRcell repre-sented by a solid arc and CRsite represented by a dashedarc)e exact values of the measured CR and OVSR in a siteand cell level are shown in Table 2 As observed in Figure 8the arc dened by the measured CR largely overlaps with theVoronoi cell of the neighbor sites is is a clear indication

0 1 2 3 4 5 60

1

2

3

4

5

6

x (km)

y (km

)

CRcell

CRsite

Figure 6 Abnormal case 1 a nearby site located in the pointingdirection

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10 12 14 16x (km)

y (km

)

CRcell

CRsite

Figure 7 Abnormal case 2 a distant site located in the pointingdirection

Table 1 Comparison of CR estimates

Case Nearby site Distant siteCRcell (km) 040 410CRsite (km) 091 160εsitecell () 128 minus61

0

1

2

3

4

5

6

0 1 2 3 4 5 6x (km)

y (km

)

CRcell

CRmeasCRsite

Figure 8 Measured versus nominal cell ranges with a nearby site

Table 2 Measured versus estimated cell ranges

Case Nearby site Distant siteCRmeas (km) 267 403CRcell (km) 040 410CRsite (km) 091 160OVSRcell 668 098OVSRsite 293 252


that the tilting angle of the cell under study is incorrectlyplanned Table 2 conrms that with CRcell the cell over-shooting indicator has a larger value and the cell wouldtherefore be prioritized in next replanning actions Incontrast using CRsite leads to a lower value of the over-shooting indicator which would be interpreted by the op-erator as if the tilt angle was not very wrongly congured oreven properly set

Figure 9 shows the other case where the closest site infront of the cell is very distant In this case the measuredCR CRmeas is similar to the nominal CR in a cell levelCRcell Table 2 conrms that the OVSR for the cell-levelsolution is close to one (ie ratioc 098) showing that thereal and nominal CRs in a cell level are pretty close usno replanning action would be triggered In contrast themeasured CR CRmeas is much larger than the nominal CRin a site level CRsite causing that the OVSR for the site levelsolution is much larger than 1 (ie ratios 252) is mighttrigger an unnecessary replanning action

From these results it can be concluded that the proposedgeometric method for estimating the nominal cell rangeoutperforms the classical approach since it gives nominalCR estimates closer to those intended in the planning stage

51 Computational Complexity e two approaches tocompute the nominal CR are tested in two scenarios theurban scenario comprising 160 cells (referred to as S1) anda larger scenario consisting of 12500 cells (referred to as S2)covering 131000 km2 with very dierent environments (ruralurban and dense urban) Table 3 shows the time required tocalculate CRcell and CRsite in both scenarios It is observed thatin the small scenario both methods have a similar execution

time However in the large scenario the proposed geometricalmethod takes one-third of the time needed for the approachbased on averaging ISDs Specically in the large scenarioCRcell time is 71 s whereas CRsite time 225 s is is explainedby the computational complexity of the methods e com-plexity the method based on average ISDs isO(n2) where n isthe total number of sites as it has to compute the distancebetween every pair of sites to identify the 6 nearest sites Incontrast the complexity of the geometric method based onFortunes algorithm is O(n log n) ese results show that theproposed method is the best option for large scenarios

6 Conclusions

In this work a geometric method for estimating the nominalcell range on a cell-by-cell basis in a cellular network has beendescribed e inputs of the method are common planningdata such as site locations antenna azimuths and antennahorizontal beamwidths e method has been tested witha real dataset taken from a live LTE network During as-sessment the proposed method has been compared with theclassical approach of estimating cell range based on averagingthe inter-site distance Results have shown that in a realscenario relative dierence in the nominal CR estimatesobtained by the methods can be of up to 128 A visualinspection of the results in specic cases has shown that theproposed geometric method leads to more realistic CR valuesis is mainly due to its capability to consider local dierencesbetween sectors of the same site en CR estimates havebeen used to build a cell overshooting indicator for each cell asin [7] Results have shown that the classical approach fails todetect overshooting cells in some casese proposed methodis conceived to be integrated in network planning and op-timization suites running in the networkmanagement systemUnlike other approaches based on propagation predictions itis easy to develop as there are very eective codes in thepublic domain implementing Fortunes algorithm Executiontimes are low enough to obtain nominal cell ranges of largegeographical areas in seconds It can also be used to obtain thenominal cell range of a newly added cell and update that ofsurrounding cells e method can be applied to any radioaccess technology Likewise it can be extended to multilay-ered heterogeneous scenarios provided that a separateVoronoi diagram is built for each network layer

Conflicts of Interest

e authors declare that they have no consecticts of interest

Acknowledgments

is work has been funded by the Spanish Ministry ofEconomy and Competitiveness (TIN2012-36455) and

0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

x (km)

y (km

)

CRcell

CRmeasCRsite

Figure 9 Measured versus nominal cell ranges with a distant site

Table 3 Execution time

S1 S2CRcell time (s) 060 710CRsite time (s) 050 225


Optimi-Ericsson and Agencia IDEA (Consejerıa deCiencia Innovacion y Empresa Junta de Andalucıa ref59288) cofunded by FEDER

References

[1] J Laiho A Wacker and T Novosad Radio Network Planningand Optimisation for UMTS John Wiley amp Sons HobokenNJ USA 2006

[2] A R Mishra Fundamentals of Cellular Network Planning andOptimisation 2G25G3G Evolution to 4G John Wiley ampSons Hoboken NJ USA 2004

[3] E Amaldi A Capone and F Malucelli ldquoRadio planning andcoverage optimization of 3G cellular networksrdquo WirelessNetworks vol 14 no 4 pp 435ndash447 2008

[4] A R Mishra Advanced Cellular Network Planning and Op-timisation 2G25G3G Evolution to 4G John Wiley ampSons Hoboken NJ USA 2007

[5] A Simonsson M Johansson and M Lundevall ldquoAntennaand propagation parameters modeling live networksrdquo inProceedings of the Vehicular Technology Conference (VTCFall) pp 1ndash5 San Francisco CA USA September 2011

[6] J Ramiro and K Hamied Self-Organizing Networks (SON)Self-Planning Self-Optimization and Self-Healing for GSMUMTS and LTE JohnWiley amp Sons Hoboken NJ USA 2011

[7] V Wille M Toril and R Barco ldquoImpact of antennadowntilting on network performance in GERAN systemsrdquoIEEE Communications Letters vol 9 no 7 pp 598ndash600 2005

[8] T Halonen J Romero and J Melero GSM GPRS and EDGEPerformance Evolution Towards 3GUMTS John Wiley ampSons Hoboken NJ USA 2004

[9] W Jianhui and Y Dongfeng ldquoAntenna downtilt performancein urban environmentsrdquo in Proceedings of the MilitaryCommunications Conference (MILCOMrsquo96) vol 3 pp 739ndash744 Reston VA USA October 1996

[10] J Niemela T Isotalo and J Lempiainen ldquoOptimum antennadowntilt angles for macrocellular WCDMA networkrdquoEURASIP Journal on Wireless Communications and Net-working vol 2005 no 5 p 610942 2005

[11] J Lempiainen and M Manninen Radio Interface SystemPlanning for GSMGPRSUMTS Springer Science amp BusinessMedia Berlin Germany 2007

[12] A Wacker J Laiho-Steffens K Sipila and M Jasberg ldquoStaticsimulator for studying WCDMA radio network planningissuesrdquo in Proceedings of the 49th Vehicular TechnologyConference vol 3 pp 2436ndash2440 Houston TX USA May1999

[13] P M Shankar Introduction to Wireless Systems Wiley NewYork NY USA 2002

[14] A E Baert and D Seme ldquoVoronoi mobile cellular networkstopological propertiesrdquo in Proceedings of the Bird In-ternational Symposium on Algorithms Models and Tools forParallel Computing on Heterogeneous Networks pp 29ndash35Vancouver Canada July 2004

[15] J An K Yang J Wu N Ye S Guo and Z Liao ldquoAchievingsustainable ultra-dense heterogeneous networks for 5Grdquo IEEECommunications Magazine vol 55 no 12 pp 84ndash90 2017

[16] M Toril V Wille and R Barco ldquoIdentification of missingneighbor cells in GERANrdquo Wireless Networks vol 15 no 7pp 887ndash899 2009

[17] M De Berg O Cheong M Van Kreveld and M OvermarsComputational Geometry Introduction Springer BerlinGermany 2008

[18] F Aurenhammer ldquoVoronoi diagramsmdasha survey of a funda-mental geometric data structurerdquo ACM Computing Surveysvol 23 no 3 pp 345ndash405 1991

[19] M Sengoku H Tamura S Shinoda and T Abe ldquoGraph ampnetwork theory and cellular mobile communicationsrdquo inProceedings of the 1993 IEEE International Symposium onCircuits and Systems (ISCASrsquo93) pp 2208ndash2211 Chicago ILUSA May 1993

[20] K Guruprasad ldquoGeneralized Voronoi partition a new tool foroptimal placement of base stationsrdquo in Proceedings of the 5thInternational Conference on Advanced Networks and Tele-communication Systems (ANTS) pp 1ndash3 Bangalore IndiaDecember 2011

[21] A Landstrom H Jonsson and A Simonsson ldquoVoronoi-based ISD and site density characteristics for mobile net-worksrdquo in Proceedings of the Vehicular Technology Conference(VTC Fall) pp 1ndash5 Quebec City Canada September 2012

[22] S Luna-Ramırez M Toril M Fernandez-Navarro andV Wille ldquoOptimal traffic sharing in GERANrdquo WirelessPersonal Communications vol 57 no 4 pp 553ndash574 2011

[23] S Fortune ldquoA sweepline algorithm for Voronoi diagramsrdquoAlgorithmica vol 2 no 1ndash4 p 153 1987

[24] S Sesia M Baker and I Toufik LTE-Be UMTS Long TermEvolution From Beory to Practice John Wiley amp SonsHoboken NJ USA 2011

[25] httpesmathworkscomhelpmatlabrefvoronoihtml 2017


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network area and different propagation models that allow tosimulate path losses in a real environment [12] Static sim-ulators obtain an accurate estimation of network parametersbut assuming a high computational load especially for high-density scenarios us cellular network planning tools areused generally in the initial preplanning stage where timerequirements are not so restrictive Alternatively a geometriccalculation of nominal cell range is also commonly used foroperators Geometric calculation is uniquely based on physicalinformation of base stations (eg location of base stations)is approach consists of a simple method that allows toobtain with a considerable grade of accuracy an estimate ofcell range with a very low computational load by avoiding touse complex tools in its process us it is an efficient al-ternative used by operator to be integrated in their networkmanagement systems for optimization processes since it isable to be executed over large geographical areas in seconds

In an ideal cellular network with regular geometry thegeometric CR (ie the distance to cell edge) can be estimatedanalytically by using the inter-site distance (ISD) [13]Specifically the CR in a hexagonal grid scenario is ISD

3

radic

with omnidirectional antennas and ISD3 with trisectorizedantennas However in a live scenario sites are unevenlydistributed to deal with factors such as topography cost oravailability causing that cell shapes are irregular [14]Moreover new radio access technologies (4G5G) will resultin the deployment of a higher number of small cells in-creasing the complexity of physical layout [15] us the CRcannot be calculated by using the distance to the nearest site

Current operator practice is to compute the nominal CRof a site by averaging the distance to some of the nearest sitesen the number of nearest sites selected is limited in anattempt to avoid considering several rings of adjacent cellsUnfortunately the best number of nearest sites is difficult todefine as it depends on the specific scenario [16] Forsimplicity such a parameter is set to a fixed value leading toinaccurate CR estimates in many cases To solve theselimitations some authors use Voronoi tessellation [17 18] todefine the polygon representing the service (or dominance)area for every site [14 19ndash22] Such a diagram can then beused to choose the nearest sites more accurately and con-sequently to estimate the ISD [21] Once the nominal ISD isobtained CR is estimated as half of the ISD value e mainlimitation of this method is that the CR assigned to all cells ina site (ie cosited cells) is the same which is seldom true inthe live network Such inaccuracies can jeopardize thebenefits of network planning and optimization methods thatrely on CR estimates (eg [7])

In this work a geometric method to calculate the CRbased on Voronoi tessellation is presented e main nov-elties are that (a) CR is calculated on a cell (and not on a site)basis (b) CR depends on the antenna pointing direction ofeach cell (ie azimuth) and (c) the antenna beamwidthvalue is used to define the cell border (ie side of the servicearea)us a more accurate estimation of the CR is obtainedwith a low computational cost e analysis is extended bychecking the impact of the proposed method on the per-formance of the cell overshooting detection algorithm de-scribed in [7]

e main contributions of this work are (a) a novel andcomputationally efficient method to estimate the CR on a per-cell basis suitable for radio network optimization processes(b) a comprehensive analysis of the proposedmethod in a realscenario showing the limitations of current practice and howthese can be solved by the new approach and (c) an eval-uation of the impact of CR estimates on the performance ofa classical cell overshooting detection algorithm in a live LTEnetwork

e rest of the work is organized as follows Section 2reviews the current method used to calculate the CR on a sitebasis Section 3 describes the method proposed to calculatethe CR on a cell basis Section 4 shows the results obtained bythe method in a real scenario Finally Section 5 presents themain conclusions of the study

2 Calculation of Cell Range on a Site Basis

In a network consisting of n sites an estimate of CR can beobtained by calculating the average distance to the k nearestsites where klt n [21] us the average ISD from site s tothe k nearest sites is defined as

ISDsk 1k

1113944

k

m1dist(s m) (1)

where dist(s m) is the Euclidean distance from site s to sitem Once the average ISD of site s is calculated with the k

closest neighbor sites the CR of cell c located in site s iscalculated as

CRsite(c)

ISDsk

2 (2)

where ISDsk is the ISD of site s calculated by using the k

nearest sites Note that CRsite(ci) CRsite(cj) forall ci cj isin sFigure 1 shows an example of how the current method

works CRsite is represented by a dashed circumference andthe pointing direction of cell by a solid arrow In this exampleit is assumed that the number of nearest sites used for ISDcalculation (represented by crosses with dotted circles) is 6and the solid arrow represents the pointing direction of thecell From the figure it is clear that the previous method hasseveral limitations the foremost of which is the calculation ofthe ISD at a site level causing that all cells in the same site areassigned the same CR value (represented by a dashed arrow)Moreover the CR of a cell is only based on the distancebetween the site where the cell is located and surroundingsites However in a real network the service area of a cell withdirectional antennas is mainly determined by the sites that arein the pointing direction of (ie in front of) the cell

3 Calculation of Cell Range on a Cell Basis

To solve the above-described problems the CR should becomputed in a cell level making the most of geometricconsiderations is is done in the method described nexte method consists of three stages Voronoi tessellationcell border definition and computation of average distanceto cell border











0 5 10 15 20 25 30 350

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dist(P L) 1lLintlL

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2 + ypprime2

radicdxprime (5)




dx 1



radic







i1 lLi

(7)







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5 Results










0500

10001500200025003000350040004500

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Outlier 2

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y = 145x ndash 44561R2 = 045

CRsite (m)

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6 Conclusions




Acknowledgments


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Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

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Biomedical Imaging





RoboticsJournal of









Volume 2018



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0 5 10 15 20 25 30 350

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x (km)

y (km

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0 05 1 15 2 25 3 35 40

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L2L1

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CD

s

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y (km

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x (km)


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5

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x (km)

y (km

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CRsite






dist(P L) 1lLintlL

0


2 + ypprime2

radicdxprime (5)




dx 1



radic







i1 lLi

(7)







Y

X

Yprime

Xprime

P

xp

yp

yprimep

xprimep

L









CRcell(c) (8)



5 Results










0500

10001500200025003000350040004500

700 900 1100 1300 1500 1700 1900

Outlier 2

Outlier 1

y = 145x ndash 44561R2 = 045

CRsite (m)

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ll (m

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CRsite


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6 Conclusions




Acknowledgments


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Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in







dist(P L) 1lLintlL

0


2 + ypprime2

radicdxprime (5)




dx 1



radic







i1 lLi

(7)







Y

X

Yprime

Xprime

P

xp

yp

yprimep

xprimep

L









CRcell(c) (8)



5 Results










0500

10001500200025003000350040004500

700 900 1100 1300 1500 1700 1900

Outlier 2

Outlier 1

y = 145x ndash 44561R2 = 045

CRsite (m)

CRce

ll (m

)







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y (km

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CRcell

CRsite


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6 Conclusions




Acknowledgments


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CRmeasCRsite






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Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in










CRcell(c) (8)



5 Results










0500

10001500200025003000350040004500

700 900 1100 1300 1500 1700 1900

Outlier 2

Outlier 1

y = 145x ndash 44561R2 = 045

CRsite (m)

CRce

ll (m

)







0 1 2 3 4 5 60

1

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4

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6

x (km)

y (km

)

CRcell

CRsite


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CRsite




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CRmeasCRsite










6 Conclusions




Acknowledgments


0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

x (km)

y (km

)

CRcell

CRmeasCRsite






References
































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in








0 1 2 3 4 5 60

1

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x (km)

y (km

)

CRcell

CRsite


0

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0 2 4 6 8 10 12 14 16x (km)

y (km

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CRcell

CRsite




0

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0 1 2 3 4 5 6x (km)

y (km

)

CRcell

CRmeasCRsite










6 Conclusions




Acknowledgments


0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

x (km)

y (km

)

CRcell

CRmeasCRsite






References
































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in









6 Conclusions




Acknowledgments


0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

x (km)

y (km

)

CRcell

CRmeasCRsite






References
































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in





References
































Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in









Advances in

FuzzySystems


Volume 2018













Journal of

Journal of



Hindawi


Advances in

Multimedia


Biomedical Imaging





RoboticsJournal of









Volume 2018



Advances in




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AGeometricMethodforEstimatingtheNominalCellRangein ...downloads.hindawi.com/journals/misy/2018/3479246.pdf · closest neighbor sites, the CR of cell clocated in site sis ... planning