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Optimization Methodsfor UMTS Radio Network PlanningAndreas Eisenblatter 1 Armin Fugenschuh 2 Hans-Florian Geerdes3 DanielJunglas2 Thorsten Koch3 and Alexander Martin21 Atesio GmbH Berlin2 Technische Universitat Darmstadt3 Konrad-Zuse-Zentrum fur Informationstechnik Berlin (ZIB)Abstract The UMTS radio network planning problem poses the challenge of designinga cost-e_ective network that provides users with su_cient coverage andcapacity We describe an optimization model for this problem that is based oncomprehensive planning data of the EU project Momentum We present heuristicmathematical methods for this realistic model including computational results1 IntroductionThird generation (3G) telecommunication networks based on UMTS technologyare currently being deployed across Europe Network operators faceplanning challenges for which experiences from 2G GSM barely carry overThe EU-funded project Momentum developed models and simulation methodsfor UMTS radio network design Among others we devised network optimizationmethods that are based on a very detailed mathematical modelMomentum constitutes of course not the only e_ort to advance methodsfor UMTS radio network planning In [13] several optimization modelsare suggested and heuristics methods such as tabu search or greedy are usedto solve them Integer programming methods for planning are shown in [12]power control and capacity issues are treated in [411] Many technical aspectsof UMTS networks and some practice-driven optimization and tuningrules are given in [10] Optimization of certain network aspects without siteselection is treated in [9]Within this article we focus on heuristic algorithms to solve the optimizationtask Methods based directly on the mathematical mixed integer programmingmodel presented in [58] will be presented in the future The preliminarycomputational results obtained within Momentum are very promising2 Optimization ApproachOur optimization approach is snapshot based A snapshot is a set of users thatwant to use the network at the same time We consider several snapshots at This work is a result of the European Project Momentum IST-2000-28088 Partly funded by the DFG Research Center Mathematics for key technologies2 Andreas Eisenblatter et alonce and try to _nd a network that performs well for these snapshots and iscost-e_ective at the same time Snapshots are typically drawn according toservice-speci_c spatial tra_c load distributions21 Optimization ModelThe following decisions have to be made for planning a networkSite Selection From a set S of potential sites (roughly equivalent to rooftops where antenna masts could be placed) a subset of sites to be openedhas to be chosenInstallation Selection At each opened site various installations (antennacon_gurations) can be employed at di_erent antenna locations From theset I of all possible installations a subset has to be selected The numberof antennas per site is limited three-sectorized sites are typicalMobile Assignment For each of the users represented by the set M ofmobiles that is possibly distributed over several snapshots we have todecide which installation serves which mobile device This is in practiceoften done on a best-server basis each mobile is served by the installationwhose signal is strongest at the mobiles locationPower Assignment Once the users are attached to installations a feasiblecombination of power values has to be found This includes transmissionpowers in uplink and downlink as well as the cells pilot powersThis is formulated as a MIP in [58] with binary variables corresponding tothe _rst three decisions and fractional power variables p

The coverage and capacity requirements are reected in so-called CIRinequalities (Carrier-to-Interference-Ratio) that have to hold for each userThese inequalities at the core of our optimization model follow the patternReceived SignalInterfering Signals + Noise _ ThresholdUsing the notation from Table 1 the CIR inequality for the uplink readsmj pm_pj 1048576 mj _m pm _ _m (1a)The CIR inequality for the downlink is somewhat more complicated sincecode orthogonality has to be considered for signals from the same celljm pj mjm_1 1048576 m_ __pj 1048576 _m pjm_+Pi6=j im _pi + _m_ _m (1b)UMTS Radio Network Planning 3_m _ 0 noise at mobile m_m _m 2 [0 1] uplinkdownlink activity factor of mobile mm 2 [0 1] orthogonality factor for mobile m_m _m _ 0 uplinkdownlink CIR target for mobile mmj jm 2 [0 1] attenuation factors between mobile m and installation jpm 2 R+ uplink transmit power from mobile mpim 2 R+ downlink transmit power from installation i to mobile m_pj 2 R+ Total received uplink power at installation j (in the snapshot)_pj 2 R+ Total downlink power emitted by installation j (in the snapshot)Table 1 Notations in CIR inequalities22 Planning DataInput data for our optimization model is derived from the planning scenariosdeveloped within the EU project Momentum The full contents of thesescenarios are described in [7] several scenarios of them are publicly availableat [13] The scenarios contain detailed data on aspects relevant to UMTSradio network planning The data can be classi_ed as followsRadio and Environment All aspects of the outside world This includesradio propagation UMTS radio bearers information on the terrain (suchas height or clutter data) and background noiseInfrastructure All aspects that are to some extent under the control ofthe network operator This includes base station hardware antennaspotential sites and antenna locations and radio resource managementUser Demand All aspects related to users such as o_ered services (e gvideo telephony media streaming) user mobility usage speci_cs andtra_c dataThe potential sites and installations for the planning scenario The Hagueare shown in Fig 1(a) the average user demand is illustrated in Fig 1(b)Darker areas indicate higher tra_c load here the users in the snapshots aregenerated according to this distribution together with additional informationon the used services equipment and mobility The actual parameters for theoptimization model [8] and the CIR inequalities (1) in particular are derivedfrom the information in the planning scenarios Table 2 gives an overview23 Preprocessing Coverage and Capacity AnalysisBefore an automatic planning process can be employed the input data isanalyzed in order to detect coverage and capacity shortages The coverageorientedanalysis is based on propagation path loss predictions for all availablesites and their antenna locations Capacity shortages are harder to detect Weuse a heuristic which is based on a tentative network design using all availablesites Employing methods similar to the ones described in [414] the average

4 Andreas Eisenblatter et al(a) Potential sites and antennacon_gurations (installations)(b) Tra_c distributionFig 1 Example of planning scenario (The Hague)Planning Scenario ParameterEquipment loss Connection lossPropagation loss Antenna gainUsage loss (e g body)9gt=gtSignal attenuation mjjmBLER requirementsUser speedRadio bearer)CIR targets _m_mUser equipment User mobilityRadio beareroActivity factors _m_mClutter typeChannel modeloOrthogonality mTable 2 Derivation of parameters from the data scenariosup- and downlink load per cell of this tentative network can be computede_ciently If the tra_c load is too high for the potential infrastructure in someregions these can be localized as overloaded cells in the tentative networkNotice that this approach merely provides lower bounds on the achievablenetwork up- and downlink capacity Methods for estimating an upper boundon the network capacity are under development3 Heuristic Planning MethodsIt turned out that solving mixed-integer program as described in its maincomponents in Section 21 exactly (using for example Cplex 81) takes signi_cant time and computing resources even for moderate sized scenariosTherefore we developed various heuristic algorithms that aim at obtaininggood (not necessarily optimal) solutions within reasonable running timesUMTS Radio Network Planning 5The explanation of all these methods including greedy-type heuristics tabusearch simulated annealing and evolution algorithms is beyond the scopeof this document We restrict ourselves to the most successful one the Set-Covering Heuristic The interested reader may refer to [56] for the descriptionof the other methods31 Set-Covering HeuristicThe idea of the Set-Covering Heuristic is to _nd for each installation i 2 I aset Mi of mobiles that this installation can cover (we will explain this inmore detail below) We assign a cost ci to each of these sets Mi and then _nda set J = fj1 jkg _ f1 jIjg of indices such that each mobile m 2M is covered by at least one Mj j 2 J and for which the cost cJ =Pj2J cj isminimal Each index in J corresponds to an installation and we will simplyselect the installations that are given by JIn order to compute the set Mi for a given installation i 2 I we proceedas follows First of all we ignore all other installations j 2 I j 6= i that iswe assume they are not selected We then consider each mobile m 2M anddetermine its distance dmi to installation i We de_ne this distance to bedmi = 1=(mi + im) if both attenuation values are non-zero (attenuation isset to zero if the corresponding pathloss exceeds a certain threshold) If theup- or downlink attenuation between mobile m and installation i is zero thismobile can never be served by installation i We then set dmi = 1

Let M denote the set of mobiles for which dmi lt 1 We initially setMi = and sort the mobiles inM by non-decreasing values of dmi Accordingto this list we check for each mobile m whether installation i can serve all mobilesin Mi [fmg simultaneously In the positive case we set Mi = Mi [fmgThe feasibility check is based on a Power Assignment Heuristic which basicallysolves two systems of linear equations that arise when inequalities (1a)and (1b) are replaced with equations see [56] for detailsThe Power Assignment Heuristic does not only check whether installationi can serve all mobiles in Mi [ fmg but also _nds minimal transmissionpowers for each mobileinstallation connection in the positive case Thesetransmission powers are used to compute a score ci for the resulting set Mici =Xm2Mi

_p +Xm2Mi

_p + Ci (2)where the terms p and p denote up- and downlink transmission powersas returned by the Power Assignment Heuristic and Ci is the cost that isassociated with installing installation i The factors _ and _ are used toweight the transmission powers in the cost for set Mi From iterating overthe list of mobiles with dmi lt 1 we obtain a set Mi together with a score(or cost) ci as desired see Algorithm 16 Andreas Eisenblatter et alAlgorithm 1 Covering a set of mobiles with a given installationInput Installation i 2 I and mobiles M _M that i may potentially cover1 Determine the mobileinstallation distance dmi for each mobile in M2 Sort Mby non-decreasing distance to i Denote result by Msorted3 Set Mreturn = and creturn = Ci4 For each mobile m 2 Msorted do(a) Set M0 = Mreturn [ fmg(b) Use Power Assignment Heuristic to check whether installation i canserve all mobiles in M0(c) If so set Mreturn = M0 and update creturn according to equation (2)5 Return Mreturn and creturnGiven the sets Mi and associated costs ci for each installation we de_nea set-covering problem Let A 2 RjMj_jIj denote the incidence matrix of M and the Mi (i e aij = 1 if and only if mobile i is in Mj) and introducebinary variables xj j = 1 jIj that are set to one if set Mj is selected andto zero otherwise The set-covering problem then reads as followsminnXi2Icixi j Ax _ 1 x 2 f0 1gjIjo(3)Notice that in the above description we implicitly assume thatSi2IMi =MIf this is not the case we simply replace M bySi2I MiAs stated earlier each set Mi is in direct correspondence with an installationi 2 I Thus given an optimal solution x 2 f0 1gjIj to (3) we simplyselect all installations i 2 I for which xi = 1 and install themThe Set-Covering algorithm as described above has three problems_ Model (3) is too simplistic it does for example not take into accountthat installations are hosted at sites Opening such a site requires a certainamount of money (typically much more than the cost for a single

antenna) and for each site there are minimum and maximum numbers ofinstallations that can be simultaneously installed_ Due to the fact that we ignore all other installation while computing theset Mi for installation i we also ignore potential interference from theseinstallations The sets Mi tend to overestimate the coverage and capacityof the installations_ The set-covering problem as de_ned in (3) may not have a feasible solutionThis can especially happen if tra_c is high and the number ofinstallations that are available per site is limitedAll three problems can be resolved In the _rst case the additional constraintsrelated to sites can easily be added to (3) In the second case weshrink the sets Mi at the end of Algorithm 1 using a shrinkage factorfshrink Or we impose some heuristically determined interference via a loadfactor fload and require that the installation may not use more than thatUMTS Radio Network Planning 7percentage of its maximum load during the algorithm We distinguish twocases if (3) is infeasible In case fshrink and fload equal one we declare theinput infeasible (which is true up to the assumption that we have performedan optimal mobile assignment) In case at least one of these factors is lessthan one we modify the factors and iterate32 ResultsUsing the Set-Covering Heuristic we are able to compute good solutions tolarge-scale real world instances We illustrate one such result for the TheHague scenario mentioned in Section 2 The instance contains 76 potentialsites 912 potential installations and 10800 mobiles partitioned into 20snapshots (approximately 540 mobiles per snapshot) For this instance weobtained the best result using a combination of the heuristic interferenceand heuristic shrinking strategies by setting fshrink = 07 and fload = 06With these modi_cations the Set-Covering heuristic took 66 minutes ona 1GHz Intel Pentium-III processor with 2GB RAM to _nd the _nal installationselection Fig 2 depicts the solution Fig 2(a) shows the selectedinstallationsantennas the load in the network is illustrated for uplink anddownlink in Fig 2(b) and Fig 2(c) (the light areas denote a load of about2530 the darker areas have less load) Our result was evaluated using advancedstatic network simulation methods developed within the Momentumproject [14] The methods reported at most 3 missed tra_c(a) Selected antennas (b) Uplink load (c) Downlink loadFig 2 Heuristic planning solution4 ConclusionWe presented an optimization problem of planning cost-e_ective UMTS radionetworks The model we use reects many aspects of reality that are essential8 Andreas Eisenblatter et alfor planning UMTS networks To our knowledge this is the most detailed andcomprehensive planning model in literature Based on this model we havedescribed some heuristic network planning methods that work well in practiceand lead to good resultsReferences1 E Amaldi A Capone F Malucelli Planning UMTS base station locationOptimization models with power control and algorithms IEEE Transactionson Wireless Communications 20022 E Amaldi A Capone F Malucelli F Signori UMTS radio planning Optimizingbase station con_guration In Proceedings of IEEE VTC Fall 2002volume 2 pp 768772 20023 E Amaldi A Capone F Malucelli F Signori Optimizing base station locationand con_guration in UMTS networks In Proceedings of INOC 2003pp 1318 20034 D Catrein L Imhof R Mathar Power control capacity and duality of upanddownlink in cellular CDMA systems Tech Rep RWTH Aachen 20035 A Eisenblatter E R Fledderus A Fugenschuh H-F Geerdes B Heideck D Junglas T Koch T Kurner A Martin Mathematical methods for automaticoptimisation of UMTS radio networks Tech Rep IST-2000-28088-

MOMENTUM-D43-PUB IST-2000-28088 MOMENTUM 20036 A Eisenblatter H-F Geerdes D Junglas T Koch T Kurner A Martin Final report on automatic planning and optimisation Tech Rep IST-2000-28088-MOMENTUM-D46-PUB IST-2000-28088 MOMENTUM 20037 A Eisenblatter H-F Geerdes T Koch U Turke MOMENTUM public planning scenarios and their XML format Tech Rep TD(03) 167 COST 273Prague Czech Republic Sep 20038 A Eisenblatter T Koch A Martin T Achterberg A Fugenschuh A Koster O Wegel R Wessaly Modelling feasible network con_gurations for UMTSIn G Anandalingam and S Raghavan editors Telecommunications NetworkDesign and Management Kluwer 20029 A Gerdenitsch S Jakl M Toeltsch T Neubauer Intelligent algorithms forsystem capacity optimization of UMTS FDD networks In Proc IEEE 4thInternational Conference on 3G Mobile Communication Technology pp 222226 London June 200210 J Laiho A Wacker T Novosad editors Radio Network Planning and Optimizationfor UMTS John Wiley amp Sons Ltd 200111 K Leibnitz Analytical Modeling of Power Control and its Impact on WidebandCDMA Capacity and Planning PhD thesis University of Wurzburg Feb 200312 R Mathar and M Schmeink Optimal base station positioning and channel assignmentfor 3G mobile networks by integer programming Ann of OperationsResearch (107)225236 200113 Momentum Project Models and simulations for network planning and controlof UMTS httpmomentumzibde 2001 IST-2000-28088 MOMENTUM14 U Turke R Perera E Lamers T Winter C Gorg An advanced approach for QoS analysis in UMTS radio network planning In Proc of the 18th InternationalTeletra_c Congress pp 91100 VDE 2003

The coverage and capacity requirements are reected in so-called CIRinequalities (Carrier-to-Interference-Ratio) that have to hold for each userThese inequalities at the core of our optimization model follow the patternReceived SignalInterfering Signals + Noise _ ThresholdUsing the notation from Table 1 the CIR inequality for the uplink readsmj pm_pj 1048576 mj _m pm _ _m (1a)The CIR inequality for the downlink is somewhat more complicated sincecode orthogonality has to be considered for signals from the same celljm pj mjm_1 1048576 m_ __pj 1048576 _m pjm_+Pi6=j im _pi + _m_ _m (1b)UMTS Radio Network Planning 3_m _ 0 noise at mobile m_m _m 2 [0 1] uplinkdownlink activity factor of mobile mm 2 [0 1] orthogonality factor for mobile m_m _m _ 0 uplinkdownlink CIR target for mobile mmj jm 2 [0 1] attenuation factors between mobile m and installation jpm 2 R+ uplink transmit power from mobile mpim 2 R+ downlink transmit power from installation i to mobile m_pj 2 R+ Total received uplink power at installation j (in the snapshot)_pj 2 R+ Total downlink power emitted by installation j (in the snapshot)Table 1 Notations in CIR inequalities22 Planning DataInput data for our optimization model is derived from the planning scenariosdeveloped within the EU project Momentum The full contents of thesescenarios are described in [7] several scenarios of them are publicly availableat [13] The scenarios contain detailed data on aspects relevant to UMTSradio network planning The data can be classi_ed as followsRadio and Environment All aspects of the outside world This includesradio propagation UMTS radio bearers information on the terrain (suchas height or clutter data) and background noiseInfrastructure All aspects that are to some extent under the control ofthe network operator This includes base station hardware antennaspotential sites and antenna locations and radio resource managementUser Demand All aspects related to users such as o_ered services (e gvideo telephony media streaming) user mobility usage speci_cs andtra_c dataThe potential sites and installations for the planning scenario The Hagueare shown in Fig 1(a) the average user demand is illustrated in Fig 1(b)Darker areas indicate higher tra_c load here the users in the snapshots aregenerated according to this distribution together with additional informationon the used services equipment and mobility The actual parameters for theoptimization model [8] and the CIR inequalities (1) in particular are derivedfrom the information in the planning scenarios Table 2 gives an overview23 Preprocessing Coverage and Capacity AnalysisBefore an automatic planning process can be employed the input data isanalyzed in order to detect coverage and capacity shortages The coverageorientedanalysis is based on propagation path loss predictions for all availablesites and their antenna locations Capacity shortages are harder to detect Weuse a heuristic which is based on a tentative network design using all availablesites Employing methods similar to the ones described in [414] the average



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