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Integer Programming Methods

for UMTS Radio Network Planning,

Andreas Eisenblatter1, Armin Fugenschuh2, Hans-Florian Geerdes3, Daniel Junglas2,Thorsten Koch3, and Alexander Martin2

1 Atesio GmbH, Berlin, eisenblaetter@atesio.de2 Darmstadt University of Technology (TUD), Department of Mathematics,

{fuegenschuh,junglas,martin}@mathematik.tu-darmstadt.de3 Zuse Institute Berlin (ZIB), {geerdes,koch}@zib.de

Abstract. Radio network planning for UMTS technology is a relevant task for operatorsin the current roll-out phase. We recall a mathematical mixed-integer programming modelfor planning cost-efficient radio networks under network quality constraints. Based on thismodel, we present network planning methods. Computational results are given for twolarge-scale, realistic scenarios, and we compare the mixed-integer programming results to

the outcome of heuristic methods.

1 Introduction

Third generation (3G) telecommunication networks based on UMTS technology are currently rolled-outacross Europe. Radio network planning is an important task in this context. The WCDMA technologyemployed for UMTS radio access differs significantly from traditional GSM networks, experiences from2G planning are therefore only useful to a limited extent. The EU-project Momentum developed modelsand methods for automatic UMTS radio network planning and evaluation.

We briefly survey a mathematical mixed integer linear program (MIP) that captures the radio networkplanning task. The full model turns out to be too complex to be solved by global optimisation for scenariosof relevant size. We therefore present a two phase planning approach that involves local optimisation

based on the MIP model. We report on computational results for realistic scenarios that have beenachieved with this procedure. The results are obtained using a MIP solver (Cplex). Even though oursnapshot-based approach does not directly consider the classical key performance indicators (KPI), weshow that the results achieve good values there. They also compare favourably to those obtained fromoptimisation heuristics presented in [1].

Optimisation models similar to ours are suggested in [24], heuristics methods such as tabu search orgreedy are used to solve instances. Many technical aspects of UMTS networks and some practice-drivenoptimisation and tuning rules are given in [5]. Integer programming methods for 3G network planning arealso presented in [6], power control and capacity issues with particular emphasis on network planning aretreated in [7, 8]. Pilot power optimisation under coverage constraints using mathematical programmingis performed in [9]. Optimisation of network quality aspects not involving site selection is treated in [10].

2 The Optimisation Model

Our mathematical model of the radio network planning task was already presented in [11, 12]. In ourmodel, the objective function to be minimised is network cost. Network quality is a constraint. Themodel can be characterised as a static snapshot-based system level simulator in which network designdecisions are left open. The input to the model is twofold: user snapshots and potential sites and installa-tions. Snapshots are random realisations of user load distributions containing users of different services.According to their service and mobility, the users have varying requirements on quality of service.

A feasible solution to the model represents one network design that provides the present users withtheir required degree of radio service in all snapshots simultaneously. The network cost objective functionto be minimised among all feasible solutions corresponds to the number of cells/installations used in thenetwork.

This work is a result of the European Project Momentum, IST-2000-28088 Supported by the DFG research center Mathematics for key technologies (FZT 86) in Berlin.

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2.1 Decisions

The decisions to be made are modelled by variables and can be grouped into two categories. The firstcategory contains the global design decisions for the resulting radio network:1. Site selection is about choosing sites from the set S of potential sites.2. Installation selection is about picking typically up to three antenna configurations (installations) for

sites from all feasible installations I.

3. Pilot power optimisation aims at minimising the uniform pilot power for all (macro cell) installations.The second category contains decisions that have to be made in all snapshots individually in order toassess the networks performance:4. Mobile assignment is about deciding the serving installations for each user in a snapshot. Best-server

restrictions typically apply, i. e., the installation with the strongest received pilot signal serves theusers mobile. Soft hand-over is not considered.

5. Power assignment is about determining the up- and downlink transmission powers for all connectionsin all snapshots. The powers have to be chosen such that interference is controlled and all users areserved as required, see below.

These decisions are formulated as a MIP in [12, 11], with binary variables corresponding to items 1, 2,and 4, and fractional power variables p for items 3 and 5. This optimisation model blends aspects fromset covering, facility location, and knapsack problems.

2.2 Network Quality: CIR Constraints

A central part of the model are coverage and capacity requirements encoded in CIR inequalities (Carrier-to-Interference-Ratio). Using the notation from Table 1 and provided that mobile m is serviced frominstallation j (which is subject to a decision), these inequalities for up- and downlink read as follows:

mj pm

pj mj

m p

m

m (1a)

jm pjm

jm

1 m

pj

m p

jm

+

i=j im p

i + m

m (1b)

The downlink case is more complex than the uplink because of interference reduction due to code orthog-

onality within cells. (Notice, strictly speaking code orthogonality does not apply for the synchronisationchannel.) The constraint imposed on network quality is that these CIR constraints have to hold foreach user. The threshold values m,

m depend on the users service and on user mobility. This model

assumes perfect power control. The chosen power values also enter the objective function, but by scalingthe network cost is strictly prioritised. This ensures that a power-efficient configuration is chosen amongall networks with minimal cost.

Table 1. Notations in CIR inequalities (single snapshot case)

m 0 noise at mobile mm,

m [0, 1] uplink/downlink activity factor of mobile m

m [0, 1] orthogonality factor for mobile mm,

m 0 uplink/downlink CIR target for mobile m

mj, jm [0, 1] attenuation factors between mobile m and installation jpm R+ uplink transmit power from mobile mpim R+ downlink transmit power from installation i to mobile mpj R+ Total received uplink power at installation j

pj R+ Total downlink power emitted by installation j

The basic mathematical optimisation model is used in four cases. The first and third cases areaddressed below, the second and fourth cases are discussed in [1].1. The original model is solved for small subproblems using mathematical programming techniques.2. The original model is solved for small subproblems using heuristics.3. We solve modified/simplified models using mathematical programming techniques on small subprob-

lems.4. We solve modified/simplified models using heuristics on the original problem.

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3 Network Planning by Solving MIPs

We rely on detailed specification of the planning task in terms of site locations, equipment capabilities,user demand, planning constraints, etc., see [1214].

3.1 Finding Candidate Installations

The first important aspect of input data provision is the definition of candidate installations for eachsite (consisting of an antenna location, type, height, azimuth, electrical and mechanical tilt). Our basicapproach is to represent each feasible azimuth (horizontal antenna direction) by one suitable candidateinstallation with a fixed antenna type, height, electrical and mechanical tilt. Azimuths might, for example,be infeasible if the antenna would point directly towards a nearby building. For a given azimuth, aninstallation is selected such that the resulting cell matches the expected traffic load in the respectivedirection best. In high traffic areas cells have to be smaller, which can, e. g., be achieved by tilting anantenna down. In areas with less traffic, cells may be bigger and coverage considerations gain importance.The shape of the cell resulting from a certain installation can, however, only be approximated at thistime, since the actual cell shape depends heavily on the design of the surrounding network.

From the resulting collection of installations for each potential site, two candidate sets are derived. Astar contains the candidate installations for all feasible azimuths in steps of 10 ; examples are shown in

Fig. 1(a). A clover leaf is a subset of a star with at most three installations, all of them differ in azimuthby at least 90. The clover are used as pre-configured three-sectorised cells, cf. Fig. 1(b).

(a) Stars (b) Clover leaves

Figure 1. Two types of site sets used for planning, Berlin Alexanderplatz; c Digital Building Model Berlin(2002), E-Plus Mobilfunk GmbH & Co. KG

3.2 Two Phase Planning Approach

The MIP-based optimisation is typically performed on the basis of 510 traffic snapshots at a time us-ing mathematical programming techniques. In principle, the model presented in Section 2 is capable ofsolving the network planning problem in one step. In order to do so, one would consider all conceiv-able/desired candidate installations simultaneously. However, experiments have shown that even whenonly the restricted candidate sets containing one single installation per azimuth the stars introducedin Section 3.1 are admitted, it becomes impossible to even find feasible solutions to the model withreasonable computing resources. This still holds true when only a single snapshot is considered. On theother hand, if we admit too few candidate installations, we cannot be sure whether or not most relevantdesign options have been considered.

Our solution to this dilemma is to subdivide the network planning task into several subproblems.This subdivision corresponds to fixing some of the decisions outlined in Section 2.1 and deciding theoptimal values for the remaining ones that are left open.

1. For site selection, all potential sites are pre-configured with clover leaves, the MIP solution determineswhich sites to be used in the network design.

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2. Starting with the result from (1), a local optimisation is carried out successively with a few neighbouringselected sites at a time. The MIP solution determines the installations to use, given that the surroundingnetwork remains unchanged. The resulting network is the basis for the next iteration, where anotherset of sites is optimised.

In terms of the decisions outlined in Section 2.1, the procedure can be described as follows: we first

fix some reasonable values for the Decisions 2 by selecting some installations. Given these decisions, weoptimise only on the variables corresponding to Decisions 1 (site selection). Given the selected sites, wenow successively optimise manageable portions of 2.

Site Selection. At this point, we do not take into account different configurations for a site. We admitonly the clover leaves, thereby fixing the decisions on installation selection. The only option left is toeither use the pre-configured site in its entirety or to switch it off. Since our objective is to minimisethe network cost, the ensemble of sites is chosen such that the traffic can be handled by as few sites aspossible.

The result of this first step is a network that has enough capacity to handle the offered traffic. Sincethe individual sites have been configured independently based on traffic consideration (cf. Section 3.1),the resulting network might still be improvable.

Local Optimisation. The sites to be optimised are supplied with a star as set of candidate installations.For the other sites, the configuration found in earlier steps is used. Despite performing only a localoptimisation, this procedure fully takes the surrounding network configuration into account, includingall interference stemming from surrounding cells. Sites that have a high level of mutual interference areselected to be optimised together in order to reduce the coupling.

In this step, it is also feasible to close down entire sites to further reduce network cost. This is some-times possible due to an optimised adjustment of neighbouring cells. The power terms in the objectivefunction also lead to more efficient result networks.

4 Planning Results

We come to computational results of our MIP based automatic planning approach. As input data we usetwo data sets from the Momentum planning scenarios [13], from which the different parameters in themodel are calculated, cf. Table 1. The example scenarios have different characteristics: the scenario forThe Hague, which is publicly available [14], has propagation grids with a resolution of 50 m. The Berlinscenario is not publicly available. It contains propagation data at a resolution of 5 m, derived from a 3Dpropagation model and taking high resolution building data into account.

The results are based on the local optimisation approach described Section 3. The site selection andlocal site optimising MIPs could be solved to optimality within a time ranging from a few minutes toone hour (using Cplex 8.0 on a standard PC with 2.4 GHz Pentium 4 processor and 2 GB RAM). Sincethere is no data on operational UMTS networks available, we lack a meaningful point of reference for the

site selection step. We thus merely state the result of the site selection step and illustrate the progressmade in our approach by comparing the following networks:

1. The reference network consists of the selected sites equipped with a regular three-sectorised layout ofcells. This regular layout was specified by the respective operator in the Momentum consortium.

2. The site selection network is the actual outcome of the site selection process: instead of a regularlayout we use the predetermined clover leaf configurations determined in the procedure described inSection 3.1.

3. The local optimisation result is the result of the iterated local optimisation routine described in Sec-tion 3.2.

Network quality is a constraint in our model in the sense that for all users in a snapshot the referringCIR target has to be reached within our perfect power control model. This means, that we do not directly

take into many classical KPI. Nevertheless, our results turn out to perform well also under the traditionalanalysis, cf. Figs. 3, 5, and Tables 2 and 3.

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4.1 The Hague

With a total of 76 potential sites, this scenario contains more sites than are needed for providing therequested capacity. The site selection step of our approach was therefore important to reduce the modelscomputational complexity. In this first optimisation, 26 sites were selected. The network configurationafter locally optimising all sites cell configuration is shown in Fig. 2(a). The number of sites has reduced

to 13. The coverage of our network is sufficient, as can be seen in Fig. 2(b) (note that the scale has beenadapted to take into account a possible indoor loss). However, since no building information is containedin the propagation grids, there could be indoor situations with bad signal reception for our network ifanalysed on the basis of more refined propagation data.

(a) Best server map (b) Coverage map

Figure 2. Planning result for The Hague

The load distribution for the downlink in the network at the different stages of the algorithm isshown in Fig. 3. The downlink direction is more demanding than the uplink in the Momentum trafficspecifications, since there are some asymmetric services with high bit rate (such as video streaming).The pictures show the gradual improvement achieved in our approach. In the reference network layout,no adjustment of installations at different sites is performed. This leads to some higher loaded areasvisible in Fig 3(a). Since the traffic demand is not very high, no overload occurs. However, capacity canbe spared when using installations adjusted to the traffic estimation, as can be seen in Fig. 3(b): thesame traffic is handled with less output power, because many cells disappear as source of interference.The local optimisation step then reduces the load in the network even further, the resulting downlinkload is shown in Fig. 3(c). The reduced load in the result network is also due to a decrease in pilot powerperformed by the optimisation algorithm.

(a) Reference network (b) Site selection (c) Local optimisation

Figure 3. Optimisation progress for The Hague: downlink load map

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4.2 Berlin

In the Berlin scenario, there are 23 possible sites. The solution resulting from our approach is shown inFig. 4, it uses 16 out of the 23 sites, employing a total of 46 cells. Among the seven unused sites are 6sites for microcells. The coverage map (Fig. 4(b)) reveals the presence of some uncovered holes (redareas). This is due to the fact that a) provably not all areas can be reached with the signal, since there

is a limited number of potential sites, and b) for the existing potential sites, a maximum of three sectorsis allowed. The load map depicted in Fig. 4(c) shows a well-balanced load distribution at an acceptablelevel.

(a) Best server map (b) Coverage map (c) Load map downlink

Figure 4. Planning result for Berlin (city centre around Alexanderplatz) c Digital Building Model Berlin(2002), E-Plus Mobilfunk GmbH & Co. KG

Again, our snapshot-based MIP approach does not directly take into account many classical KPI

such as pilot Ec

or Ec

/I0

coverage. However, analysis reveals that our approach significantly improvesthe networks performance under the classical measure. For pilot coverage, this can be traced in Fig. 5 andTable 2. The reference network (Fig. 5(a)) suffers from some large areas with bad pilot E c/I0 coverage.Reconfiguring the sites with the clover leaves already shows a significant effect on the pilot E c/I0 map.The local optimisation step solves many of the remaining problems, as can be seen in Fig 5(c). Thegradual improvement of pilot Ec and Ec/I0 coverage can also be traced in Table 2. (The dissatisfying Ecsituation is due to the inevitable coverage holes, see above.)

(a) Reference network (b) Site selection (c) Local optimisation

Figure 5. Optimisation progress for Berlin: Pilot Ec/I0 map c Digital Building Model Berlin (2002), E-PlusMobilfunk GmbH & Co. KG

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Table 2. Comparison of pilot coverage

The Hague BerlinRef. Site Sel. Local Opt. Ref. Site Sel. Local Opt.

Pilot Ec 100.0% 100.0% 100.0% 82.0% 83.3% 85.2%Pilot Ec/I0 96.2% 100.0% 99.5% 95.0% 96.9% 97.6%

4.3 Comparison with Heuristics

Heuristic approaches for the optimisation problem presented in Section 2 have been proposed in [1]. Acomparison of key performance and cost indicators for the resulting networks can be found in Table 3. Theheuristic approaches require less computation time, but in terms of network cost, the original optimisationobjective, we see that the MIP based solutions are better. This superiority of the MIP solutions still holdstrue when other indicators are analysed. The missed traffic values in Table 3 are derived from staticsystem-level simulations within the Momentum project [15]. This more accurate view on the quality ofour networks reveals that the additional effort for solving the MIPs pay out in terms of missed traffic(blocking or dropping). In the MIP solutions, this performance indicator lies always below 1 % comparedto around 3 % for the heuristic solutions.

Table 3. Key performance and cost indicators for MIP and heuristic approach

The Hague Berlin Ref.Heuristics MIP Heuristics MIP

# Sites 28 13 20 16# Cells 35 39 44 46% Missed Traffic 2.92 0.81 3.00 0.70

5 Conclusion

We recalled a mixed-integer mathematical programming model for the radio network planning task. For

coping with the large complexity of the problem, we developed an automatic, two phase network planningapproach based on successively solving instances of the model with mathematical programming softwareand involving local optimisation. Using this approach, we presented the first computational results for thedetailed Momentum data scenarios. Detailed analysis shows the improvement in different performanceindicators typically used for network assessment. We also showed that the results of our optimisationapproach show better performance than the outcomes of heuristic solution methods.

Future research will focus on refinements of our approach, such that larger instances can be considered.We will also consider other problems related to UMTS radio network design, such as network tuning,where the basic network design is given, but only certain adjustments can be made in order to improvethe networks quality. This includes, for example, antenna tilt and pilot power optimisation.

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14. Momentum project IST-2000-28088: Momentum public UMTS planning scenarios. Avaliable online athttp://momentum.zib.de (2003)

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