- Research Article
- Open Access

# Novel Heuristics for Cell Radius Determination in WCDMA Systems and Their Application to Strategic Planning Studies

- A. Portilla-Figueras
^{1}, - S. Salcedo-Sanz
^{1}Email author, - Klaus D. Hackbarth
^{2}, - F. López-Ferreras
^{1}and - G. Esteve-Asensio
^{3}

**2009**:314814

https://doi.org/10.1155/2009/314814

© A. Portilla-Figueras et al. 2009

**Received:**24 March 2009**Accepted:**20 August 2009**Published:**12 November 2009

## Abstract

We propose and compare three novel heuristics for the calculation of the optimal cell radius in mobile networks based on Wideband Code Division Multiple Access (WCDMA) technology. The proposed heuristics solve the problem of the load assignment and cellular radius calculation. We have tested our approaches with experiments in multiservices scenarios showing that the proposed heuristics maximize the cell radius, providing the optimum load factor assignment. The main application of these algorithms is strategic planning studies, where an estimation of the number of Nodes B of the mobile operator, at a national level, is required for economic analysis. In this case due to the large number of different scenarios considered (cities, towns, and open areas) other methods than simulation need to be considered. As far as we know, there is no other similar method in the literature and therefore these heuristics may represent a novelty in strategic network planning studies. The proposed heuristics are implemented in a strategic planning software tool and an example of their application for a case in Spain is presented. The proposed heuristics are used for telecommunications regulatory studies in several countries.

## Keywords

- Time Division Multiple Access
- Cell Radius
- Wideband Code Division Multiple Access
- Combine Algorithm
- National Regulatory Authority

## 1. Introduction

*Base Station Subsystem*(BSSs) in 2G systems like GSM, and

*UMTS Terrestrial Radio Access Network*(UTRAN) in 3G systems like UMTS. The backbone network corresponds to Network Switching Subsystems in GSM and to the Core Network in UMTS. Figure 2 shows an example of these architectures.

One critical problem in mobile network design is the determination of the cell radius [1]. The underestimation of the cell radius leads to an overestimation of the number of Base Stations (BTS) required to provide service in an specific area, and hence excessive deployment investment costs. This is obviously bad news for the business of the network operator. On the other hand, an overestimation of the cell radius results in the installation of fewer BTSs than needed, and then in shadow areas. This means the network operator provides bad Quality of Service (QoS) in terms of coverage, and customers will complain.

Most of second generation systems, like GSM, use Time Division Multiple Access (TDMA) as radio access technology and therefore, they can be defined as hard blocking systems, that is, the number of users in the system is limited by the amount of hardware installed in the Base Station (BTS). Therefore, in GSM systems, the cell radius is mainly determined by the coverage planning (in this paper the term *coverage* refers to *radio propagation coverage*). In case that the QoS required (expressed as the blocking probability) is not fulfilled, the network operator must install more electronic equipment to incorporate more traffic channels to the BTS. It is a relatively simple task in TDMA systems.

Most of third generation systems, like UMTS, are based on WCDMA. These are soft blocking systems, where the number of users is not limited by the amount of channels in the BTS, but by the interference generated by their own users, and the users in neighbor cells. The maximum interference allowed in the system can be measured by a parameter named *interference margin*, which is used in the calculation of the link budget at the coverage planning process, and also to calculate the maximum number of users in the capacity planning process. Note that there is a tight relationship between the capacity and coverage planning processes in this case. Furthermore, the design of 2G systems is mainly oriented to the voice service [2], but 3G systems are designed to handle traffic from different sources, with different bit rates and, obviously, different requirements in terms of Grade and Quality of Service [3]. It is straightforward that this issue increases the planning complexity.

Cell radius calculation in WCDMA systems has been extensively studied before in the literature [4–8]. However, most of these models only consider a single service, which may result in a nonaccurate estimation of the cell radius in multiservice environments. In addition the studies of multiservice environments are usually based on simulation [9, 10], which requires a large set of input parameters. Moreover, user and service simulation models are usually quite complex. As we will see in the body of the paper, the problem of the cell radius determination in WCDMA systems is equivalent to a problem of capacity assignment among different services. Another approach to this complex problem starts from the cell radius, and finds the optimal capacity assignment to the services [11] or to study the maximum throughput.

Currently most operators are deploying their *3G and beyond* networks in order to offer high speed data services to their customers. Furthermore in developing countries, or in some rural areas where the 2G deployment is not completely finished, the operators are studying whether implement a proper 3G infrastructure or subcontract it to the dominant operator. Note that a very relevant factor in this decision will be the price that the dominant operator establishes, which may be sometimes conditioned by the National Regulatory Authority (NRA). The determination of the interconnection, roaming or termination price must be based on technoeconomic studies under the so-called Bottom-Up Long Run Incremental Cost model (LRIC) [12, 13] which is recommended by the European Union [14]. The objective of the LRIC is to estimate the costs incurred by an hypothetical operator with the same market power of the operator under study, that tries to implement his network with the best suitable technology. To do this, a complete design of the network has to be done at a national level, that is, to calculate the network equipment for each city, town, rural area, highway, road, and so on. Based on this, the mobile operator will have enough information to make the decision about *built or buy*, and/or to claim to the NRA with objective data to obtain better price.

It is straightforward that constructing a LRIC model requires the calculation of a large number of different scenarios, where the cell radius of the Nodes B (the 3G Base Stations), has to be estimated. Therefore the heuristic model used for this estimation has to be general enough to be applied to a large set of scenarios with a reduced set of parameters, so simulation is not valid. Furthermore, note that obtaining a good LRIC model for a country involves thousands of B Nodes, so the heuristics applied must be computational efficient. Thus, modern heuristics as evolutionary computation are limited approach in this case. Finally the selected calculation method has to be able to provide a fair estimation of the cell radius.

This paper proposes several novel algorithmic approaches to the cell radius determination problem under the constraints presented previously. Our approach starts from a multiservice scenario and the maximum capacity of the cell, and based on the services parameters we obtain the optimal capacity assignment for each service, and then, as final objective, we obtain the optimal cell radius. We propose the following heuristics. First, an iterative load factor reassignment heuristic is presented, which is able to solve the problem giving encouraging results. An analytical algorithm is also proposed and compared with the iterative heuristic. Finally, a combination of both algorithms is also tested, where the analytical approach is used to generate an initial solution for the iterative approach. We will show the performance of our approaches in several test problems considering WCDMA multiservice scenarios. With the proposed heuristics we fulfil all the requirements defined in the paragraph previously, that is, a fast procedure that is able to provide good estimations of the cell radius using a limited set of input parameters, and hence easy to use in different scenarios.

The rest of the paper is structured as follows. Next section defines the cell radius determination problem in WCDMA networks. In Section 3 we propose the heuristics for solving the problem, and in Section 4 we show the performance of the heuristics proposed by performing some experiments in WCDMA multiservice scenarios. We also present the implementations of our heuristics in a software tool named DIDERO and their applications in different regulatory projects. Section 6 concludes the paper giving some final remarks.

## 2. Cell Radius Determination in WCDMA Networks

Let us consider a 3G mobile network based on WCDMA technology, where the mobile operator provides a set of services (voice, data 16 kbps, data 64 kbps, etc.) each one defined by a set of parameters (binary rate, user density, quality of service, etc.). The mobile operator needs to have an estimation of the number of B Nodes in each area and thus it is required to calculate the cell radius for each B Node. As it is mentioned in the introduction, cell radius determination in WCDMA is a complicated process because, opposite to TDMA, the number of users and the total throughput is limited by the amount of interference in the radio interface. Of course, this interference not only limits the capacity of the system, but also the coverage by propagation, because the total noise in the system increases as more users are active.

Propagation coverage studies mainly imply two steps. The first one is to calculate the maximum allowed propagation loss in the cell, defined here as , and the second is to use an empirical propagation method to calculate the cell radius for this pathloss. Typical methods are the Okumura Hata COST 231 model, [15], or the Walfish and Bertoni [16].

The value of is calculated using a classical link budget equation

where is the transmitter power, is the sum of all gains in the chain, transmitter antenna, receiver antenna, and soft handover gain, is the sum of all the losses in cables, body losses, and in-building losses, is the receiver sensitivity which includes the required , thermal noise, receiver noise figure, and processing gain, and finally, is the different margins we need to take into account, fast fading margin, log-normal fading margin, and the interference margin, . This interference margin is a very relevant value, because it measures the maximum interference allowed in the system due to its own users. Therefore this value indirectly limits the maximum number of users in the system. Note that all the parameters in (1) are inputs of the system and therefore can be obtained from this equation.

As it was mentioned before the cell radius by propagation is obtained applying the into an empirical propagation method. In our work we have used the 231-Okumura Hata model because it is broadly considered as the most general one in mobile networks applications [17]

where is the frequency in MHz, is the height of the Node B in meters, is the height of the mobile user in meters, and is the cell radius by propagation in Km. Note that and are parameters defined in the COST 231 specification. They provide the influence of the height of mobile terminal and the type of city, respectively, and they are defined as follows:

Note that as the value of changes for the different services, the propagation coverage study has to be done specifically for each one, and of course for the uplink and the downlink. Therefore the formulation explained previously, and the value , has to be applied for each service and each direction (Uplink (UL) and Downlink (DL)) obtaining a set of two vectors containing, for each service, the cell radius by propagation, ( and )

Now we focus on capacity studies. As it is done in propagation studies, cell radius must be calculated independently for the uplink and the downlink. The equations that determines the radius in both directions are quite similar. Then for simplicity reasons, this paper focuses in the calculation of the cell radius for the downlink case, since this is the most restrictive direction [18–20].

The interference margin used in (1) determines the maximum load of the cell, , by means of the following relation, [18, 21]

This factor indicates the load of the cell. If there is no user in the system. On the opposite if , the amount of interference in the system grows to and hence the system goes to an unstable state. Therefore typical values of the are between 3 and 6 dB, which means a load of 0.5–0.75.

Although in the real operation of the system, there is no capacity reservation between the different services, in the dimensioning process it is required to allocate part of the capacity to each service. Therefore the load factor, that is, the capacity of the cell, must be allocated to the different services, resulting the load factors of the each service

The number of active connections of each service is calculated by dividing the total load factor of each service type over the average individual downlink load factor of the connections of the service

where the downlink load factor is defined by the following equation:

where is the so-called downlink orthogonality factor, is the binary rate, is the so-called activity factor of the service , is the average intercell interference factor, and is the bandwidth of the WCDMA system.

The total offered traffic demand, in Erlangs, is obtained by using the inversion of the Erlang B Loss formula [22]. The inputs for this algorithm are the maximum number of active connections in the cell and the Quality of Service (QoS) of the service expressed by the blocking probability

Note that in (9) the total offered traffic demand, , is divided by the factor and the maximum number of active connections, , of the service is multiplied by it. This is included to considerer the soft blocking feature inherent to the WCDMA system, [23].

Multiservice traffic in UMTS has been extensively studied in the literature [24]. However in the strategic planning mobile operators trend to use simplified models that provides under estimations of the cell capacity to be in the safe side when they estimate the number of Node B's to provide service to the customers in the area under study, [25]. Because of the reasons stated in the previous sentence, in this proposal we use the Erlang B formulation. However it is and independent part that can be substituted by any other traffic model formulation.

The number of users in the cell (
) is obtained from the division of the total offered traffic demand for service *i*, (
in Erlangs), by the individual traffic of a single user of this service (obtained from the connection rate
and the mean service time
):

The cell radius for each individual service is calculated as a function of the number of sectors in the BTS,
, the number of users of service *i* per sector
and the user density
as follows (note that a Node B may be divided into several sectors. Each sector corresponds to a cell):

Note that this process has to be done also for the uplink direction (UL). Therefore, at the end we have obtained another set of two vectors (one for the uplink and one for the downlink), with the cell radius by capacity of each service:

Note that the values of and largely depend on the distribution of the capacity over the different services by means of the total load factor allocated to each service and . A bad allocation will lead to large differences in the values of the radius, while an equilibrated one will produce approximately the same value for all the services.

Note that at the end of this process we have obtained a set of four vectors, , , , and . The final cell radius, will be the minimum value between and which represents the most restrictive cell radius under propagation and traffic criteria respectively

*outer problem*and

*inner problem*, as it is shown in Figure 3.

- (1)
The

*outer problem*is to find the best value for the Interference Margin, . This will be the value when the cell radius by capacity (traffic), , is the same as by propagation, . - (2)
The

*inner problem*that is to find the best capacity allocation, given a value of the over the complete set of services . With this the cell radius by capacity, , is maximized.

The outer problem is solved just making an iterative process to equilibrate the value of the cell radius between the resulting value calculated by propagation studies and the resulting one calculated by capacity studies. This is done by means of increasing the value of the interference margin,
, when the cell radius by propagation is higher than by capacity or vice versa. The *inner problem* is much more complicated because it implies the use of the traffic concepts and nonlinear process which underlies to (9)–(12).

This paper focuses on the design of heuristics for solving the inner problem (from now on we will focus on the donwlink direction, we therefore do not include the DL subindex in the formulation since it is assumed). With the definitions given before, the cell radius determination problem by capacity criterium can be defined as follows:

which maximizes . Note that we focus on the inner problem, where the traffic is the most restrictive factor, therefore, in this case.

## 3. Proposed Heuristics

### 3.1. Iterative Load Factor Redistribution Heuristic

This first heuristic we propose for the cell radius determination problem starts from an initial load factor assignment, usually provided by estimations of the network planner [7]. From this initial assignment , we can calculate an initial solution for the cell radius using (7) to (11). If this initial cell radius is not the optimal one, the only service which is using its total capacity is the one with minimum value of associated. The following example shows it in detail.

Let us consider a scenario with three services, voice at 12.2 Kbps, data at 64 Kbps and data at 144 Kbps. Let us also consider that a initial load factor assignment is . With this, the values of the cell radius are meters. Note that the limiting value is the cell radius of the first service , that is 343 meters. With this value of the cell radius , the load factors that the services are really using are . So it is obvious that the initial load factor assignment is not correct, because we are not optimizing the cell usage (note that this example is a hard simplification of the complete process).

Note that the rest of the services will use less capacity than they have initially assigned. Let us call this capacity as . Therefore, there is some remaining capacity, defined as

This remaining capacity has to be redistributed over the considered services, so that a new cellular radius can be calculated using (11). This will produce new values of . This iterative process is followed until the difference between two consecutive cell radius is less than a given threshold , usually .

Several procedures can be applied for the distribution over the different services. The simplest one is to find the balanced distribution of among all services in the system. This method leads, however, to suboptimal solutions, since the service with the most restrictive cell radius in one assignment is kept again as the most restrictive one in the new assignment. A better distribution can be obtained by assigning a larger part of the exceeding load factor, , to the service with most restrictive cell radius, , by means of a prioritizing factor ( ), and a balanced division among the rest of services:

The value of the prioritizing factor, , depends on the differences of the values of the cell radius of the different services. If the difference - is large the value of will be near to ; otherwise, it will be near to .

The main drawback of this method is the dependency on the initial solution, that is, the dependency on the initial load factor assignment. Note also that the convergence of the algorithms depends on how the remainder capacity (given by ) is distributed over the different services. A poor distribution procedure may result in a high number of iterations or even may fail to find the solution.

### 3.2. The Reduced Algorithm

The second approach we propose to solve the cell radius determination problem is to find a mathematical model, which calculates an accurate value of the cell radius, under any service scenario and any initial conditions, expressed in terms of the load factor and the parameters of the services .

The proposed model is named *reduced algorithm*, since it reduces all the services in the system to a single artificial service to solve the problem. The method starts considering an arbitrary cell radius, typically
. Then, the model calculates the total traffic demand offered to the cell,
, for each service
, by means of the user density of each service,
, the individual call rate,
, and the mean call duration,
.

The reduction of the set of services to a unique artificial/equivalent one is performed by a procedure based on a proposal of Lindberger for ATM networks [28]. This proposal is obviously extended to the singularities of the WCDMA cell design. The artificial service is defined in terms of equivalent parameters: binary rate, , call rate, , mean call duration, , blocking probability, , activity factor, and user density, . Following the Lindberger formulation, the parameters of the artificial service are calculated on the basis of the traffic, , and the binary rate, , of each service considered in the scenario. The complete set parameters are defined by the following equations:

Considering this new artificial service, the reduced method calculates a corresponding value of the cell radius, , assigning the whole load factor, , to the artificial service. From the obtained , the load factors for each individual service, , can be calculated inverting the cell radius calculation process shown in Section 2, see [18, 21] which is summarized as follows. From the , it is possible to calculate the maximum number of users of each service per sector, and hence the total traffic offered to the system. Using the Erlang formula, with the blocking probability, , the number of active connections, , of each service is obtained. Finally the value is calculated by means of the individual load factor of the service, , times the number of active connections, .

The total load factors of each service are obtained by simple reduction to the whole load factor, ,

Considering these values of the load factors, a new solution of the cell radius for each individual service is calculated following the process in Section 2, obtaining the solution vector, which minimum value is the cell radius.

### 3.3. Combined Heuristic

The third heuristic we consider is to find the hybridization of the two algorithms previously described. The reduced algorithm, which does not require an initialization of the load factors, is used for calculating the starting point for the Iterative load factor redistribution heuristic. Thus, it is expected a better performance of the iterative heuristic since it starts from a better initial solution.

## 4. Computational Experiments and Results

In order to validate the heuristics presented in this paper, we have tested them in several experiments based on scenarios with different service combinations. Specifically, we have defined mixtures of two, three and four services, each one having its own requirements in terms of binary rate, quality of service, user movement speed and user density in the area under study. Furthermore we have modified the traffic figures of the services to consider balanced and unbalanced traffic. Balanced traffic means that the individual throughput of each service is similar to the throughput of the other services.

Radio propagation parameters.

Node B parameters | Mobile terminal parameters | ||
---|---|---|---|

Height B (m) | 50 | Height (m) | 1.75 |

Power (W) | 10 | Power (W) | 0.25 |

Antenna gain (dB) | 10 | Antenna gain (dB) | 0 |

Cable loss (dB) | 3 | Skin loss) | 3 |

Noise figure (dB) | 5 | Noise figure (dB) | 7 |

Frequency (MHz) | 1950 | Frequency (MHz) | 2140 |

Common parameters | |||

Log normal fading margin (dB) | 7.3 | Fast fading margin (dB) | 2 |

UL intercell interference ratio | 0.88 | Soft handover gain | 3 |

DL intercell interference ratio | 0.88 | Interference margin (dB) | 6.02 |

Sectors | 1 |

Traffic figures for balanced traffic experiments.

Traffic figures for unbalanced traffic experiments.

Cell radius (in metres) for each experiment calculated using the proposed heuristics.

Experiment | Iterative | Reduced | Combined |
---|---|---|---|

Radius (m)/Iters | Radius (m) | Radius (m)/Iters | |

Exp-1 | 530/4 | 529 | 530/2 |

Exp-2 | 616/7 | 616 | 616/1 |

Exp-3 | 322/6 | 322 | 323/2 |

Exp-4 | 572/9 | 572 | 572/2 |

Exp-5 | 422/10 | 400 | 422/6 |

Exp-6 | 532/13 | 352 | 532/13 |

Exp-7 | 187/6 | 188 | 188/1 |

Exp-8 | 475/7 | 466 | 475/3 |

As it was mentioned in Section 2, the optimum value of the cell radius is obtained when there are quite small differences in the cell radius of the different services. We will illustrate this in Experiment
. In this experiment, we have compared the results obtained by the three heuristics proposed against the cell radius calculated with an assignment done using the binary rate and the user density, let us name it *free assignment* (FA) following the equation

Note that the cell radius of each service is quite similar in the three proposed heuristics but in the FA the cell radius of the is almost 50% larger than .

Finally, regarding the computation time, the three algorithms we propose in this paper for the cell radius determination problem obtain the solution to the problem in less than 1 second. This is a very important point for the inclusion these algorithms in a strategic network planning tool, where a large number of scenarios have to be calculated.

### 4.1. Validation and Limitations of the Proposed Heuristics

Services mixtures in [26].

Service combination | Mix 1 | Mix 2 | Mix 3 |
---|---|---|---|

Voice | 95 | 80 | 10 |

Data 64 Kbps | 3 | 15 | 30 |

Data 144 Kbps | 1.5 | 4 | 30 |

Data 384 Kbps | 0.5 | 1 | 30 |

Total bandwidth (Kpbs) | 557 | 809 | 1104 |

Comparison of the resulting cell radius.

Service combination | Value in [26] | Combined heuristic |
---|---|---|

Mix 1 | 535 | 552 |

Mix 2 | 528 | 544 |

Mix 3 | 527 | 520 |

As final remarks for this section, note that the main limitation of the proposed heuristics in this paper is that they consider trunk reservation for the capacity assignment. This means that the capacity allocated to service is reserved for this service exclusively, and no other can use it, even when there is some free capacity. In the practical operation of the UMTS system, the capacity is available for all services and only when the system goes to a heavy loaded situation, the capacity reservation will be activated. This also means that, in practice, the cell radius will be slightly larger than the one calculated with the proposed algorithms. However, since the algorithms provide a conservative estimation, they are valid to estimate the maximum network investment.

## 5. Implementation, Application, and Real Cases

### 5.1. Implementation and Application

The proposed algorithms are implemented in a software tool for the strategic design of hybrid 2G and 3G networks. An earlier version software tool named DIDERO, was originally presented in [32].

Using this tool we present a study carried out for Spain. The objective of this study is to compare the differences in the number of Node Bs and in the total network investment cost using different allocations of the load factors to the services. We will use the combined heuristic presented before and three different assignments ( , , ) for comparison purposes, based on the binary rate, user density and the traffic, that are the assignments done by a common network planner.

The assignment is done considering the binary rate of the service, that is, a service with higher binary rate gets more capacity following the equation

The assignment takes into account also the user density:

Finally the third assignment considers also the individual traffic

Set of 50 cities considered in the scenario.

City | Inhabitants | City | Inhabitants | |||
---|---|---|---|---|---|---|

Vitoria | 277 | 235 622 | Logroño | 80 | 147498 | |

Albacete | 1126 | 171 450 | Lugo | 9856 | 99571 | |

Alicante | 201 | 333 250 | Madrid | 607 | 3294932 | |

Almeria | 296 | 189 669 | Malaga | 395 | 584158 | |

Avila | 232 | 55 433 | Murcia | 882 | 446483 | |

Badajoz | 1470 | 152 549 | Pamplona | 24 | 203111 | |

Palma de M. | 213 | 388 512 | Ourense | 85 | 108421 | |

Barcelona | 91 | 165 2876 | Oviedo | 187 | 233453 | |

Burgos | 108 | 175 894 | Palencia | 95 | 82195 | |

Caceres | 1768 | 95 834 | Palmas de G.C. | 101 | 376116 | |

Cadiz | 12 | 137 138 | Pontevedra | 117 | 80441 | |

Castellón | 108 | 181 181 | Salamanca | 39 | 163641 | |

Ciudad Real | 285 | 78 642 | S.C. Tenerife | 151 | 223406 | |

Cordoba | 1252 | 330 410 | Santander | 35 | 184435 | |

Coruna | 37 | 252 542 | Segovia | 164 | 57349 | |

Cuenca | 954 | 54 917 | Sevilla | 141 | 739016 | |

Girona | 39 | 99 561 | Soria | 272 | 38778 | |

Granada | 88 | 249 530 | Tarragona | 62 | 144006 | |

Guadalajara | 36 | 76 249 | Teruel | 438 | 35253 | |

San Sebastian | 61 | 190 099 | Toledo | 232 | 83811 | |

Huelva | 149 | 153 699 | Valencia | 135 | 819969 | |

Huesca | 15 | 50 704 | Valladolid | 198 | 324334 | |

Jaén | 424 | 125 212 | Bilbao | 41 | 355064 | |

León | 402 | 136 845 | Zamora | 11 | 65025 | |

Lleida | 212 | 131 985 | Zaragoza | 1059 | 667781 |

Resulting number of Node B's.

City | Combined | City | Combined | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Vitoria | 44 | 108 | 72 | 44 | Logroño | 23 | 72 | 44 | 44 | |

Albacete | 23 | 72 | 73 | 45 | Lugo | 107 | 107 | 107 | 107 | |

Alicante | 44 | 150 | 107 | 73 | Madrid | 394 | 973 | 557 | 557 | |

Almeria | 23 | 72 | 72 | 44 | Malaga | 72 | 200 | 107 | 107 | |

Avila | 9 | 23 | 23 | 24 | Murcia | 73 | 150 | 72 | 72 | |

Badajoz | 23 | 72 | 44 | 45 | Pamplona | 44 | 72 | 44 | 44 | |

Palma de M. | 44 | 200 | 107 | 72 | Ourense | 23 | 44 | 23 | 23 | |

Barcelona | 257 | 973 | 557 | 321 | Oviedo | 45 | 72 | 44 | 44 | |

Burgos | 23 | 72 | 72 | 44 | Palencia | 24 | 45 | 23 | 23 | |

Caceres | 24 | 44 | 45 | 23 | Palmas de G.C. | 72 | 107 | 72 | 72 | |

Cadiz | 23 | 150 | 150 | 44 | Pontevedra | 24 | 46 | 23 | 23 | |

Castellón | 23 | 72 | 72 | 44 | Salamanca | 23 | 72 | 44 | 44 | |

Ciudad Real | 24 | 44 | 23 | 23 | S.C. Tenerife | 45 | 72 | 44 | 44 | |

Cordoba | 44 | 150 | 107 | 73 | Santander | 23 | 77 | 44 | 44 | |

Coruna | 44 | 150 | 107 | 72 | Segovia | 9 | 23 | 24 | 24 | |

Cuenca | 9 | 23 | 23 | 24 | Sevilla | 109 | 200 | 150 | 150 | |

Girona | 23 | 44 | 44 | 23 | Soria | 9 | 24 | 9 | 9 | |

Granada | 44 | 107 | 107 | 44 | Tarragona | 23 | 44 | 45 | 45 | |

Guadalajara | 23 | 44 | 23 | 23 | Teruel | 9 | 24 | 9 | 9 | |

San Sebastian | 45 | 107 | 72 | 44 | Toledo | 24 | 45 | 23 | 23 | |

Huelva | 23 | 72 | 44 | 45 | Valencia | 107 | 257 | 150 | 150 | |

Huesca | 9 | 44 | 23 | 23 | Valladolid | 44 | 107 | 73 | 73 | |

Jaén | 23 | 73 | 44 | 23 | Bilbao | 72 | 107 | 72 | 72 | |

León | 23 | 73 | 44 | 23 | Zamora | 9 | 44 | 23 | 23 | |

Lleida | 23 | 72 | 44 | 23 | Zaragoza | 72 | 200 | 107 | 107 | |

Total number of Node Bs | ||||||||||

Combined | ||||||||||

2396 | 7297 | 5283 | 3219 |

*€*), and that the investment in the cell deployment is about 60%, [33] of the total network investment in a mobile network we can estimate the total network investment for the four cases presented. These results are shown in Table 16.

The most impact result is the big difference in the total investment in the different cases. Comparing with the second best, that is, with the scenario A3, the difference is about 547 million (*€*). This is equivalent to the 0.05% of the total Spanish Gross Domestic Product which is 1.12 billion of euros. This result shows the relevance for the network operator of an accurate network planning.

### 5.2. Real Cases

## 6. Conclusions

This paper proposes three different algorithms for the calculation of the cell radius under traffic criteria in multiservices scenarios, named iterative, reduced and combined. We have shown that the three algorithms are able to solve the cell radius determination problem, providing good quality solutions. However, the reduced algorithm is not able to produce optimal solutions when the users are moving at different speeds. The iterative and combined heuristics provides the optimal solution in all the cases studied, but the combined approach converges faster than the iterative heuristic.

The combined heuristic has been implemented in existing strategic planning software tool to calculate the Node B deployment in a whole country. We have presented a work scenario in Spain were our proposed heuristic obtains better solutions in terms of number of Node Bs, which represents a great investment cost saving. This heuristic has been applied in several regulatory processes under the supervision of the corresponding National Regulatory Authority.

## Declarations

### Acknowledgments

This work has been partially supported by Comunidad de Madrid, Universidad de Alcalá and Ministerio de Educación of Spain, through Projects CCG06-UAH/TIC-0460, CCG08-UAH/AMB-3993 and TEC2006-07010. The authors would like to thank also the support offered by WIK Consult GmbH, in the different projects, both with their expertise and funding.

## Authors’ Affiliations

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