A corrigendum for this article has been published. To view the corrigendum, please click here.

Mobile Information Systems

Volume 2018, Article ID 3479246, 8 pages

https://doi.org/10.1155/2018/3479246

## A Geometric Method for Estimating the Nominal Cell Range in Cellular Networks

^{1}Departamento de Ingeniería de Comunicaciones, Universidad de Málaga, Málaga, Spain^{2}Ericsson, Málaga, Spain

Correspondence should be addressed to A. J. García; se.amu.ci@pgja

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

Academic Editor: Ioannis D. Moscholios

Copyright © 2018 A. J. García et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

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

#### 1. Introduction

With the increasing complexity of mobile networks, radio network planning has become a challenging task for mobile operators. The aim of planning is to find a cost-effective deployment solution to offer subscribers the best network performance in terms of coverage, capacity, and connection quality [1–3]. For this purpose, in the initial preplanning stage, the required site density is estimated based on link budgets. Then, in the nominal planning stage, optimal site locations are determined in terms of network coverage and capacity. In the final detailed planning stage, the best site configuration is selected. In all these processes, estimating the nominal (i.e., planned) Cell Range (CR) is a critical task since it influences the number of required base stations, their geographical location, and the optimal antenna settings (e.g., transmit power or tilt angle) [1, 2, 4, 5].

An improper network modeling during the planning stage can lead to suboptimal system performance during network operation. This problem can be solved by improving network models with live measurements (a.k.a. measurement-based replanning) or counteracted by tuning radio network parameters (a.k.a. network optimization). In both cases, an accurate estimation of the nominal cell service areas is critical to obtain good results [4, 6]. An example of such a need is the automatic method proposed in [7] to detect cells with overshooting problems. In that method, the actual (i.e., measured) cell range, obtained from Time Advance (TA) statistics [8], is compared with the nominal cell range. In such a comparison, any deviation of the nominal cell range causes that a cell is classified as an overshooter or not. Similarly, the planning methods proposed in [9, 10] for selecting the best antenna tilt angle based on geometric considerations strongly depend on the nominal CR.

Traditionally, operators use two different approaches to estimate the nominal cell range in mobile networks. The first approach consists of using commercial cellular network planning tools [11], mainly based on static system-level simulators that allow analyzing coverage, capacity, and quality of service related issues. One of the key processes performed during a step simulation is the dominance area calculation and, thus, nominal cell range. In this process, the link losses from each base station to each position in its calculation area are estimated by using network configuration parameters for base stations, mobiles stations, and the network area and different propagation models that allow to simulate path losses in a real environment [12]. Static simulators obtain an accurate estimation of network parameters but assuming a high computational load, especially for high-density scenarios. Thus, cellular network planning tools are used, generally, in the initial preplanning stage where time requirements are not so restrictive. Alternatively, a geometric calculation of nominal cell range is also commonly used for operators. Geometric calculation is uniquely based on physical information of base stations (e.g., location of base stations). This approach consists of a simple method that allows to obtain, with a considerable grade of accuracy, an estimate of cell range with a very low computational load by avoiding to use complex tools in its process. Thus, it is an efficient alternative used by operator to be integrated in their network management systems for optimization processes since it is able to be executed over large geographical areas in seconds.

In an ideal cellular network with regular geometry, the geometric CR (i.e., the distance to cell edge) can be estimated analytically by using the inter-site distance (ISD) [13]. Specifically, the CR in a hexagonal grid scenario is with omnidirectional antennas, and with trisectorized antennas. However, in a live scenario, sites are unevenly distributed to deal with factors such as topography, cost, or availability, causing that cell shapes are irregular [14]. Moreover, new radio access technologies (4G/5G) will result in the deployment of a higher number of small cells, increasing the complexity of physical layout [15]. Thus, the CR cannot be calculated by using the distance to the nearest site.

Current operator practice is to compute the nominal CR of a site by averaging the distance to some of the nearest sites. Then, the number of nearest sites selected is limited in an attempt to avoid considering several rings of adjacent cells. Unfortunately, the best number of nearest sites is difficult to define, as it depends on the specific scenario [16]. For simplicity, such a parameter is set to a fixed value, leading to inaccurate CR estimates in many cases. To solve these limitations, some authors use Voronoi tessellation [17, 18] to define the polygon representing the service (or dominance) area for every site [14, 19–22]. Such a diagram can then be used to choose the nearest sites more accurately and, consequently, to estimate the ISD [21]. Once the nominal ISD is obtained, CR is estimated as half of the ISD value. The main limitation of this method is that the CR assigned to all cells in a site (i.e., cosited cells) is the same, which is seldom true in the live network. Such inaccuracies can jeopardize the benefits of network planning and optimization methods that rely on CR estimates (e.g., [7]).

In this work, a geometric method to calculate the CR based on Voronoi tessellation is presented. The main novelties are that (a) CR is calculated on a cell (and not on a site) basis, (b) CR depends on the antenna pointing direction of each cell (i.e., azimuth), and (c) the antenna beamwidth value is used to define the cell border (i.e., side of the service area). Thus, a more accurate estimation of the CR is obtained with a low computational cost. The analysis is extended by checking the impact of the proposed method on the performance of the cell overshooting detection algorithm described in [7].

The main contributions of this work are (a) a novel and computationally efficient method to estimate the CR on a per-cell basis suitable for radio network optimization processes; (b) a comprehensive analysis of the proposed method in a real scenario, showing the limitations of current practice and how these can be solved by the new approach, and (c) an evaluation of the impact of CR estimates on the performance of a classical cell overshooting detection algorithm in a live LTE network.

The rest of the work is organized as follows. Section 2 reviews the current method used to calculate the CR on a site basis. Section 3 describes the method proposed to calculate the CR on a cell basis. Section 4 shows the results obtained by the method in a real scenario. Finally, Section 5 presents the main conclusions of the study.

#### 2. Calculation of Cell Range on a Site Basis

In a network consisting of sites, an estimate of CR can be obtained by calculating the average distance to the nearest sites, where [21]. Thus, the average ISD from site to the nearest sites is defined aswhere is the Euclidean distance from site to site . Once the average ISD of site is calculated with the closest neighbor sites, the CR of cell located in site is calculated aswhere is the ISD of site calculated by using the nearest sites. Note that .

Figure 1 shows an example of how the current method works. is represented by a dashed circumference and the pointing direction of cell by a solid arrow. In this example, it is assumed that the number of nearest sites used for ISD calculation (represented by crosses with dotted circles) is 6, and the solid arrow represents the pointing direction of the cell. From the figure, it is clear that the previous method has several limitations, the foremost of which is the calculation of the ISD at a site level, causing that all cells in the same site are assigned the same CR value (represented by a dashed arrow). Moreover, the CR of a cell is only based on the distance between the site where the cell is located and surrounding sites. However, in a real network, the service area of a cell with directional antennas is mainly determined by the sites that are in the pointing direction of (i.e., in front of) the cell.