# RSS-Based Localization and Mobility Evaluation Using a Single NB-IoT Cell+
## 4 RSS-Based Localization Algorithms
### Range-Based Localization  
In RSS-based ranging approaches, the RSS from a UE to a specific eNB is translated into a distance by means of a propagation channel model or path loss model. Most path loss models can be customized by setting parameters, depending on the environment. Given the urban nature of our large-scale environment, we set the height of the mobile station \(h_{MS}\) to \(2\,\mathrm{m}\) and the height of the base station \(h_{BS}\) to \(27\,\mathrm{m}\). The carrier frequency \(f\) varies between 800 and \(900\,\mathrm{MHz}\) and the transmission power is set to \(14\,\mathrm{dBm}\).  
In this paper, we evaluate the performance of four urban path loss models. The Hata model is an empirical path loss model based on the widely used model of Okumura [28], and the path loss \(L_{P}\) of the urban variant can be characterized as follows:  
\[L_{P,Hata}=A+B\log_{10}(d), \tag{1}\]  
with  
\[A =69.55+26.16\log_{10}(f)-13.82\log_{10}(h_{BS})-a(h_{MS}), \tag{2}\] \[B =44.9-6.55\log_{10}(h_{BS}), \tag{3}\]  
where  
\[a(h_{MS})=3.2*[\log_{10}(11.75*h_{MS})]^{2}-4.97. \tag{4}\]  
The European Cooperation in Science and Technology (COST) received funding to extend the Hata model, resulting in the COST-231 model [28]:  
\[L_{P,COST-231}=A+B\log_{10}(d)+C, \tag{5}\]  
with  
\[A =46.3+33.9\log_{10}(f)-13.28\log_{10}(h_{BS})-a(h_{MS}), \tag{6}\] \[B =44.9-6.55\log_{10}(h_{BS})\text{, and}\] (7) \[C =3. \tag{8}\]  
Next, two empirical outdoor path loss models based on the 3 GPP Spatial Channel Model (SCM) were proposed by the IEEE TGah group, which standardizes IEEE 802.11 ah. Although the original models were devised for LTE, they have been transformed for use in sub-gigahertz (sub-GHz) frequency bands [29]. The first model targets a macro Line-of-Sight (LoS) deployment scenario (further referred to as _AH-macro_) and can be expressed as in the following equation:  
\[L_{P,AH-macro}=8+36.7\log_{10}(d). \tag{9}\]  
A second 3 GPP model targets a pico deployment scenario (further referred to as _AH-pico_) and can be characterized using the formula:  
\[L_{P,AH-pico}=23.3+36.7\log_{10}(d)+c_{pico}, \tag{10}\]  
with  
\[c_{pico}=21\log_{10}(f/900). \tag{11}\]  
Given the mobility issues addressed in Section 1, it is not possible to retrieve information about multiple neighboring cells in NB-IoT. In other words, only the antenna of the serving eNB can be used to estimate the location of a UE. As a consequence, well known ranging localization approaches such as triangulation or multilateration cannot be applied. Therefore, we introduce a novel algorithm thatestimates the position of a UE based on the combination of the serving cell and sector information. First, we estimate the distance \(d\) between the UE and eNB using one of the four previously presented path loss models. This results in a circle around the eNB with a radius equal to \(d\), representing all possible UE locations. With the aim to further improve the localization accuracy, we take into account the azimuth of the directional antenna of the serving cell, which covers a sector of \(120^{\circ}\). Thus, the antennas provide a spatial filter, eliminating location estimates located outside a given sector. As we assume the location of the UE on the resulting arc to be Gaussian distributed, the final location estimate is set to the center of the arc, as illustrated in Figure 4.