# Location-Awareness for Failure Management in Cellular Networks: An Integrated Approach
## 3 Proposed System
### Indicators Generation  
In this stage, the indicators (counters, statistics...) are calculated based on the previously acquired data. Here, it is where the use of location implies an explosion in the number of available features in comparison with classical approaches. Contextualized indicators are based in the integration of both context and network data keeping the time-series nature of the resulting feature. To do so, firstly, any terminal, \(u_{i}\) of the network is considered to be a source of both network-related measurements and context data [19], in particular, its position. In this way, for a specific UE \(u_{i}\), its location \(u_{i}(\tau)\) at an instant \(\tau\), can be represented as a multidimensional vector:  
Figure 2: Proposed system scheme. \[\iota_{u_{i}}(\tau)=\{x_{u_{i}}(\tau),y_{u_{i}}(\tau),z_{u_{i}}(\tau)\}. \tag{1}\]  
Additionally, each UE generates different measurements of different radio or service provision parameters, where we can express any of them as \(\kappa_{u_{i}}(\tau)\). In order to keep the time-series format, common for counters and KPIs, any new contextualized feature/metric \(f[t]\) should be established as a function of both the positions and the network measurements that were gathered during a certain measurement period \(T_{t}\):  
\[f[t]=\Phi(\{\kappa_{u_{i}}(\tau),\iota_{u_{i}}(\tau)|\forall\kappa_{u_{i}}\in K _{t},\forall u_{i}\in U_{t},\tau\in T_{t}\}), \tag{2}\]  
where \(K_{t}\) is the set of samples gathered during the period for any reporting UE in \(U_{t}\), which represents the set of reporting UEs during the period \(T_{t}\), and the scenario of analysis. In classical metrics, \(U_{t}\) is equivalent to the total of users being served by one cell and metrics are separately generated per cell. For example, the average RSRP power in cell A is the average calculated from all of the served UEs in such a cell. To have \(f[t]\) as a time series, function \(\Phi\) combining network and location measurements shall be variable: \(\Phi:\mathbb{R}^{|K_{t}|}\times\mathbb{R}^{|K_{t}|}\rightarrow\mathbb{R}\), where \(|K_{t}|\) is the number of samples gathered during the period \(T_{t}\). \(|K_{t}|\) typically changes for each period due to the variable number of UEs and their generated reports. The time variable \(t\) is discrete, as \(f[t]\) would provide one value per each observation period \(T_{t}\) (e.g., one hour). Statistical functions, such as averages, percentiles, etc., are compliant with the variadic requirement for \(\Phi\) and are the most used in the generation of network metrics. Weighted statistics can then be applied order to enrich these statistics with the location information. In this way, the weight of each sample into the statistic can be established based on the location where it has been gathered. This is applicable to any statistic, i.e. mean, median, percentile, etc. An example of a weighted statistic is a weighted mean, which calculation is formulated as:  
\[f_{w}[H]=\Phi_{w}(\{\kappa,\iota_{\kappa}|\forall\kappa\in K_{t}\})=\frac{ \sum_{\kappa\in K_{t}}\kappa\times w(\iota_{\kappa})}{\sum_{\kappa\in K_{t}}w (\iota_{k})}, \tag{3}\]  
where the notation of the set of measured samples and their associated locations has been simplified, as follows:  
\[\{\kappa_{u_{i}}(\tau),\iota_{u_{i}}(\tau)|\forall u_{i}\in U_{t},\forall \kappa_{u_{i}}\in K_{t},\tau\in T_{t}\}=\{\kappa,\iota_{\kappa}|\forall\kappa \in K_{t}\}). \tag{4}\]  
In the expression shown in Figure 3, each possible weight function, \(w:\mathbb{R}^{|K_{t}|}\rightarrow\mathbb{R}\) will lead to a different weighted mean \(\Phi_{w}\) and therefore a different feature/indicator \(f_{w}[H]\). Here, the definition of specific weight functions to be applied for failure management is one of the main challenges to overcome. A straightforward approach for the definition of these weight functions is the use of binary weights \(w:\mathbb{R}^{|K_{t}|}\rightarrow\{0,1\}\), which is equivalent to filter the samples, depending on their location.