# Positioning by Multicell Fingerprinting in Urban NB-IoT Networks +
## 5 Performance Evaluation
### Results for the Oslo Dataset
#### 5.2.2 Performance under Limited Information  
Results presented in Section 5.2.1 were obtained using all the available information in the dataset, both in terms of (a) spatial density, measured by the number of data points, and (b) network deployment, measured by the number of NPCIs detected at each location. In both cases, however, it is worth investigating how positioning performance is affected by reduced available information. 1. Spatial density. Given the positioning service area, the desired spatial density determines the number of data points to be collected and, in turn, the time and effort spent in data collection during the offline phase: reducing this number may thus improve the positioning system scalability, making it easier to setup and maintain. In order to assess the impact of a decrease in spatial density, additional experiments were performed, where, in each run, a fraction \(P_{RP}<1\) of the points originally labeled as RPs were randomly selected and kept in the offline database. Figure 10 shows the minimum average positioning error as a function of \(P_{RP}\) for all strategies using SINR for all but _Net_. The results in Figure 10 show that all strategies are affected by a decrease in spatial density but not all to a similar extent. The _Coverage_ strategy, in particular, is heavily affected by the reduction of RPs, with the highest positioning error for low \(P_{RP}\) values, which questions its robustness. The _Single Cell_ approach shows a relatively low error for \(P_{RP}=0.01\) on par with the _Weighted Coverage_ strategy; this comes, however, at the price of a low percentage of TPs for which the position is estimated at all. As \(P_{RP}\) decreases, in fact, there is an increasing probability that no RP has NPCIs in common with a TP, making position estimation impossible. Although this is true for all strategies, _Single Cell_ is the most affected, with only 89% of the TPs with a position fix for \(P_{RP}=0.01\) vs. 96% or higher for the other strategies. Note that the optimal \(k\) value leading to the minimum average positioning error will in general depend on \(P_{RP}\); the optimal \(k\) as a function of \(P_{RP}\) is presented in Figure 11, highlighting a trend, common to all strategies, to require a higher optimal \(k\) as the spatial density increases, suggesting that as more RPs become available, strategies benefit from including a larger number of nearest neighbors. Figure 10: Minimum average positioning error as a function of \(P_{RP}\) for the proposed strategies vs. _Single Cell_[7] using SINR in all strategies but _Net_. 2. Number of detected NPCIs. Devices might be able to only detect and/or report the strongest detected cells based on their radio and processing capabilities [7]. It is therefore relevant to assess the impact of a reduction in the number of detected NPCIs at each location. This only affects fingerprints collected by the target device and has no effect on the offline database built by the operator. Therefore, experiments were carried out that only preserved the \(N_{NPCI}\) strongest/best NPCIs in points to be labeled as TPs; no change was made to data points labeled as RPs. Figure 12 shows the minimum average positioning error for all the proposed strategies as a function of \(N_{NPCI}\) in the range [1; 9]. The results show that, for all strategies, the positioning error decreases as the number of NPCIs used for each TP increases; in all cases, the error is close (within \(<\)2%) to the one obtained using all NPCIs (see Table 3) if at least 7 best NPCIs are used. This suggests that a trade-off can be found between complexity (i.e., the amount of information to be collected and sent by the target device) and positioning accuracy. The results also show that as in the case of spatial density, the _Coverage_ strategy is the one most affected by a reduction in the number of NPCIs, confirming its poor performance under conditions of scarcity of information.