# Analysis of the Scalability of UWB Indoor Localization Solutions for High User Densities
## 6 Application of the Scalability Model
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Data Rate (Mbps)** & **PRF (MHz)** & **SHR (ns)** & **PHR (ns)** & **Data (ns)** \\ \hline
0.11 & 16 & 993.59 & 8205.13 & 8205.13 \\
0.11 & 64 & 1017.63 & 8205.13 & 8205.13 \\
0.85 & 16 & 993.59 & 1025.64 & 1025.64 \\
0.85 & 64 & 1017.63 & 1025.64 & 1025.64 \\
6.81 & 16 & 993.59 & 1025.64 & 128.21 \\
6.81 & 64 & 1017.63 & 1025.64 & 128.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: DW1000 Symbols duration. * \(T_{bacon}=T_{packet}\) with max payload (1023 bytes)  
An extra mode, called \"theoretical limit\" is also shown in Figure 7 for the TDoA w/o synchronization case. The purpose is to show the upper theoretical limit, in which no contention access period is present since all the slot contention and assignations are done at another level, e.g., using a backbone network. This also reduces the \(T_{bacon}\) since no scheduling has to be distributed among the tags, i.e., \(T_{bacon}=T_{packet}\). The main outcome is that the settings that determine the duration of the packet are very important when design an UWB indoor localization system. It is clearly shown that a short packet, i.e., configuration 1, outperforms a longer one in terms of tag density. In TDoA-TDMA, when adopting short packet option, the system is capable of supporting up to 6171 updates per second in the limit case, while using the longer 4.7 ms packet, only 211 tags are supported, which is around 97% less than in theoretical limit 1 case. Moreover, the localization scheme has also a big influence on the system scalability. When working with the same MAC approach, i.e., TDMA, the difference in tag density between TDoA and TWR is significant. The latter can only support 22% of the maximum number of tags in the short packet theoretical limit mode. For reference configuration 2, TWR-TDMA supports 53% less tags than the correspondent TDoA-TDMA case. As each application scenario has its own requirements in terms of tag density, a random access approach (ALOHA) combined with short TDOA packets can still be considered scalable, i.e., 1135 supported updates/s are probably enough to guarantee access in a single-floor scenario with a few offices. On the other hand, TWR-ALOHA has a very limited number of updates/s, both in configuration 1 and 2. The only advantage of this configuration is that ALOHA is easy to implement on the mobile tags and the infrastructure nodes do not need synchronization. Therefore, when only a few tags need to be localized at low update frequency this working setup can be used. The scalability model allows for further analysis that can be useful in various applications. In Figure 8, the number of supported updates/s is plotted against the frame duration. Between the two configurations used in this Section, more frame lengths have been used. Afterwards, the study has been applied to different UWB schemes, i.e., TDOA-TDMA, TWR-TDMA, TDOA-ALOHA and TWR-ALOHA. The graph clearly shows a non linear behaviour as the tag density drops dramatically for frame lengths bigger than 0.5 ms and then decreases slowly to the minimum, which in this case  
Figure 7: Tag density computed applying the scalability model with two different UWB configurations and two extra reference modes for TDMA w/o synchronization. corresponds to configuration 2. To obtain this graph, we applied formulas of the scalability models that are described in Section 4, wherein the different MAC protocols and localization techniques are defined. When designing an UWB system for indoor localization, if the target density is known, a graph like the one in Figure 8, can be used to find which UWB schemes satisfy the requirements. For example, if 1000 is the required tag density, there are mainly three options: TWR-TDMA or TDOA-ALOHA with a frame duration of 0.16 ms or alternatively TDOA-TDMA with around 1.1 ms packet length. More configuration, custom packets and options can be tested and evaluated using the model provided in this paper.