# Analysis of the Scalability of UWB Indoor Localization Solutions for High User Densities
## 4 Localization Schemes and MAC Considerations
### MAC Considerations
#### 4.3.1 Aloha  
A typical random access method is ALOHA. This protocol requires no sensing actions to be performed by the nodes before transmitting a packet, i.e., no transmission schedule is necessary. Although simple and straightforward to implement, ALOHA can result in collisions, thereby impacting the scalability of the overall system. In pure ALOHA or simply ALOHA, a transmitting station does not check whether the channel is free or not before transmitting its packet: whenever it has data to send, it transmits. In this scenario the success is only determined by the collision probability with other transmitting nodes. Following the existing scientific literature [26], the maximum channel utilization when using ALOHA is equal to 0,186 which means that only 18.6% of the time can be used for successful, collision free communications. Below this value, 97% of the transmissions are likely to succeed without collisions [27]. This channel utilization can be considered as the capacity of the random access channel. The maximum number of mobile tags with update frequency \(\lambda\), supported in the system is [26]:  
\[N=(2\cdot e\cdot T_{packet}\cdot\lambda)^{-1} \tag{8}\]  
\[\lambda\in[f_{min},f_{max}]\]  
where \(T_{packet}\) = transmission duration and \(e\) = [PERSON]'s number.  
More nodes can be added to the network but this would quickly deteriorate the performance of the protocol as shown in [26].  
Independently from the localization scheme, ALOHA remains the same. However, when TWR is adopted, we assume that within one frame, two messages are consecutively exchanged between the tag and the anchor in line with the TWR scheme previously described in Section 4.2. As a result, the ALOHA protocol becomes problematic especially when dealing with long messages (\(T_{packet}\)). The resulting total transmission time \(T_{total-TX}\) is computed as follows:  
\[T_{total-TX}=n_{anchors}\cdot[n_{exchange}\cdot(T_{tx}+T_{guard})+(n_{exchange }-1)\cdot T_{reply}] \tag{9}\]  
where \(n_{exchange}\) is the number of exchanged messages, e.g., 2 in the TWR case and 4 for SDS-TWR scheme and \(n_{anchors}\) is the number of anchors involved in the positioning process, i.e., 4 in a single cell system.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Symbol**} & \multicolumn{1}{c}{**Variable Name**} & \multicolumn{1}{c}{**Unit**} \\ \hline \(T_{reply}\) & Reply time in TWR & ms \\ \(T_{tx}\) & Transmission duration & ms \\ \(T_{sync}\) & Synchronization beacon duration & ms \\ \(T_{encon}\) & Beacon duration & ms \\ \(T_{CAP}\) & Contention Access Period (CAP) duration & ms \\ MAC & \(T_{CFP}\) & Contention Free Period (CFP) duration & ms \\ \(T_{superframe}\) & Superframe duration & ms \\ \(n_{resources}\) & Resources available & unitless \\ \(n_{anchors}\) & Number of anchors & unitless \\ \(n_{exchange}\) & Number of message exchanges & unitless \\ \(N\) & Number of supported tags & unitless \\ \(\Lambda\) & Position update frequency & Hz \\ \hline LDC & \(T_{on}\) & Transmitter on time & ms \\ \(T_{off}\) & Transmitter off time & ms \\ \hline DAA & \(D_{thresh}\) & Power level threshold & dBm \\ \(P_{TXcoint}\) & Transmit power of victim system & dBm \\ \(I\) & Minimum needed isolation & dBm \\ \hline \hline \end{tabular}
\end{table}
Table 6: _Cont._