# Analysis of the Scalability of UWB Indoor Localization Solutions for High User Densities
## 6 Application of the Scalability Model  
In this section, we validate the scalability model defined in Section 5 mainly using MATLAB to compare different scenarios. To this end, we refer to UWB properties of the commercial DW1000 chip by Decawave Ltd., which allows to easily adjust operational modes. Since we also want to show the impact of different UWB configurations on user density, we define and use two of them in combination with diverse MAC protocols and localization approaches. Configuration 1  
* System type: LT1
* Channel: 5 (center frequency = 6489.6 MHz and bandwidth = 500 MHz)
* bitrate: 6.81 Mbps
* Preamble: 128 symbols
* PRF: 16 MHz
* Payload: 3 bytes
* Number of anchors: 4  
Configuration related variables: \(T_{packet-conf1}\) = packet duration, \(S_{i-conf1}\) = receiver sensitivity, \(d_{MAX-conf1}\) = maximum theoretical range. Figure 5: Cell size definition problem. Figure 6: Final step to output the maximum user density achievable (**a**) Standard constraints (**b**) MAC protocol (**c**) localization technique. Configuration 2
* System type: LT1
* Channel: 5
* bitrate: 110 kbps
* Preamble: 4096 symbols
* PRF: 64 MHz
* Payload: 3 bytes
* Number of anchors: 4  
Configuration related variables: \(T_{packet-conf2}\) = packet duration, \(S_{i-conf2}\) = receiver sensitivity, \(d_{MAX-conf2}\) = maximum theoretical range. The first step requires to have a full understanding of the system. According to standard definitions [25] and UWB regulations (see Section 3), we assume that both configurations are LT1 type operating in channel 5. Moreover, considering that localization is done indoor, the two systems do not have to use any mitigation technique. To compute the frame duration for each scenario, we have to introduce the Decawave symbol duration table, which reports all the timings depending on the frame part. Using the values of Table 7 and (3) we find the frame duration for configuration 1 and 2, which are \(T_{packet-conf1}=162\) us and \(T_{packet-conf2}=4.7\) ms.  
Before using these values in the scalability model, we want to calculate the achievable range, which is the second step of the scalability model described in Section 5.1 and in turns defines the maximum cell size. As shown in Figure 5, we still need to define the transmission power, the receiver sensitivity and the path loss model. In this case, the latter is the Free Space path loss (FSPL), which is derived from Friis Transmission formula [28]. The equation to describe the attenuation in dB is the following:  
\[FSPL(dB)=32.45+20 log(d[km])+20 log(f[MHz]) \tag{12}\]  
As we also assume to have 0 dBi for the antenna gain and no other attenuation, (12) can be used to obtain the \(d_{MAX}\). To quantify the maximum range, it is necessary to link the transmission power \(P_{TX}\) and the receiver sensitivity \(S_{i}\), which can be found in the Decawave manual and it corresponds to \(S_{i-conf1}=-93\) dBm and \(S_{i-conf2}=-106\) dBm. Together with \(P_{TX}=-14.3\) dBm, this results in available link margin of 82 dB (configuration 1) and 92 dB (configuration 2). Therefore, from (12) and using the available link budget, we find that \(d_{MAX-conf1}=46\) m and \(d_{MAX-conf2}=146\) m.  
Finally, the last step of the model takes all aspects into account (Figure 6) and depending on localization scheme and MAC protocol, it outputs the maximum user densities, as shown in Figure 7. In Section 4.3, we explained how the available resources per tag are computed and for that we also defined other variable, which are common to both configurations and here listed:  
* \(T_{reply}=400\) us
* \(T_{superframe}=1\) s
* \(T_{CAP}=100\) ms
* \(T_{synch}=0\) (no synch) or \(T_{synch}=T_{packet}\)