# Extending the Coverage of IEEE 802.15.4z HRP UWB Ranging
## 3 Link Analysis of HRP UWB Communication
### Link Analysis of Preamble in TWR Procedure  
In Section 3.3, we analyzed the link characteristics in the DP of HRP UWB. In this section, we analyze the ranging accuracy when data are successfully exchanged. In UWB communication, the ranging accuracy is related to the preamble, and the root mean square (RMS) value of the ranging accuracy of the preamble is given by the Cramer-Rao bound (CRB). In general, the RMS of the ranging accuracy is given as a function of the SNR and effective bandwidth as shown in Equation (7) [31; 32]:  
\[RMS(d)\geq\sqrt{CRB}=\frac{c}{2\sqrt{2}\pi BW_{eff}\sqrt{SNR}} \tag{7}\]  
where \(c\) is the speed of light, \(SNR\) is the signal-to-noise ratio of the preamble, and \(BW_{eff}\) is the effective bandwidth, which corresponds to 500 MHz in the case of the IEEE 802.15.4z HRP UWB standard [9]. Based on Equation (7), the ranging accuracy is expressed as a function of the SNR and effective bandwidth as shown in Figure 7.  
Figure 6: Example of increased output power via gating gain. If the ranging accuracy is 1 cm, then the SNR of the UWB preamble requires 16 dB according to Equation (7). In other words, unlike the SNR value required by the DP in the UWB packet, the preamble requires a 12.6 dB higher SNR value. To this end, the SNR value is increased by repeatedly transmitting the same symbol in the preamble. At this time, the processing gain is given by the number of symbol repetitions as shown in Equation (8):  
\[PG[\mathrm{dB}]=10 log_{10}\left(N_{p}\right) \tag{8}\]  
where \(N_{p}\) means the number of symbols used for ranging in the preamble. The number of symbols to be used for the processing gain of Equation (8) among the number of symbols in the preamble is defined by the PSRs and PACs. Now, the transmitted power of the preamble of the HRP UWB is given as shown in Equation (9) because the processing gain is added, unlike Equation (4):  
\[P_{TX,Preamble}[\mathrm{dBm}]=PSD_{TX}+BW+GG+PG \tag{9}\]  
where \(P_{TX,Preamble}\) is the transmitted power of the preamble in dBm, \(PSD_{TX}\) is the average power regulation of \(-41.3\) dBm/MHz, \(BW\) is the bandwidth in dBMHz, and \(GG\) and \(PG\) are the gating gain and the processing gain, respectively. Finally, the received power is based on the Friis transmission formula, which is a path loss model in free space. Now, using Equations (3)-(9), the link budget for each preamble and the DP of IEEE 802.15.4z UWB communication are calculated as shown in Table 3. In Table 3, CH9, which is currently available worldwide, was used as the UWB frequency. Among the results in Table 3, the preamble link and the DP link with a data transmission rate \(R_{b}\) of 6.8 Mbps are represented graphically as shown in Figure 8. As can be seen in Table 3, the link performance of the preamble was better than that of the DP. In other words, when the distance increases, the preamble may be received, but the data link may be broken. This has been experimentally presented in related papers [33; 34]. In addition, it can be seen that in the DP, sending data at a low speed of 850 kbps rather than a data rate of 6.8 Mbps can improve the performance by about 9 dB. This is consistent with the results provided by the chip manufacturer [23]. Figure 7: Cramer–Rao bound (CRB) for IEEE 802.15.4z HRP UWB ranging. The arrow indicates the SNR value at which the theoretical lower bound (CRB) reaches 1 cm, highlighting the required link quality for high-accuracy ranging. Our analysis results are summarized in Figure 9. The ranging coverage of UWB communication at a data rate of 850 kbps is more than twice as large as that for a data rate of 6.8 Mbps. The link performance of the preamble, which is the basis for synchronization and ranging, varies depending on the length of the preamble. In the IEEE 802.15.4z HRP UWB standard, the length of the preamble varies from a minimum of 16 to a maximum of 4096, and thus a longer preamble has larger ranging coverage than a shorter preamble. However, the preamble is not a good indicator of the preamble's performance.