# Extending the Coverage of IEEE 802.15.4z HRP UWB Ranging
## 3 Link Analysis of HRP UWB Communication
### Link Analysis of Data Portion in TWR Procedure  
In order for the TWR process of HRP UWB explained in Section 3.2 to be successful, packets related to ranging must first be successfully exchanged. To this end, there must be no preamble errors and no DP data errors. In other words, the link budget of the preamble and the link budget of the DP must be considered simultaneously.  
First, let us look at the DP link. The link performance of the DP is determined by whether the packet reception is successful or not and is usually given as the packet error rate (PER). In this study, we assume a PER of 1% or more as the link performance criterion. This value is a value commonly discussed in the current next-generation UWB standard IEEE 802.15.4 ab [8]. The PER performance of BPM-BPSK used in UWB communication is generally given as shown in Equation (2) [31]:  
\[PER=N\mathrm{Q}\left(\sqrt{\gamma\frac{E_{b}}{N_{0}}}\right) \tag{2}\]  
where \(N\) is the number of bits per packet, \(\gamma\) is the coding gain, \(E_{b}\) is the bit energy, and \(N_{0}\) is the power density spectrum of noise. As shown in Figure 5b, the 'Poll', 'Response', and 'Final' packets are required for ADS-TWR, and the longest packet is the 'Final' packet with a size of 24 bytes. Thus, this packet should be used as the criterion for PER evaluation; that is, since \(N\) is 192 bits, \(E_{b}/N_{0}\) of the DP corresponds to 9.0 dB, assuming 1% PER. Next, the IEEE 802.15.4z HRP UWB standard uses convolutional channel coding and Reed-Solomon channel coding, and thus it has a channel coding gain of about 5.6 dB [14]. Therefore, the DP of the IEEE802.15.4z HRP UWB standard should have an \(E_{b}/N_{0}\) value of about 3.4 dB [23]. In addition, since the IEEE802.15.4z HRP UWB standard spreads one bit over multiple chips, the signal-to-noise ratio (SNR) is given by Equation (3):  
\[SNR=\frac{E_{b}}{N_{0}}\frac{R_{b}}{BW}=\frac{E_{b}}{N_{0}}\left(\frac{R_{b}}{ R_{c}}\right) \tag{3}\]  
where \(BW\) is the bandwidth, \(R_{b}\) is the bit rate, and \(R_{c}\) is the chip rate. Based on the IEEE 802.15.4z HRP UWB standard, when \(R_{b}\) is 850 kbps, the SNR is calculated to be about \(-24.3\) dB, and when \(R_{b}\) is 6.8 Mbps, the SNR is calculated to be \(-15.3\) dB. In other words, if the data rate is as low as 850 kbps, then there is a 9 dB link margin, and thus a wider communication range can be achieved than in the case of 6.8 Mbps.  
Now that we know the SNR value, let us analyze the DP link based on the transmitter parameters of the IEEE 802.14z HRP UWB standard and the power regulation in Table 2. The transmitted power is given by Equation (4):  
\[P_{TX,DP}\big{[}\mathrm{dBm}\big{]}=PSD_{TX}+BW+GG \tag{4}\]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 \(GG\) is the gating gain. The gating gain is given by Equation (5):  
\[GG[\mathrm{dB}]=10 log_{10}\bigg{(}\frac{1[\mathrm{ms}]}{T_{p}}\bigg{)} \tag{5}\]  
where \(T_{p}\) corresponds to the time length of the packet. In other words, if the packet length is less than 1 ms, it indicates that the output can be increased by that amount according to the local regulation. Figure 6 shows a case where the output power is doubled by GG when \(T_{p}\) is 0.5 ms. Typically, UWB IC manufacturers such as Qorvo and NXP provide a function that can control power through the gating gain if the packet length is shorter than 1 ms [23]. Finally, the receiver sensitivity is given by Equation (6):  
\[S_{DP}[\mathrm{dBm}]=-174+BW+NF+SNR_{\mathrm{min}} \tag{6}\]  
where \(SNR_{\mathrm{min}}\) is the minimum SNR, which is given by Equation (3), and NF is the receiver's noise figure. Finally, the received power is calculated based on the Friis transmission formula, which is a path loss model in free space.