# A Pilot-Based Integration Method of Ranging and LS Channel Estimation for OFDM Systems
## 4 Simulation Results  
In Sections 2 and 3 of this paper, the general model of this design has been discussed, and in this section, we will simulate and verify the analysis of the proposed algorithm model. The transmission and reception simulation flow are shown in Figure 4.  
As shown in Figure 4, the transmitter inserts different ranging codes into the transmission signal from the frequency domain as pilots. The receiver utilizes these pilots for LS channel estimation and distance measurement, which improves the spectrum utilization of LS channel estimation. The paper has analyzed the recovery of received signal when using the ranging pilot and traditional pilot through simulation. Moreover, the acquisition and tracking performance of ranging with these pilots under different signal-to-noise ratios (SNRs) is also analyzed. Table 2 shows the parameters adopted in this simulation. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Number** & **Period** & **Maximum Unambiguous Distance** \\ \hline
2 & 2, 7 & 7 km \\
3 & 2, 7, 11 & 77 km \\
4 & 2, 7, 11, 15 & 1155 km \\
5 & 2, 7, 11, 15, 19 & 21,945 km \\
6 & 2, 7, 11, 15, 19, 23 & 504,735 km \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Maximum unambiguous distance of coprime ranging codes with different periods. Figure 4: (**a**) Block diagram of the OFDM transmitter. (**b**) Block diagram of the OFDM receiver. As shown in Table 2, three different ranging codes are selected as pilots in this simulation, and their cycles are, respectively, 15, 19, and 23 chips. According to (15), the maximum unambiguous distance that the three ranging sub codes can range is 3,277,500 m, which can be completely applied to most UAV working environments. Figure 5 shows the comparison of the BER performance of the ranging pilot and the original pilot. As shown in Figure 5, compared with the original pilot, the BER performance of the OFDM system has been improved after utilizing ranging pseudocodes as pilots. In the case of the same BER, when utilizing ranging codes as pilots, the requirement for SNR is reduced by about 1 dB. Therefore, this method can well realize the channel estimation function of the original pilot and improve the channel estimation performance. After channel estimation, the receiver will continue to utilize these range codes for ranging. Since the period of different ranging codes is relatively small, this method consumes less time to acquire and track them. Figure 6 shows the acquisition probability of the receiver for the composite code and each range code under different SNRs. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of total subcarriers & \(N=64\) \\ Length of cyclic prefix & \(N_{cp}=16\) \\ Modulation scheme & QPSK \\ Signal frequency & \(f\) & 34.8 MHz \\ Sampling frequency & \(f_{s}\) & 348 MHz \\ Subcarrier frequency & \(f_{sc}\) & 0.6 MHz \\ Code frequency & \(f_{code}\) & 0.6 MHz \\ Code sampling frequency & \(f_{s-code}\) & 6 MHz \\ Channel mode & AWGN \\ DLL bandwidth & 1 Hz \\ DLL correlator spacing & 0.25 chip \\ Number of pseudo-random codes & 3 \\ The period of pseudo-random codes & 15, 19, 23 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. Figure 6 shows that the receiver can perform stable acquisition for each ranging code when the SNR is \(-5\) dB or more. In the actual OFDM system application, the SNR requirement of OFDM is generally above \(10\) dB. Therefore, in the OFDM application scenario, the acquisition performance of this system can satisfy the application requirements. From Figure 6, the acquisition probabilities of the three ranging codes are not consistent. However, the receiver needs to successfully acquire each ranging code to correctly range the transmission distance. Therefore, the overall acquisition performance can more directly  
Figure 5: Performance comparison chart of ranging pilot and original pilot. Figure 6: Acquisition probability of different ranging codes. reflect the actual SNR requirement of the system.