# A Low-Ambiguity Signal Waveform for Pseudolite Positioning Systems Based on Chirp
## 5 Simulation  
In order to explore the signal performance, the computer simulation is performed, with the method shown Figure 11. First, the digital IF navigation signal is generated by MATLAB, and saved in a disk. Second, we load this signal samples, add noise and multipath signal to the original samples with a specified CN0 and MDR when we use. Then, the signal samples are processed by a software defined receiver (SDR). Finally, the signal performance is evaluated by the tracking results output from SDR. Figure 12 shows the simulated PSDs of ChPN(5,1), ChPN(4,2), ChPN(3,3), ChPN(10,1) and BOC(5,1), which quite match with Figure 4. According to Figure 12, a signal with a wider sweep bandwidth owns a flatter PSD; the signals of situation 1 differ in characteristics, ChPN(3,3) is similar to BPSK, ChPN(4,2) is similar to BOC, and ChPN(5,1) is similar to chirp; for situation 2, ChPN(5,1) has a more flatter PSD than BOC(5,1) while BOC(5,1) has more high-frequency components; for situation 3, ChPN(10,1) has a flatter and wider PSD than ChPN(5,1). Figure 13 shows the simulated tracking errors of different signals, which is drawn with an ELS of 5.86 m, a sampling rate of 61 MHz, a code loop bandwidth of 0.5 Hz, and a coherent integration time of 1 ms. According to the figure, we can draw some conclusions: (1) either the tracking error or the tracking error difference between different signals decrease when the C/N0 increase; (2) the tracking errors become smaller when the PDB increase; (3) a wider sweep bandwidth leads to better tracking performance for the signals that own the same or different MLBs; (4) BOC(5,1) owns smaller tracking errors than ChPN(5,1) with the same MLB. Figure 11: Simulation method. Figure 10: Cross correlation analysis. As we can see from Figures 6 and 13, the two figures are similar in variation trend, but differ in numerical value. Figure 6 is obtained by calculating with a mathematical model. As some factors that impact the tracking errors are not considered in that model but encountered in SDR, such as carrier phase differences, carrier frequency differences and sampling frequency. MPEE reflects the maximum ranging error caused by one-ray multipath with specific parameters, which is the theory limit calculated by mathematical model. Hence, it is hard for us to obtain MPEEs from a SDR, but multipath errors are reachable. Figure 14 shows the simulated multipath errors for various signals, which is drawn under the condition that C/N0 is 40 dB-Hz, ELS is 5.86 m, sampling rate is 61 MHz, the code loop bandwidth is 0.5 Hz, MDR is \(-6\) dB, PDB is 24 MHz. According to Figures 14 and 15, some conclusions can be drawn. First, for situation 1, the signal with a wider sweep bandwidth has a smaller multipath error among the alternative signals, such as ChPN(5,1) has the smallest multipath error and the fastest convergence speed followed by ChPN(4,2) and ChPN(3,3). Secondly, for situation 2, ChPN(5,1) has a smaller multipath error than BOC(5,1), the convergence speed is faster than that of BOC(5,1). Thirdly, for situation 3, ChPN(10,1) has a smaller multipath error and a faster convergence speed than ChPN(5,1). The variation trends are similar to Figure 7, as well as the conclusions. Figure 12: Simulated PSD of various signal. Figure 13: Simulated tracking errors of various signals with bandwidth of 12 MHz and 24 MHz. Figure 15 shows the standard deviation of multipath error of various signals, which reflects the jitter of multipath error. ChPN(5,1) has the smallest multipath error standard deviation among the signals of situation 1. Both ChPN(5,1) and ChPN(10,1) has the smaller multipath error standard deviation than BOC(5,1). In order to explore the ACF peaks ambiguity of the signals, we carry out the Monte Carlo simulation with 10,000 runs. Figure 16 shows the simulated false locking probability (FLP) caused by ACF side-peaks, which is drawn with a PDB of 24 MHz, a sampling rate of 61 MHz, and a coherent integration time of 1 ms. Generally, the FLP become smaller when the C/N0 increase.