# A Novel Signal Design and Performance Analysis in NavCom Based on LEO Constellation
## 4 Performance Evaluation
### Navigation Performance Analysis  
In this subsection, we will compare CE-OFDM-PM (2) with signals from major existing systems such as BPSK (1), BPSK (4), BOCs (5, 2), and SRC (0.2, 1). We will also compare it with different parameters and compare it to the classical modulation signals such as BOCs (5, 2.5) and MSK (10), as proposed by [PERSON] [60] and [PERSON] [61], respectively. * Accuracy potential  
It can be seen from Figure 8 that when the front-end bandwidth of the receiver increases in the range of 7-10 MHz, the Gabor bandwidth increases sharply, and the cost performance between the positioning performance and the overhead is the highest at this time. When the receiver front-end bandwidth is between 10 and 40 MHz, the Gabor bandwidth is constant, which means that the blind receiver front-end bandwidth is cost-effective for the signal scheme proposed in this article. Figure 8 shows the Gabor bandwidth of different spread spectrum-modulated signals. The higher the frequency of the power spectrum of the modulated signal, the larger the Gabor bandwidth value will be. When the receiver bandwidth B is below 13.5 MHz, the Gabor bandwidth of the proposed scheme is very small. When the receiver bandwidth B = 15 MHz, the Gabor bandwidth of the proposed scheme is equivalent to the Gabor bandwidth of BPSK (1), and when the receiver bandwidth B = 16.5 MHz, the Gabor bandwidth of the proposed scheme is the same as that of MSK (10) The bandwidth is equivalent, reaching 2.3586 MHz, which is better than that of BPSK (4) but lower than the Gabor bandwidth of BOCs (5, 2) and BOCs (5, 2.5) at 4.29469 MHz. Figure 9 shows the Gabor bandwidth of CE-OFDM-PM at different modulation orders n. It is not difficult to see that CE-OFDM-PM (2), which is shown by the grey dashed line, has a comparatively high receiver front-end bandwidth at 16.5 MHz. The Gabor bandwidth is better than that of the other schemes, allowing the receiver bandwidth to be fixed when the receiver bandwidth is used to obtain the best positioning performance. Figure 10 shows the code tracking error of different spread spectrum-modulated signals. It can be seen from the figure that when the \(C/N_{0}\) is 15 dB, the code tracking error (grey dashed line) of the proposed scheme is about 1.2 m and the performance is obviously better than that of BPSK (1) and BPSK (4) and slightly better than that of BOCs (5, 2), BOCs (5, 2.5), and MSK (10). Additionally, the positioning error is inferior to that of SRC (0.2, 1). As the noise ratio increases, the code tracking accuracy will sharply improve; when the CNR is 20 dB-Hz, the code tracking accuracy will reach about 0.85 m, which is significantly better than that of other candidate signals in the S-band. Figure 11 shows that when the modulation order n is different, the code tracking error of the scheme proposed in this paper is slightly smaller than that of CE-OFDM-PM (1) and significantly smaller than that of CE-OFDM (4). Therefore, it can be found that our proposed signal has a good performance in terms of positioning accuracy. Figure 8: Proposed signals’ Gabor bandwidths compared with BPSK (1), BPSK (4), BOCs (5, 2), BOCs (5, 2.5), SRC (0.2, 1), and MSK (10). For bandwidths of 16.5 MHz at the front end of the receiver, the gray dashed line has a Gabor bandwidth that can exceed the green solid line and the blue, while the performance is shown by the dark red. Figure 10: Proposed signals’ code tracking errors compared with BPSK (1), BPSK (4), BOCs (5, 2), BOCs (5, 2.5), SRC (0.2, 1), and MSK (10). For a carrier-to-noise ratio of 15 dB-Hz, the code tracking error indicated by the gray dashed line is about 1.2 m, which is much better than others, except for the dark red. This shows that CE-OFDM-PM (2) has outstanding potential for use in code tracking. Figure 9: Comparison of the Gabor bandwidth under the conditions of \(k=1\), 2, 4, 8.