# A Novel Signal Design and Performance Analysis in NavCom Based on LEO Constellation
## 4 Performance Evaluation
### Navigation Performance Analysis
Figure 15 shows the multipath error envelope of different spread spectrum-modulated signals under the condition of multipath delay within 4000 m. From the envelope, the multipath error of the scheme proposed in this paper is slightly better than SRC (0.2,1). However, it is far superior to other spread spectrum-modulated signals, which means that CE-OFDM-PM is the best choice of the spread spectrum signal against the multipath in the case of a large multipath delay. Figure 16 shows the average multipath error envelope of different spread spectrum-modulated signals under the condition of multipath delay within 4000 m. It can be seen from this that the average multipath error of the scheme proposed in this paper is maintained at different multipath delay conditions. Within 0.1 m, this level is significantly ahead of that of other signal systems. Figure 17 shows the multipath error envelope of CE-OFDM-PM under different modulation orders n. It can be seen from this that under the condition of a short-distance multipath delay of 300 m, the scheme proposed in this paper compared with CE-OFDM-PM (1), CE-OFDM-PM (4), and CE-OFDM-PM (8) has a smaller multipath error envelope. Figure 14: Proposed signals’ multipath error envelope compared with BPSK (1), BPSK (4), BOCs (5, 2), BOCs (5, 2,5), SRC (0.2, 1), and MSK (10) within 500 m. The grey dashed line shows that the multipath error envelope within 500 m of the multipath delay is much smaller than that of other lines. This means that the proposed spread spectrum signal itself has very remarkable multipath suppression capabilities. Figure 16: Proposed signals’ average multipath error envelope compared with BPSK (1), BPSK (4), BCCs (5, 2), BCCs (5, 2.5), SRC (0.2, 1), and MSK (10) within 4000 m. In terms of the statistical indicators of the multipath envelope, the grey dashed line maintains an average value of between 0.08 and 0.11 m while the multipath delay is within 4000 m.  
Figure 15: Proposed signals’ multipath error envelope compared with BPSK (1), BPSK (4), BCCs (5, 2), BCCs (5, 2.5), SRC (0.2, 1), and MSK (10) within 4000 m. Obviously, the grey dash line also has a smaller multipath error envelope over long distances. This means that the proposed signal also has a better adaptability in scenarios on more reflective surfaces or longer reflection distances. Figure 18 shows the multipath error envelope of CE-OFDM-PM with different values of n under the long-distance multipath delay condition of 4000 m, as well as the multipath error envelope of the short-distance multipath delay condition of 300 m. The conclusions are similar. Compared with CE-OFDM-PM (1), CE-OFDM-PM (4), and CE-OFDM-PM (8), the scheme proposed in this paper (marked by the grey dashed line) has the advantage of having a long-distance multipath delay. The smaller multipath error envelope means that this scheme has a more significant anti-multipath advantage in the modulation order under the same spread spectrum modulation signal scheme. Figure 17: Comparison of multipath error envelope with CE-OFDM–PM under the conditions of \(k=1\), 2, 4, 8 within 500 m. The proposed signal marked by the gray dashed line has a smaller multipath error envelope than the signal of the CE–OFDM–PM signal family within 500 m.  
Figure 10:0 Comparison of multipath error envelope with CE-OFDM–PM under the conditions of \(k=1\), 2, 4, 8 within 4000 m. The proposed signal also has a smaller multipath error envelope than the signal of the CE–OFDM–PM family within 4000 m.  
Above all, the scheme proposed in this article has an overwhelming advantage over the other listed schemes in terms of its multipath error envelope and average multipath envelope. * Anti-jamming  
Figure 19 shows the anti-jamming performance of different spread spectrum-modulated signals when the bandwidth is 16.5 MHz. It is not difficult to see that the tracking and matching spectrum, demodulation and matching spectrum, tracking and narrowband, and merit factors of demodulation and narrowband are 73.297, 23.8182, 61.3182, and 12.1418 dB.