## 4 Results and Application
### Application of Coherent Integration Time Optimization Model
#### 4.2.2 Model Application: Extrapolation to Spaceborne Scenario
With an increase in wind speed from 4 m/s to 10 m/s, the optimal precision decreases from 0.57 m to 0.85 m. At low wind speeds, the sea surface is smooth, the waveform coherence is strong, and the effective incoherent average is small. However, the SNR is high, which enhances precision. The optimal coherent integration time will increase from 1.6 ms to 3 ms with wind speed. This is because high wind speed increases ocean scattering. Simultaneously, the higher the wind speed, the worse the SNR, and the greater the precision improved by the optimal coherent integration time. (3) In Figure 9C, the optimal precision increases from 0.94 m to 0.63 m as the elevation angle changes from 40\({}^{\circ}\) to 80\({}^{\circ}\). On the one hand, increasing the elevation angle shortens the propagation path of the navigation signal, which reduces the signal energy loss. On the other hand, according to Figure 3, the iso-delay area decreases with the elevation angle, thereby increasing the effective incoherent average. Since both the altimetric sensitivity and the effective incoherent average decrease with the elevation angle, the balance between the two leads to little change in the optimal coherent integration time. Accordingly, as the elevation angle increases, the SNR of the reflected signal upgrades and the improvement of the precision by the optimal coherent integration time becomes insignificant. (4) As illustrated in Figure 9D, when the antenna gain is increased from 15 dBi to 30 dBi, the optimal precision improves from 0.72 m to 0.31 m. The high gain antenna can increase signal energy and upgrade the SNR. When the antenna gain is increased from 25 dBi to 30 dBi, the optimal precision is only improved from 0.34 m to 0.31 m. This indicates that an increase in antenna gain will not be sufficient to improve precision at high SNRs. Similarly, the optimal coherent integration time does not greatly improve the precision in the case of high gain. Since the change of the antenna gain does not affect the effective incoherent average, the optimal coherent integration time does not change much with the antenna gain. (5) In general, the optimal coherent integration time calculated in the spaceborne simulation is shorter than that for the airborne scenario. This is because the satellite receiver has a high velocity, making the Doppler bandwidth and the effective incoherent average large. The shorter coherent integration time can effectively reduce the influence of speckle noise. The simulation analysis of the above parameters indicates that the coherent integration time optimization model improves the precision more significantly when the SNR of the reflected waveform is relatively weak. Limited by the code bandwidth, improving the SNR of the signal does not increase the precision infinitely but approaches the limit value. Additionally, the optimal coherent integration time varies with the simulation parameters, and the spaceborne scenario tends to be shorter than the airborne scenario. Increasing the altitude of the orbit and the wind speed will also increase the optimal coherent integration time.