## 2 Materials and Methods
For space-based radar detection, the coordinate transformation is generally adopted, that is \(S_{s}\to S_{g}\to S_{i}\to S_{e}\to S_{n}\), where \(S_{s}\), \(S_{g}\), \(S_{i}\), \(S_{e}\), and \(S_{n}\) stand for the Satellite Body-fixed Coordinate, Geocentric Orbit Coordinate, Geocentric Equatorial Inertial Coordinate, Geocentric Equatorial Rotating Coordinate, and East North Up Coordinate, respectively. In this section, target detection processes are performed in the ENU (East North Up) coordinate by employing the coordinate system transformation operation. The sub-satellite point is the coordinate origin, and thus the geometric center coordinate of the distributed coherent radar is given by [0 km, 0 km, 500 km]. In terms of the far-field boundary condition and the system link, the available detection range interval in regard to the above-mentioned distributed satellite constellation configuration is given by 600 km-1000 km. The coherent integration efficiency of the typical missile target is demonstrated in Figure 5, where its size is given by 20 \(\times\) 1.8 m\({}^{2}\). From Figure 5a, the target coherent integration efficiency \(\eta_{\rm T}\) tends to be 1 under ideal conditions as the detection range increases. In this case, extended target detection can be regarded as equivalent to point target detection, while the detectable coherent range interval in Figure 5b is restricted under coherent detection constraints, far-field constraints, and system link constraints. Evidently, the target coherent integration efficiency \(\eta_{\rm T}\) also tends to be 1 in the far-field region, and the coherent range interval is only restrained by the geometric relationship between the distributed satellite constellation and the target. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Platform Height** & **Signal Bandwidth** & **Coherent Processing Interval** & **RCS** \\ \hline
**Value** & 500 km & 1 MHz & 5 ms & 0.03 m\({}^{2}\) \\ \hline
**Parameters** & **Peaktransmission power** & **Antenna gain** & **Radar system loss** & **Noise coefficient** \\ \hline
**Value** & 5 kw & 34 dB & 8 dB & 2 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. Figure 5: Target coherent integration efficiency map. (**a**) Target coherent integration efficiency under ideal conditions in the whole detection space; (**b**) target coherent integration efficiency with detection range constraints in the whole detection space. The coherent integration efficiency of the distributed satellite constellation system is 90%, and the boundary condition related to the time synchronization error, phase synchronization error, beam pointing error, and that caused by the high-speed motion platform is represented in Figure 6. Here, the time synchronization accuracy and the phase synchronization accuracy should be better than 60 ps and 27\({}^{\circ}\). The ratio of the beam pointing error to the mainlobe width should be less than 0.25. Furthermore, the upper bound of the relative tangential velocity between the satellite and the target should not exceed 23,700 m/s. These boundary values provide an effective reference for designing system and synchronization terms. According to the theoretical analysis presented in Section 2, the coherent integration efficiency can be measured quantitatively based on the system synchronization errors, among which the time synchronization error, the channel consistency error, the position error, and the relative frequency stability are set to 48 ps, 5\({}^{\circ}\), 5 mm, and 10\({}^{-12}\) in turn, and the corresponding coherent integration efficiency losses caused by the above terms are given as 7.74%, 0.02%, and 1.69%, respectively. Hence, the total coherent integration efficiency is better than 90%. Based on the above satellite constellation configuration, the virtual aperture can be formed by utilizing the rotation characteristics of these satellites in the temporal domain.