###### Abstract  
For distributed satellite constellations, detection performance can be equivalently regarded as a single large satellite by the cooperative operation of multiple small satellites, which is a promising research topic of the Next-Generation Radar (NGR) system. However, dense grating lobes inevitably occur in the synthetic transmit pattern due to its distributed configuration, as a result of which the detection performance of dynamic coherent radar is seriously weakened. In this paper, a novel transmit beampattern optimization method for dynamic coherent radar based on a distributed satellite constellation is presented. Firstly, the effective coherent detection range interval is determined by several influence factors, i.e., coherent detection, far-field, and system link constraints. Then, we discuss the quantitative evaluation method for coherent integration in terms of synchronization error, beam pointing error, and high-speed motion characteristics and we allocate the corresponding terms in a reasonable way from the perspective of engineering. Finally, the space-time-frequency degrees of freedom (DOFs), which can be collected from satellite spacing carrier frequencies, and platform motion characteristics, are utilized to realize a robust transmit beampattern with low sidelobe by invoking a genetic algorithm (GA). Simulation results validate the effectiveness of our theoretic analysis, and unambiguous coherent transmit beamforming with a satellite constellation of limited scale is accomplished. coherent radar; coherent integration efficiency; synchronization error; distributed satellite constellation +
Footnote †: journal:  
0000-0001-4618-0000-0000-0000-0000-0000-0000-00000-0000-00000-00000-0000-00000-00000-00000-00000-00000-00000-00000-00000-000000-00000-000000-000  
The MIT Lincoln Laboratory and the Chinese Academy of Astronautics and Astronautics have carried out distributed coherent experiments of closed-loop systems [11; 12]. For the latter, an open-loop system does not depend on the prior target information, which is more suitable for large-scale early-warning applications. The key point lies in the space-time-frequency synchronization strategy [13; 14; 15]. Space-time-frequency synchronization includes three aspects, i.e., space, frequency, time, and phase synchronization. Space synchronization means high-precision calibration for radar array configuration. In [16], the ranging accuracy could reach the milli-meter level by employing a sparse spectrum signal instead of a broadband signal, but there exists a time delay ambiguity problem. By combining a dual-frequency waveform and step frequency waveform, the ranging ambiguity issue can be solved [17]. Further, the relative positions among subarrays can be obtained by means of least square (LS) estimation methods [18; 19; 20]. As for frequency synchronization, it is accomplished by an auxiliary utilizing Global Positioning System (GPS) signals [21], but the estimation accuracy is somewhat low. In [22], a dual-frequency continuous wave (CW) signal was adopted to realize frequency synchronization, and its effectiveness was verified in a two-node system. For time and phase synchronization, time synchronization errors with regard to different signal waveforms are analyzed in [23] and signal phase differences before and after passing through the oscillator are measured by a phase detector to estimate initial phases in [13]. In [24], the identifiability analysis of the phase synchronization error was studied, and it proved that only their relative values are identifiable. For dynamic coherent radar based on distributed satellite constellation, the signal envelope movement between radar nodes can be ignored because the detection range is larger than that of the radar-radar spacing. Meanwhile, the detection area needs to be quickly covered by the angle scanning mode, which is not suitable for the grid scanning mode starting from real-time processing requirements.