# Airborne Radar Staggered PRF Coherent Processing Method for Down-Looking Target Detection
## 4 Simulation Results
### Multi-PRF Result Analysis of Airborne Radar with Orthogonal Signals  
This section simulates the entire process of airborne radar down-looking mode using the proposed method. The simulation involves the use of five different PRFs for staggered-transmission in the down-looking mode. Each group employs different DFC signals. The PRFs for the five groups of signals are [4.3 kHz, 4.2 kHz, 3.7 kHz, 3.5 kHz, 4.1 kHz], with the corresponding start times of the first transmit pulse being [0 \(\upmu\)s, 32.6 \(\upmu\)s, 88.4 \(\upmu\)s, 144.2 \(\upmu\)s, 195.3 \(\upmu\)s]. Assuming a target distance of 12 km, a target speed of \(-45\) m/s, and the target being coincident with the clutter front, it is assumed that the 5 PRFs are unaffected by clutter, thus placing the targets within the noise region. Airborne radar simulation parameters are shown in Table 1.  
Figure 11: Comparison of multi-target de-ambiguous and coherent processing before and after. Figure 10: The result of multi-target de-ambiguous and coherent processing. (**a**) Multi-target DFT results. (**b**) The result of multi-target de-ambiguous and coherent processing. According to the antenna simulation parameters, the antenna pattern has a beam width of approximately 4 and a maximum gain of 53 dB. The simulation sets the aircraft's flight altitude to 8000 m and its heading speed to 100 m/s. The simulated ground clutter range is 34.8 km \(\times\) 34.8 km. Based on the aircraft track and antenna pattern, the corresponding antenna gain for each ground grid can be calculated. Within the main beam's irradiation range of the ground clutter, the Doppler bandwidth is approximately 600 Hz. For the echo simulation of each PRF signal group, clutter, and target parameters, DFT processing is performed without noise. The DFT frequency interval is set to 100 Hz, and the RD maps of the four PRF signal groups are depicted in Figure 12. The figure reveals that the target's Doppler frequency is 3900 Hz. After DFT processing, the ambiguous frequencies for different signal groups are [\(-400\) Hz, \(-300\) Hz, \(200\) Hz, \(400\) Hz, \(-200\) Hz]. The clutter Doppler center is at 4600 Hz, and there are ambiguities in various PRF signal groups. Performing ambiguity resolution and coherent fusion processing between multiple frames is based on the initial moment of each frame signal transmission. Doppler ambiguity is resolved by selecting data according to the corresponding ambiguity Doppler index for each Doppler spectrum line, followed by coherent processing on the selected data. Figure 13a displays the processing results without noise. In the figure, the correct Doppler spectrum for the target and the clutter area (around 4900 Hz) exhibits significant energy, while the remaining ambiguous areas contain only residual energy. For a clearer analysis of the coherent effect and ambiguity suppression performance, the signal from the range bin containing the target is examined. Figure 13b presents the Doppler spectrum of the target's range bin. In the figure, the target's Doppler is accurately resolved and its coherent accumulation achieves an energy gain of 13.38 dB, close to the theoretical value of 13.97 dB. In non-target areas, there is residual energy from Doppler ambiguity resolution, resulting in energy distribution in some regions. The energy of ambiguity resolution is suppressed by approximately 50 dB. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & \begin{tabular}{c} **Center** \\ **Frequency** \\ \end{tabular} & **Bandwidth** & **Pulse Width** & \
\begin{tabular}{c} **Code** \\ **Number** \\ \end{tabular} &
\begin{tabular}{c} **Transmit** \\ **Power** \\ \end{tabular} \\ \hline Value & 9.4 GHz & 40 MHz & 10 \(\mu\)s & 20 & 10 kW \\ \hline \hline \end{tabular}  
Radar antenna parameters are shown in Table 2.  
\end{table} 
Table 1: Radar simulation parameter.