# Airborne Radar Staggered PRF Coherent Processing Method for Down-Looking Target Detection
## 4 Simulation Results
### Effectiveness Analysis of Doppler Ambiguity Resolution with Coherent Processing  
The introduced airborne radar down-looking target detection method utilizes the staggered-PRF transmission mode. It integrates multi-PRF ambiguity resolution coherently based on pulse transmission timing. Firstly, the method conducts coherence validity analysis of the multi-PRF pulse group signals, disregarding the influence of target distance. The radar samples the target's Doppler frequency, 3300 Hz, using three PRFs: 4000 Hz, 3900 Hz, and 4100 Hz, with a first sampling interval of 80 \(\upmu\)s and sampling 128 times per PRF. The DFT results for the range bins where the targets are located are depicted in Figure 7a, indicating Doppler frequency ambiguity for the targets. During coherent processing, the Doppler frequency is subject to ambiguity. Coherent processing is applied to each Doppler point within the range of [\(-\)5000 Hz, 5000 Hz]. For ambiguous Doppler frequencies, coherent processing is only conducted when all three PRFs exhibit ambiguity and the signal amplitude is assessed. If the selected post-ambiguous frequency values all contain peak amplitudes, the corresponding peaks are either set to zero or assigned a small value (effectively discarding the selected frequency point as it does not represent a real target). As shown in Figure 7b, in the range of Doppler frequency, due to the existence of Doppler ambiguity, there is a period extension under different PRFs. Only at the frequency of 3300 Hz, the DFT results of the three PRFs coincide. By eliminating false frequency points, the correct result of resolving ambiguity can be obtained, as shown in Figure 8.  
The results of resolving ambiguity and coherent processing for three PRFs are shown in Figure 8a. The output reveals a single peak at 3300 Hz, indicating successful elimination and suppression of ambiguous components in the Doppler frequency. The remaining energy is below 50 dB. Figure 8b illustrates the comparison of normalized Doppler spectra before and after coherent processing, where coherent processing is performed using a staggered PRF signal group with \(PRF_{N}=3\). After coherent processing, the signal gain  
Figure 8: De-ambiguous coherent processing results. (**a**) De-ambiguous coherent processing results. (**b**) Comparison of coherent processing before and after. Figure 7: The result after DFT processing. (**a**) DFT result at a single frequency point. (**b**) The DFT results within the frequency measurement range. is enhanced by a factor of \(PRF_{N}^{2}\), as observed from the results. The peak output energy is increased by 9.5 dB, consistent with theoretical expectations. In the presence of noise, the noise energy is increased by a factor of \(PRF_{N}\) after coherent processing, leading to an improved SNR by \(PRF_{N}\) times. However, the figure shows the presence of high sidelobes near the mainlobe, which can be mitigated through windowing. DFT-induced high sidelobes necessitate sidelobe suppression using windowing. The following results compare the outcomes before and after applying a Hamming window. Figure 9a illustrates that windowing reduces the remaining coherent energy to below \(-60\) dB, thereby enhancing the suppression of ambiguities. Figure 9b demonstrates that the coherence performance remains unaffected by the addition of the window. Even after coherence processing, the signal energy remains 9.5 dB higher compared to before coherence processing. In target detection, verifying the capability of coherent processing for ambiguity resolution in the presence of multiple frequencies, considering multiple targets with different Doppler frequencies in a range bin, is essential. For this purpose, a simulation experiment is conducted with three targets having Doppler frequencies of 3300 Hz, 1251 Hz, and \(-1300\) Hz, respectively. Figure 10a displays the DFT results of different PRFs in the presence of multiple targets, where each repetition frequency exhibits three peaks.