# Feasibility Study of Passive Bistatic Radar Based on Phased Array Radar Signals
## 4 Coherent Integration Method Based on Radon-NUFFT
### Simulation Results  
In order to validate the performances of the proposed method, simulation experiments are conducted. The simulated parameters ofthe radar and moving target are listed in Table 1, which is based on the monostatic radar model.  
Suppose the SNR of the received target echo before pulse compression is 10 dB. Figure 8 shows the range-time map of signal after pulse compression. It can be seen that the trajectory of target is not  
\begin{table}
\begin{tabular}{c c} \hline \hline
**System Parameters (Unit)** & **Values** \\ \hline Carrier frequency (MHz) & 680 \\ Bandwidth (MHz) & 2 \\ Sampling frequency (MHz) & 5 \\ Pulse width template library (us) & [40 80 120 160 200] \\ Average PRI (us) & 1500 \\ Variation range of PRI (us) & [1000 2000] \\ Number of coherently integrated pulses & 128 \\ Initial distance of target (km) & 90 \\ Radial velocity of target (m/s) & 800 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Simulated parameters.  
Figure 7: Flowchart of the proposed method.  
a straight line due to the irregular RCM and range-Doppler coupling. In addition, the amplitude of different pulse is different because the amplitude of signal after pulse compression is proportional to \(\sqrt{B\tau_{m}}\), and \(\tau_{m}\) is staggered.  
Figure 9a shows the result of the signal after compensation for irregular RCM via Radon algorithm by using the accurate velocity of target. It can be seen that the trajectory of the target is still not a vertical straight line due to the irregular range-Doppler coupling. Figure 9b is the result of Figure 9a after compensating for range-Doppler coupling. It can be seen that the envelope of the target is aligned on the same vertical line.  
Figure 10 compares the results of coherent integration via four methods. Figure 10a is the result of moving target detection (MTD), i.e., perform FFT directly in the slow time dimension without compensation, which cannot obtain any apparent peak in the range-velocity plane. Figure 10b shows the result of RFT, i.e., perform FFT in the slow time dimension after compensation of RCM and range-Doppler coupling, which cannot obtain any apparent peak either. Therefore, we can get the conclusion that FFT cannot solve the nonuniform phase fluctuations among different pulses, which has a very serious influence on the coherent integration.  
Figure 10c shows the result of using NUFFT among a slow time dimension without compensation of RCM and range-Doppler coupling, and Figure 10d shows the result of Radon-NUFFT. It can be seen that both of them show a peak in the range-velocity plane, which reveals the coherently integrated echo signals. However, in Figure 10c, the estimated initial range and velocity of the target indicated by the peak location in the range-velocity domain is inaccurate, since the irregular RCM and range-Doppler coupling are not compensated. Moreover, it can be seen that the peak value in Figure 10d is higher  
Figure 8: Range-time map after pulse compression.  
Figure 9: Results of signal after compensation. (**a**) Result after compensation of irregular RCM; (**b**) Result after compensation of irregular RCM and range-Doppler coupling.  
than that in Figure 10c, and the initial range and velocity indicated by the peak position in Figure 10d are both accurate, which proves the effectiveness of the proposed method.