# Clutter Cancellation and Long Time Integration for GNSS-Based Passive Bistatic Radar
## 4 Simulation Results and Discussion
### Simulation Results
#### 4.1.1 Detection Results of Target with Smooth Motion  
We consider the target with smooth motion and the acceleration is set as zero. At first, the conventional detection approach looking for the peak that the RD map got over a CPI is applied to detect the target. The RD map is obtained by performing a slow-time FT for the range-compressed echo. Figure 4 shows the RD map without considering the clutter cancellation. It can be seen that, except for the direct and multi-path echo located in zero Doppler, there is no bright spot that can be associated to the target. It can be deduced that the clutter and low power target echo affect the target detection performance. Subsequently, we take clutter cancellation into consideration. Figure 5 shows the coherent processing results which both the direct and multipath signal at zero Doppler from the first 50 range cells (4400 m) are cancelled. Figure 5 provides the RD map obtained by the traditional FT. A clear spot that corresponds to the actual position of the target can be identified from Figure 5. However, the target energy has not been correctly gathered in the Doppler dimension due to the long integration time. The Doppler frequency of the target migrate several Doppler cells. When the echo signal is low, the target cannot be detected effectively. Moreover, the spread Doppler will affect the following parameter extraction. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Setting Value** & **Parameter** & **Setting Value** \\ \hline Carrier frequency & 1575.42 MHz & Bandwidth & 1.023 MHz \\ Complex sampling rate & 4.092 MHz & Pulse repeat frequency & 1000 Hz \\ Pulse number & 3000 & Range resolution & 146.6 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the radar system. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **SNR (dB)** & **Sample Delay** \\ \hline Direct signal & 0 & 0 \\ Multipath 1 & \(-\)7.96 & 5 \\ Multipath 2 & \(-\)6.02 & 9 \\ Target echo & \(-\)40 & 33 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Related simulation parameter. Subsequently, the long time integration method that is based on modified radon Fourier transform (MFRT) is applied as comparison. Figure 6 shows the RD map obtained by MFRT. When compared with the RD map in Figure 5, it can be seen that the Doppler spread has been effectively eliminated. However, a slight spread is still existing in Doppler dimension. It can be deduced that the spread is caused by the parameter estimation error. Figure 4: RD map based on Fourier transform (FT) without clutter cancellation. Figure 5: RD map based on FT with clutter cancellation. Figure 6: RD map based on modified radon Fourier transform (MFRT). Next, the new proposed method is applied to deal with the data. Firstly, Figure 7a shows the instantaneous Doppler frequency versus the slow time. The red curve shown in Figure 7a is the real instantaneous Doppler frequency during the CPI, and the blue one is the result after curve fitting. It can be seen that the Doppler frequency is time varying and a slow-time FFT cannot effectively integrate the target energy. Figure 7b shows the errors between the real and fitting Doppler, from which it is seen that the errors are increased with the coherent integration time. The maximum error is 0.12 Doppler cell within the CPI, which can be negligible. It can also be noticed that the second-order expansion is sufficient for describing the Doppler variation during the dwell time. Figure 8 is the parameter estimation result of signal in 33 rd range cell by FrFT. The search interval of the rotation angle \(p\) was set to \([0,\pi]\) with a step length of \(0.005\pi\). The estimation result indicates that the DR and DMR are 3.14 and \(-56.12\), respectively. The rough RA can be calculated according (21) and it is \(-0.056\). The accurate RA is obtained by maximizing the EIR and the search interval is set to \([-0.066,-0.046]\), with a step length of 0.001.