## 4 Results  
To test the performance of the introduced method, an experiment under the condition where the BDS B1I signals are corrupted by two simulation chirps is carried out for several scenarios. The main hardware parameters of the down converter and ADC are recorded in Table 1.  
First, the JNR is set to 0 dB, 6 dB and 12 dB. The instantaneous frequency of one chirp interference is from 50 MHz to 30 MHz, and the instantaneous frequency of the other chirp interference is from 30 MHz to 50 MHz. The sweep period is 2.56 us and the sample length is 512. The Hough transforms combined by WVD and RSPWVD are shown as Figure 4. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Bandwidth & 20 MHz \\ Intermediate frequency & 40 MHz \\ Down Converter Gain & 60 dB \\ Dynamic range in Down Converter & 70 dB \\ Sampling Rates & 200 MHz \\ Bits Per sample & 14 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Down-converter digitizer parameters. Figure 4a shows that the WVD of two chirps suffers from cross-term interferences seriously due to the interaction of different chirp signal components; the outline of two chirps are not clear. Figure 4b depicts the RSPWVD of two chirps, the outline of which are clear. The cross-terms are less than those in Figure 4a. Figure 4c presents the WVD of chirps with a higher JNR and its energy distribution is clear and suffers from less cross-term interferences compared with Figure 4a. Figure 4d represents a clear RSPWVD which suffers from fewer cross-term interferences compared with that in Figure 4c. Although the power of chirps is 12 dB above that of noise, the WVD of chirps in Figure 4e still suffers from cross-term interference, while in Figure 4f, the outline of RSPWVD is very clear and its energy distribution hardly suffers from cross-term interference. However, Figure 4 shows that the common frequency (overlapped frequency) which belongs to chirp one as well as chirp two cannot be identified by the peak detection method. As a result, it is difficult to estimate instantaneous frequency in overlapped parts for each chirp. In order to deal with  
Figure 4: The WVD and RSPWVD of BDS B1I signals with two chirps, \(C_{0}/N\) is 43 dB-Hz and the JNR is 0 dB, 6 dB and 12 dB. (**a**) WVD, JNR is 0 dB. (**b**) RSPWVD, JNR is 0 dB. (**c**) WVD, JNR is 6 dB. (**d**) RSPWVD, JNR is 6 dB. (**e**)WVD, JNR is 12 dB. (**f**) RSPWVD, JNR is 12 dB. this problem, the experiment with the condition where the Hough transform is combined with WVD and RSPWVD is conducted; the experimental setup is as in Figure 4 and the results are shown in Figure 5.  
Figure 5a shows the Hough transform of WVD and there are three peaks in the Hough domain. The peak on the right is the pseudo peak. It is a cross-term, which is integrated by Hough transform in the TF plane and formed into a peak. What is shown in Figure 5b is similar to that in Figure 5a. Although the RSPWVD can reduce cross-term interferences, the power of chirps is as strong as that of noise. As a result, the RSPWVD reallocates the noise energy which is integrated by the Hough transform in the TF plane and is formed into a strong peak. Figure 5c depicts two strong peaks and a weak pseudo peak, while in Figure 5d there are only two strong peaks without a pseudo peak. In Figure 5e,f, there are two peaks without a pseudo peak. Figure 5 depicts that although the WVD suffers from cross-term interferences, the Hough transform can help to reduce the effect of the cross-term interferences when the chirp signals are strong. In addition, the RSPWVD can eliminate the cross-term interference at the expense of its good localization and concentration properties; the combination of RSPWVD and Hough transform can effectively reduce the effect of cross-term interferences. Figure 5: The Hough transform of WVD and RSPWVD with BDS BII signals corrupted by two chirps, \(C_{0}/N\) is 43 dB-Hz. (**a**) Hough transform of WVD, JNR is 0 dB. (**b**) Hough transform of RSPWVD, JNR is 0 dB. (**c**) Hough transform of WVD, JNR is 6 dB.