# A Novel GNSS Interference Detection Method Based on Smoothed Pseudo-Wigner-Hough Transform
## 6 Performance Evaluation
Figure 10a depicts the Wigner-Ville distribution of the GPS L1-C/A signal in the presence of the sweep interference, with the corresponding contour of the calculated Wigner-Ville distribution in Figure 10b. From Figure 10, the sweep interference component shows a linear behavior in the time-frequency plane, which is located in the limited linear area of the time-frequency space. In particular, in Figure 10b, a straight line of the frequency modulation law corresponding to the sweep interference present in the received GNSS signal can be clearly observed in the time-frequency plane. However, this improved time-frequency resolution is at the price of the unavoidable cross-terms present in the time-frequency plane, which bring much error to the characteristic parameters' estimation of the GNSS interfering signal and make signal interpretation difficult and incorrect. Due to the presence of a cross-term problem in the Wigner-Ville distribution, the GNSS interference essential features cannot be correctly extracted. In order to solve the problem of the cross-term with the Wigner-Ville distribution, Wigner-Hough transform is employed in the interference detection test for GNSS receivers, which is illustrated in Figure 11. In Figure 11a, the Wigner-Hough transform of the interfered GNSS signal is given in the \(\rho-\theta\) plane. From Figure 11b, it is clear that the  
Figure 10: The Wigner-Ville distribution (WVD) of the GPS L1-C/A signal disturbed by the sweep interference; **(a)** WVD; **(b)** WVD’s contour. Figure 9: The spectrogram of GPS L1-C/A signal disturbed by the sweep interference; **(a)** window size = 31; **(b)** window size = 63.  
sinusoids corresponding to the white Gaussian noise or GNSS useful signal components are randomly distributed and cannot be accumulated in effect. On the contrary, the energy peak of Wigner-Hough transform is evidently located in the parameter space, which represents the sweep interfering signal occurring in the received GNSS signal. Therefore, the GNSS interference feature can be distinguished from those of the white Gaussian noise or the useful GNSS signal. In Figure 11b, the contour of the computed Wigner-Hough transform is shown, where concurrent sinusoids pass through a specific single point in the \(\rho-\theta\) transform space, with each sinusoidal curve corresponding to a single point on the line of GNSS sweep interference frequency modulation law in the time-frequency plane. In this way, in the time-frequency plane, the detection of the straight line of GNSS interference frequency modulation law has been converted to the equivalent determination of the position of the intersection of the concurrent sinusoidal curves by searching for the energy peak in the \(\rho-\theta\) transform space. Therefore, the points in the time-frequency plane generally map to the corresponding sinusoidal curves in the \(\rho-\theta\) transform space. In particular, collinear points along the straight line of GNSS sweep interference frequency modulation law in the time-frequency plane map to the corresponding concurrent sinusoidal curves intersected in the \(\rho-\theta\) transform space. The pseudo-Wigner-Ville distribution is adopted to mitigate the cross-interfering term present in the Wigner-Ville distribution in the detection of GNSS interference. The pseudo-Wigner-Ville distribution of the disturbed GPS L1-C/A signal is shown in Figure 12a, with the corresponding contour of the calculated pseudo-Wigner-Ville distribution provided in Figure 12b. It can be seen that the sweep interfering signal shows a linear behavior denoting its frequency modulation law in the time-frequency domain, and the cross-interfering terms are alleviated to some extent due to the use of the low-pass filtering window function in the pseudo-Wigner-Ville distribution.