# A Novel GNSS Interference Detection Method Based on Smoothed Pseudo-Wigner-Hough Transform
## 6 Performance Evaluation
It is notable that the realized suppression of the undesired cross interfering terms within the quadratic time-frequency distributions is gained at the price of attenuating the property of the time-frequency aggregation with the pseudo-Wigner-Ville distribution. Figure 11: The Wigner–Hough transform (WHT) of the GPS L1-C/A signal disturbed by sweep interference; (**a**) WHT; (**b**) WHT’s contour. In Figure 13a, the pseudo-Wigner-Hough transform is used in the detection of the sweep interfering signal, with its contour shown in Figure 13b. From the figure, the intensity of the energy peak corresponding to the sweep interference present in the received GPS L1-C/A signal can be strengthened at the intersection of the concurrent sinusoidal curves in the \(\rho-\theta\) transform space, which, respectively, map to the collinear points located in the same line of GNSS sweep interference frequency modulation law in the time-frequency plane obtained by the pseudo-Wigner-Ville distribution. When the position of the intersection of the concurrent sinusoidal curves is determined in the \(\rho-\theta\) transform space, the characteristic parameters of the sweep interference can be estimated. The obtained energy peak of the pseudo-Wigner-Hough transform is accumulated at the intersection since the concurrent sinusoidal curves all pass through the same point in the \(\rho-\theta\) transform space. However, in the other areas excluding the intersection, the pseudo-Wigner-Hough transform energy distributions from the white Gaussian noise or the GNSS useful signal have not been accumulated. Furthermore, these energy distributions corresponding to white Gaussian noise or GNSS useful signal become sparse when compared with the case of Wigner-Hough transform, as can be seen in Figure 13b. To effectively deal with the problem of the cross-interfering terms present in the Wigner-Ville distribution, the smoothed pseudo-Wigner-Ville distribution is adopted for GNSS interference detection. In Figure 14a, the smoothed pseudo-Wigner-Ville distri  
Figure 12: The pseudo-Wigner–Ville distribution (PWVD) of the GPS L1-C/A signal disturbed by the sweep interference; (**a**) PWVD; (**b**) PWVD’s contour. Figure 13: The pseudo-Wigner–Hough transform (PWHT) of GPS L1-C/A signal disturbed by the sweep interference. (**a**) PWHT; (**b**) PWHT’s contour. bution of the interfered GPS L1-C/A signal is shown, where the peaks of the smoothed pseudo-Wigner-Ville distribution clearly emerge in the time-frequency plane, representing the contribution from the GNSS sweep interfering signal. The corresponding smoothed pseudo-Wigner-Ville distribution's contour is provided in Figure 14b. The undesired sweep interfering signal shows a linear characteristic in frequency denoting its frequency modulation law, which can be observed in the limited linear area within the time-frequency space. In comparison to the Wigner-Ville distribution and pseudo-Wigner-Ville distribution approaches, the cross-terms are effectively suppressed in the time-frequency plane by the smoothed pseudo-Wigner-Ville distribution through the use of two-dimensional smoothing function. However, this benefit is achieved at the cost of a deterioration in the time-frequency localization property for the analyzed signal. In Figure 15, the smoothed pseudo-Wigner-Hough transform is employed for GNSS interference detection. From Figure 15a, the intensity of the energy peak representing the sweep interference in the received GPS L1-C/A signal can be clearly observed in the intersection of the concurrent sinusoidal curves in the \(\rho-\theta\) transform space, which, respectively, correspond to the collinear points distributed on the same frequency modulation line of the sweep interference in the time-frequency plane obtained by the smoothed pseudo-Wigner-Ville distribution.