# A Novel GNSS Interference Detection Method Based on Smoothed Pseudo-Wigner-Hough Transform
## 6 Performance Evaluation
In comparison to the Wigner-Hough transform and pseudo-Wigner-Hough transform approaches, the smoothed pseudo-Wigner-Hough transform energy distributions contributed from the white Gaussian noise or the GNSS useful signal are much more weakened in the \(\rho-\theta\) transform space, as can be seen in Figure 15b. The smoothed pseudo-Wigner-Ville distribution energy distributions have been effectively strengthened at the intersection of the corresponding concurrent sinusoidal curves in the parameter space, forming a sharp energy peak. However, in other regions, excluding the intersection in the \(\rho-\theta\) transform space, the energy distributions from the white Gaussian noise or the useful GPS L1-C/A signal have not been accumulated but suppressed to very low levels even equal to zero. Therefore, the sweep interfering signal can be clearly distinguished from the others, and its signal features can be easily extracted using the proposed smoothed pseudo-Wigner-Ville distribution method. Figure 14: The smoothed pseudo-Wigner–Ville distribution (SPWVD) of the GPS L1-C/A signal disturbed by the sweep interference; (**a**) SPWVD; (**b**) SPWVD’s contour. In comparison to the global detection of many collinear points on the straight line in the time-frequency space by using the smoothed pseudo-Wigner-Ville distribution technique, the proposed smoothed pseudo-Wigner-Hough transform method easily deals with sweep interference detection since it only needs to check the local energy peak at a particular intersection within the \(\rho-\theta\) transform space. The smoothed pseudo-Wigner-Hough transform-based GNSS interference detection can be implemented by the accumulator through the voting scheme in the \(\rho-\theta\) transform space. Therefore, the characteristic parameters related to the sweep interference frequency modulation law in the time-frequency plane can be determined. When the position of the intersection of the concurrent sinusoidal curves is determined in the \(\rho-\theta\) transform space, the characteristic parameters of the GNSS sweep interference can be then precisely estimated. This is the subject of future research. Moreover, in order to further verify the GNSS interference detection performance improvement of the proposed smoothed pseudo-Wigner-Hough transform method in comparison to the other Hough transform-based techniques, the zero Hough-transformed energy percentage metrics are, respectively, evaluated for the Wigner-Hough transform, the pseudo-Wigner-Hough transform and smoothed pseudo-Wigner-Hough transform in the detection of the interfered GPS L1-C/A signal, as can be shown in Figure 16. In the zero Hough-transformed energy percentage performance analysis, the C/N\({}_{0}\) of the used GPS L1-C/A signal is 46 dB-Hz, the JNR values of the sweep interference range from \(-8\) dB to 4 dB; and the size of the local neighborhood domain in the \(\rho-\theta\) parameter space is set to be an \(80\times 80\) matrix, i.e., \(80\times 80\) cells are contained in the local neighborhood domain, where the main energy peak of any Hough-transformed distribution is localized. In the evaluation of the zero Hough-transformed energy percentage for any Hough-transformed distribution in the GNSS interference detection, only the Hough-transformed energy distributions in the cells of the region within the parameter space excluding the determined local neighborhood area are considered; hence, the higher the proportion of cells with zero Hough-transformed energy distribution value in the region within the parameter space, the better performance of zero Hough-transformed energy percentage can be obtained. From Figure 16, it can be seen that as the JNR values of the interfered GPS L1-C/A signal increase, the zero Hough-transformed energy percentage results of the Hough transform-based GNSS interference detection techniques increase monotonously.