## 5 Performance Evaluation
Figure 9: Spectrogram of the GPS L1 signal with sweep interference. The spectrogram has been evaluated by using a Hamming window. \(C/N_{0}\) = 46 dB-Hz, JNR = \(-2\) dB. (**a**) Window size = 31; (**b**) Window size = 63. In order to deal with the TF resolution trade-off problem with the spectrogram approach, the WVD of the GPS L1 signal with the sweep interference is depicted in Figure 9(a), and correspondingly, the contour of the computed WVD is presented in Figure 9(b). The interfering term presents a linear behavior in frequency, which is well localized in the restricted area of the TF plane. Due to the interaction of the different components in the interfered GPS L1 signals, the presence of serious cross-terms is apparently observed in Figure 9(b), which makes interpretation quite difficult and brings much error to the estimation of the instantaneous frequency of the interfering signal. The price paid for good TF resolution with the WVD approach is the undesirable cross-terms present in the TF plane. Therefore, in order to improve the TF energy concentration properties and to avoid the cross-terms present in the quadratic TF distribution at the same time, a novel TF distribution by using the reassigned spectrogram has been proposed in interference detection for GNSS receivers. The reassigned spectrogram of the interfered GPS L1 signal is depicted in Figure 9(a), and the corresponding contour of the reassigned spectrogram is provided in Figure 9(b). In Figure 9(a), it is clear that the proposed reassigned spectrogram yields very sharp peaks in the TF plane denoting the undesired sweep interfering term in the interfered GPS L1 signal; accordingly, in Figure 9(b), in the TF plane, there exists a very strict line representing the instantaneous frequency of the sweep interfering signal by using the reassigned spectrogram method, which provides representations that are easy to interpret in interference detection for GNSS receivers. The reassigned spectrogram squeezes the TF energy distributions concentrated at the instantaneous frequency line in the TF plane, where the TF energy density components are apparently strengthened. The reassigned spectrogram greatly improves the sharpness of the ridges of the sweep interfering term, which are highly localized at the instantaneous frequency line in the TF plane, since the spread energy of the spectrogram is relocated from the geometrical center to the gravity center in the TF energy distribution. Therefore, the instantaneous frequency of each component of the sweep interfering signal can be revealed by detecting the local energy peaks in the reassigned spectrogram. The reassigned spectrogram makes the TF energy of the sweep interference concentrate at the instantaneous frequency line, which presents good readability in the TF plane. Much improved TF aggregation properties can be achieved in comparison to the conventional spectrogram approach; and meanwhile, the reassigned spectrogram is free of cross-term artifacts during the TF analysis; this is its advantage when compared with the WVD approach. This proposed TF analysis based on the reassigned spectrogram solves the cross-term problem of the bilinear TF distribution and keeps good TF resolution in the TF plane, which has been proven to be valid and effective to adopt in interference detection for GNSS receivers in jamming environments. With this developed technique, the interfering signal can be correctly identified and its instantaneous frequency can be precisely estimated. The estimated instantaneous frequency of the interfering signal can be used in the notch filter, which is used in the interference mitigation unit of the GNSS receiver for the removal of the interfering signal. In order to analyze the performance of the interference mitigation unit and, in particular, the impact of a notch IIR filter adopted in the GNSS receiver, ROC curves under different signal scenarios have been evaluated by Monte Carlo simulations.