## 5 Performance Evaluation  
In this section, the performance of the proposed interference detection method based on the TF analysis by using the reassigned spectrogram is analyzed. In particular, this proposed algorithm, which adopts the reassigned spectrogram to detect sweep interference in GNSS receivers, is compared to the conventional interference detection approaches in the disturbing scenario. The mentioned interference detection approaches are tested on real GPS data collected by using the GNSS software receiver developed at Beihang University, China [24]. The scheme of the test is reported in Figure 6, while an image of the experimental setup adopted for collecting the GPS data corrupted by sweep interference is depicted in Figure 7. The real GPS samples are collected by using the GNSS software receiver connected to the Trimble Zephyr Geodetic 2 antenna placed on the roof of the new main building at Beihang University in an open-sky static condition; the software interferer is adopted for generating the sweep interfering signal for GNSS applications. The generated sweep interference is added to the GPS samples collected by the GNSS receiver front-end. Figure 6: Scheme of the measurement test in the lab. Figure 7: Experimental setup of the measurement test in the lab. In the experiment, the scenario adopted for the test is characterized by the setting parameters listed in Table 1, representing the real GPS L1 signal in zero mean Gaussian noise corrupted by a constant amplitude linear frequency-modulated interference (linear chirp), which is commonly considered as a test bench in interference detection for GNSS receivers. In the experiment settings, the carrier power to noise power density ratio \(C/N_{0}\) is 46 dB-Hz, and the JNR value of the sweep interference is set to be \(-2\) dB; in a linear chirp, the instantaneous frequency \(f_{inst}\) of the interfering signal evolves linearly with time over the interval \([f_{\text{L1}}+\Delta f_{0},f_{\text{L1}}+\Delta f_{1}]\), where \(f_{\text{L1}}\) is the GPS L1 signal center frequency, \(\Delta f_{0}=+5\) MHz and \(\Delta f_{1}=-7\) MHz. In Figure 8a, the ambiguity function of the GPS L1 signal without interference is shown as a spike. In the case with the presence of sweep interference, the ambiguity function of the interfered GPS L1 signal is depicted in Figure 8b, where the disturbing effect can be clearly observed. The adoption of the ambiguity function is beneficial to better monitor the interference contribution in the interfered GPS L1 signals. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Sampling frequency, \(f_{s}\) & 24 MHz \\ Intermediate frequency, \(f_{IF}\) & 40.42 MHz \\ Code length & 1023 chips \\ Sweep period & 1 ms \\ Spectrogram analysis window & Hamming \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental setting parameters. Figure 8: Ambiguity function of the GPS L1 signal. \(C/N_{0}\) = 46 dB-Hz. (**a**) Without interference; (**b**) With interference, JNR = \(-2\) dB. In Figure 9, the spectrogram of the GPS L1 signal with sweep interference is depicted, where the Hamming window function is chosen. In Figure 9a, the window size is 31 samples, where the disturbing term more or less emerges in the TF plane, but very poor TF localization properties are obtained. In order to evaluate the TF characteristics of the spectrogram by increasing the length of the analysis window, the spectrogram of the interfered GPS L1 signal is presented in Figure 9b, where the window length is increased to 63 samples. From Figure 9, it is clear that a long time window leads to improved frequency resolution and inevitably yields poor resolution in time. The spectrogram is nonlinear, but this nonlinearity results from the operation of the squared magnitude and, therefore, does not lead to undesirable cross-terms in the TF distribution. Figure 10: WVD of the GPS L1 signal with sweep interference. \(C/N_{0}\) = 46 dB-Hz, JNR = \(-2\) dB. (**a**) WVD; (**b**) Contour of WVD.