## 5 Performance Evaluation  
In this section, the performance of the proposed interference detection method based on joint TF analysis by using RSPWVD is analyzed. In particular, this proposed new algorithm, which  
Figure 4: Joint TF distribution based on reassigned smoothed pseudo Wigner–Ville distribution (RSPWVD) in interference detection for GNSS receivers. adopts RSPWVD to detect sweep interference in GNSS receivers, is compared with 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 [28]. The scheme of the test is reported in Figure 5, while an image of the experimental setup adopted for collecting the GPS data corrupted by sweep interference is depicted in Figure 6. 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 developed 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. In the experiment, the scenario adopted for the test is characterized by the setting parameters provided in Table 1, representing the real GPS L1 signal in zero mean Gaussian noise corrupted by a constant  
Figure 5: Scheme of the measurement test in the lab. Figure 6: Experimental setup of the measurement test in the lab. amplitude linearly frequency modulated interference (linear chirp), which is commonly considered as a test bench in interference detection for GNSS receivers. In the experiment settings, the JNR value of the sweep interference is set to be \(-1\) 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, \(\Delta f_{0}=+7\) MHz and \(\Delta f_{1}=-9\) MHz. In Figure 7a, 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 7b, where the disturbing effect can be clearly observed. The adoption of the ambiguity function of the received interfering signal is beneficial to better monitor the interference contribution in the received GNSS signals. In Figure 8, the spectrogram of the GPS L1 signal with sweep interference is depicted, where the Hamming window function is chosen. In Figure 8a, the window size is 63 samples, where the disturbing \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Carrier-to-noise ratio, \(C/N_{0}\) & 46 dB-Hz \\ 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 7: Ambiguity function of the GPS L1 signal. \(C/N_{0}\) = 46 dB-Hz. (**a**) Without interference; (**b**) with interference, jammer-to-noise ratio (JNR) = \(-1\) dB. term more or less emerges in the TF plane, but very poor TF localization properties are obtained with this approach. 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 8b, where the window length is increased to 127 samples. 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 squared magnitude and, therefore, does not lead to undesirable cross-terms present in the WVD.