# An Anti-Interference Method Based on Energy Residual Searching in GNSS Positioning Applications
## 5 Simulation and Results  
The experiments were conducted in a high-performance computing environment, to ensure efficient execution of the complex algorithms and data processing tasks. The hard ware configuration included an Intel Core i7-12700K CPU with 12 cores and 20 threads, operating at a base clock of 3.6 GHz and capable of reaching a maximum turbo frequency of 5.0 GHz. The system was equipped with 16 GB of DDR4 RAM, operating at 3200 MHz, providing sufficient memory for large-scale data processing and memory-intensive computations. Additionally, an NVIDIA GeForce RTX 2070 GPU with 8 GB of GDDR6 memory was utilized to accelerate the image processing and deep learning model training. The software environment for this study was MATLAB 2023b, which was employed for its robust mathematical computation and simulation capabilities, along with various toolboxes for data processing, algorithm development, and simulation. This setup provided the necessary computational resources to ensure the reliability and accuracy of the experiment's results. To validate the effectiveness and feasibility of the proposed interference detection method based on the fractional Fourier transform (FrFT), multiple tests were conducted, with the relevant parameters listed in Table 1. The intermediate frequency (\(f_{IF}\)) of the GNSS software receiver((FGI-GSRx v2.0.1)) was set to 40.42 MHz, and the sampling frequency (\(f_{s}\)) was set to 25 MHz, in accordance with the bandpass sampling theorem. The collected GPS L1-C/A signals were disturbed by constant-amplitude linear frequency modulation (LFM) interference (i.e., linear chirp) in zero-mean white noise, which is commonly used as an interference detection test platform in GNSS applications. In the GNSS interference detection tests, the jamming-to-noise ratio (JNR) of the linear chirp was set to \(-4\) dB, the sweep period was set to 0.5 ms, and the chirp rate was set to 25 GHz/s. In time-frequency analysis, there is an inherent trade-off between time resolution and frequency resolution. When analyzing the GPS L1-C/A signals in the presence of sweep interference, the Hamming window was chosen as the window function for the spectral analysis. As shown in Figure 2b, when the analysis window length was 31 sample points, the time-frequency resolution was insufficient to distinguish the sweep interference, resulting in the interference effect being indistinct on the time-frequency plane, and the sweep interference could not be accurately detected. To improve the time-frequency resolution, the spectrogram method's time-frequency characteristics were studied by increasing the size of the analysis window. As shown in Figure 2a, when the analysis window length was increased to 63 sample points, the linear frequency modulation interference in the received GPS L1-C/A signal became more recognizable on the time-frequency plane. However, as the window length increased, the resolution in the time dimension significantly decreased, leading to suboptimal time-frequency localization characteristics. This demonstrated that while increasing the window length improved frequency resolution, it inevitably compromised time resolution. This trade-off is clearly evident in Figure 2, where it is shown that the spectrogram method struggles to provide precise instantaneous frequency estimation in practical applications. Although interference signals can be approximately assessed by appropriately selecting the window length, the spectrogram's inability to simultaneously achieve high time and frequency resolution when processing GNSS inter \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Carrier-to-noise ratio, \(C/N_{0}\) & 46 dB-Hz \\ \hline Jammer-to-noise ratio, \(JNR\) & \(-4\) dB \\ \hline Sampling frequency & 25 MHz \\ \hline Intermediate frequency & 40.42 MHz \\ \hline Frequency rate of change & 25 GHz/s \\ \hline Sweep period & 0.5 ms \\ \hline Spectrogram analysis window & Hamming \\ \hline \hline \end{tabular}
\end{table}