# Interference Mitigation for GNSS Receivers Using FFT Excision Filtering Implemented on an FPGA
## 3 Proposed Methodology
### Scenarios: Different Types of Interference  
This scheme was evaluated using different scenarios that have been discussed according to the related works in [13, 38, 39]. There are main parameters for each scenario, which are the centre frequency (\(f_{0}\)) of the jamming signal, the intermediate frequency (\(IF\)) of the jamming signal, and the jamming to noise density ratio (\(J/No\)). The centre frequency (\(f_{0}\)) is a measure of the centre frequency between the upper and lower cut-off frequency. The centre frequency is relative to the RF front-end's intermediate frequency  
Figure 3: Operational scheme of the proposed methodology.  
(\(IF\)). The intermediate frequency (\(IF\)) is a frequency in which a carrier wave is shifted as an intermediate step in transmission or receiving. In this work, \(IF\) was selected to be 6.5 MHz and the jamming to noise density ratio (\(J/No\)) increased with the amplitude of the jamming signals. The applied jamming interferences in the simulation were continuous-wave (CW) interference and the sweeping frequency jammer.  
Table 1 shows the parameters of these scenarios carried out in this work. The first scenario was simulated using one continuous-wave jammer that had a centre frequency (\(F_{0}\)) at 6.5 MHz and the interval frequency was between \(-1\) and 1 MHz with a jamming to noise (\(J/No\)) ratio from 0 to 130 dB-Hz. The second scenario was simulated using multiple continuous-wave jammers with the same parameters as the first scenario. We followed the same approach in [13, 39] to simulate the frequency fixed jammer to achieve the first and second scenarios using the following Equation (1):  
\[J(t)=\sum_{i=0}^{p}~{}A~{}\sin(2\pi(f_{0}+df_{i})t) \tag{1}\]  
where \(p\) is the number of jammers (equal to one in the first scenario and equal to 2 or 3 or a higher number than 1 in the second scenario). \(f_{0}\) is the centre frequency and \(df_{i}\) is the change in the frequency due to the interval. \((f_{0}+df_{i})\) is included in the interval [5.5-7.5] MHz as mentioned in Table 1. The jamming signal amplitude increases with (\(J/No\)) in the simulations. However, the amplitude does not vary between multiple jammers in the same simulation file and the phase of the jammer is omitted from this definition and set to zero in our simulations. Figure 4 shows an example of a continuous-wave jammer at (\(J/No\)) = 80 dB-Hz.  
The third scenario was simulated using a sweep jammer that had a certain frequency of 6.5 MHz and the swept bandwidth was \(-1\) to 1 MHz with a jamming to noise ratio from 0 to 130 dB-Hz and the frequency rate was set to 8.4 GHz/s for a comparison with the results given in [13]. The sweeping frequency jammers were defined with the following Equation (2):  
\[J(t)=A~{}\sin(2\pi(f_{0}+df_{i}(t))t)\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenarios** & **Number of Jammers** &
\begin{tabular}{c} **Jammer Centre** \\ **Frequency.\(f_{0}\) (IF = 6.5 MHz)** \\ \end{tabular} & **Frequency Sweep Rate** & **Jamming Levels (\(J/No\))** \\ \hline Scenario 1 & One Jammer & \(-5.5\) MHz to 7.5 MHz & 0 Hz & 0 to 130 dB-Hz \\ \hline Scenario 2 & Multiple Jammers (2 to 10) & \(-5.5\) MHz to 7.5 MHz (equally spaced across the band) & 0 Hz & 0 to 130 dB-Hz \\ \hline Scenario 3 & (Sweeping Frequency) & \(-5.5\) MHz to 7.5 MHz & 0 to 20 GHz/s & 0 to 130 dB-Hz \\ \hline \hline \end{tabular}
\end{table}
Table 1: The considered interference scenarios for evaluating the scheme.  
Figure 4: Example of a continuous-wave jammer with (\(J/No\)) = 80 dB-Hz.  
where \(df(t)\) is a time-varying frequency offset. Figure 5 shows an example of the frequency variation of a jammer sweeping at a sweeping rate of 8.4 GHz/s (with a sampling frequency of 26 MHz).