# Optimal Order of Time-Domain Adaptive Filter for Anti-Jamming Navigation Receiver
## 5 Experimental and Analysis
### Measured Data Analysis  
A practical test was performed in a controlled environment with interference sources of different power and bandwidth to verify the applicability of this approach in GNSS receivers' real-world scenarios. The interference source controls the power and bandwidth of interference signals, and the desired navigation signal is a Beidou B3 civil signal originating from the No.7 satellite. Our experimental platform is depicted in Figure 10.  
The parameters of the practical test are as follows: the data length is 1 ms; the sampling rate is 75.12 MHz; the receiver's bandwidth is 20 MHz; the correction value \(\Delta M\) is set to be 0; the maximum CNR loss for designing the optimal filter order is 8 dB\(\cdot\)Hz; the CNR of undisturbed signals is 58 dB\(\cdot\)Hz. This paper adopts six interference scenes.  
1. Set interference bandwidth to 2 MHz, and JSR to approximately 50 dB.
2. Set interference bandwidth to 2 MHz, and JSR to approximately 40 dB.
3. Set interference bandwidth to 1 MHz, and JSR to approximately 50 dB.
4. Set interference bandwidth to 1 MHz, and JSR to approximately 40 dB.
5. Set interference to be single-frequency interference, and JSR to approximately 50 dB.
6. Set interference to be single-frequency interference, and JSR to approximately 40 dB.  
The interference suppression performance for the above six scenarios is shown in Table 1, which shows that the CNR loss with optimal filter order under real-world scenarios is less than 8 dB\(\cdot\)Hz, and the optimal filter order increases with the bandwidth and power of the interference signal. Besides, the CNR loss (<8 dB\(\cdot\)Hz) also increases with the interference power, which means that the error between calculated optimal filter order and actual filter order is minor for larger interference bandwidth and JSR. The results from signal-frequency signals show that this approach is more suitable for narrow-band interference suppression.  
Figure 11 illustrates the estimated CNR for the four narrow-band interference suppression scenes. The interference suppression performance increases and tends to be stable with the adaptive filter tap-length increases, accompanied by a slight decrease trend. By comparing Table 1 and Figure 11, it can be found that the calculated optimal filter order is  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Interference Suppression** & **JSR (dB)** & **Optimal Filter Order** & **CNR loss (dB\(\cdot\)Hz)** \\ \hline Single-frequency & 40 & 31 & 2.907 \\  & 50 & 41 & 3.503 \\  & 40 & 35 & 2.726 \\
1 MHz & 50 & 47 & 4.839 \\  & 40 & 45 & 3.571 \\
2 MHz & 50 & 59 & 6.198 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Interference Suppression Performance Comparison.  
Figure 10: Platform of the practical test.  
much larger than the actual one under the practical test. In all cases, the sampling rate is 75.12 MHz, larger than the Nyquist frequency, which results in the anti-jamming adaptive filter designed through Kaiser-window longer than the actual optimal filter.  
In conclusion, we have demonstrated that the narrowband interference embedded in navigation signals can be suppressed by the adaptive LMS filter with optimal tap-number, ensuring a short filter to meet the anti-interference requirements of the navigation receiver. However, this method needs to limit the sampling rate as close to the Nyquist sampling rate as possible, especially in practical receiver applications.