# Optimal Order of Time-Domain Adaptive Filter for Anti-Jamming Navigation Receiver
## 5 Experimental and Analysis  
### Simulation and Analysis  
The simulation experiment is conducted in a software receiver composed of data generation, anti-jamming, and performance evaluation. The length of navigation signal data is set to 1 s, and the sampling rate is set to 25 MHz. The narrowband interference bandwidth differs from 5% to 15% of the PRN code bandwidth. The modulation method is P-code BPSK modulation. That is, the PRN code rate is 10.23 MHz. Set the intermediate carrier frequency to be the same as the narrowband interference center frequency, and the interference signal ratio ranges from 30 dB to 50 dB.  
Figure 7a,b verify the monition increasing relation between the interference suppression performance and the filter order. As the anti-jamming filter extends, the estimated CNR increases, suggesting that more extended filters can generate better interference suppression performance. While the filter order continued to increase, the growth rate of CNR  
Figure 6: Frequency response of an anti-jamming filter.  
slowed down. Figure 7a is the influence of filter order on the CNR under different JSR. For the same length filter, the greater the interference power, the smaller the estimated CNR, and the ultimate performance achieved by the finite-length filter is inversely proportional to JSR. Figure 7b shows the effect of filter order on CNR under different bandwidth interference. For the same length filter, the larger the interference signal bandwidth, the smaller the estimated CNR, and the ultimate anti-jamming performance of adaptive filters decreases as the interference bandwidth increases.  
The simulation obtains the optimal filter order for the interference suppression of anti-jamming filters designed by the Kaiser window function, and the Monte Carlo simulations are carried out 100 times. Figure 8 verify the interference suppression performance of the Wiener filter under the calculated optimal order. As shown in Figure 7, the estimated CNR after the Wiener filter of calculated optimal order can meet the anti-jamming demand for navigation receiver, and the room for filter shortened decreases with the increase of interference bandwidth.  
Figure 8: Performance of Wiener filter under the calculated optimal order. (**a**) Interference suppression performance of Winner filter; (**b**) Frequency response.  
Figure 7: Effect of the filter orders on anti-jamming performance. (**a**) Impact analysis of JSR; (**b**) Impact analysis of Interference Bandwidth Ratio.  
Due to the limitation of algorithm parameters, the adaptive filter may not necessarily converge to the Wiener solution, resulting in the actual optimal filter order of adaptive filters being longer than the Winner solution. Besides, there are generally differences in the performance between the LMS adaptive filter and the Kaiser one because of the different design principles. Therefore, there is an error between the calculated optimal filter order and the actual value. When the JSR is 30 dB, the calculated optimal filter order can meet the interference suppression demand of adaptive filters. When the JSR increases, the gap between the calculated optimal filter order and the actual optimal filter order increases. The optimal order of the corrected time-domain adaptive filter is:  
\[M_{\min}=\left\{\begin{array}{rl}\min\{M|\Delta CNR\leq 3\;\mathrm{dB}\},&JSR \leq 30\;\mathrm{dB}\\ \min\{M|\Delta CNR\leq 3\;\mathrm{dB}\}+4,&30\;\mathrm{dB}</SR<40\;\mathrm{dB}\\ \min\{M|\Delta CNR\leq 3\;\mathrm{dB}\}+6,&40\;\mathrm{dB}\leq/SR\leq 50\; \mathrm{dB}\\ \end{array}\right., \tag{33}\]  
Figure 9 illustrates the performance comparison between the actual optimal filter order and the calculated value. It is shown that the interference suppression requirements can be well met by designing digital filters based on the Kaiser window.  
Figure 9: The anti-jamming performance under optimal filter order. (a) JSR = 30 dB; (b) JSR = 35 dB; (c) JSR = 40 dB; (d) JSR = 50 dB.