# Anti-Jamming Method and Implementation for GNSS Receiver Based on Array Antenna Rotation
## 5 Simulation Results and Analysis
### Efficiency Evaluation of the Variable-Step Iteration Algorithm Based on Gradient Descent  
Taking an application to the PI algorithm as an example, four interferences with different intensities were arbitrarily selected to validate the efficiency of the proposed implementation algorithm. The maximum azimuth intersection angle \(\Delta\Psi=90^{\circ}\). The interference parameters are shown in Table 4 and the other simulation parameters are the same as those in Table 3.  
Figure 10: Anti-jamming ability of rotating antenna array algorithm. (**a**) The anti-jamming ability of the PI algorithm for arbitrary (azimuth) antenna array attitude. (**b**) The anti-jamming ability of the MVDR algorithm for arbitrary (azimuth) antenna array attitude. (**c**) Array anti-jamming abilities and their maximum improvements applying the proposed method to the PI algorithm. (**d**) Array anti-jamming abilities and their maximum improvements applying the proposed method to the MVDR algorithm. Figure 11 shows the relationship between the accuracy of the traversal algorithm and the search step size. In observing the partially enlarged map, it turned out that when the search resolution increases from 0.01\({}^{\circ}\) to 0.001\({}^{\circ}\), the maximum value of the \(ICR\) varies slightly. Therefore, the maximum \(ICR\) corresponding to 0.001\({}^{\circ}\) search resolution was set as the theoretical optimal \(ICR\). Under the interference parameters in Table 4, the theoretical optimal value of the interference suppression ratio is about 45.57 dB. The \(ICR\) error raised by implementation algorithm is defined as the difference between the maximum \(ICR\) and the theoretical optimal value. Requiring the \(ICR\) error to be less than 0.5 dB, the statistical search resolution was set to 0.1\({}^{\circ}\) and the search time turned out to be 600. This is taken as the benchmark \(N_{s}\) in Formula (31). Under the same interference parameters, the effect of the proposed implementation algorithm is shown in Figure 12a-c. The number of iterations is 23 when the iteration meets the aforementioned 0.5 dB demands. The corresponding optimal rotation angle is 18.93\({}^{\circ}\). The iteration step in the process is shown in Figure 12c. In the simulation, the empirical value of \(c_{itr}\) in Equation (25) was determined by off-line statistics. Based on a great number of experiments, a possible \(c_{itr}\) and an iteration step were obtained:  
\[\mu(l)=\frac{y(l)}{(\Sigma\,p_{j_{k}})\times 10^{17.5-0.4616\lg(\frac{\Sigma\,p_{j _{k}}}{p_{n}})}} \tag{32}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Interference Parameter** & **Angle in Elevation** & **Angle in Azimuth** & \(\boldsymbol{JSR}\) \\ \hline Interference 1 & \(-15^{\circ}\) & \(28^{\circ}\) & 65 dB \\ Interference 2 & \(-2^{\circ}\) & \(18^{\circ}\) & 70 dB \\ Interference 3 & \(-6^{\circ}\) & \(-42^{\circ}\) & 62 dB \\ Interference 4 & \(-10^{\circ}\) & \(-62^{\circ}\) & 70 dB \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Interference parameters. Figure 11: Relationship between traversal accuracy and search step size. From Equation (32), the iteration step is related to the total power of input interferences. Figure 12d shows the number of iterations and the optimal rotation angle under different \(JSR\) conditions. In order to further illustrate the reasonability of \(c_{itr}\) and the efficiency improvement of the proposed iteration algorithm, a Monte Carlo experiment was repeated 3000 times (the variables are interference DOAs). Please refer to Table 3 for jammer incident parameters. The calculated average iteration number is shown in Figure 13a. It reveals that the iteration step in Equation (32) meets the demand for a variety of jammer incident angles and intensities. Average efficiency improvement under different interference intensity conditions, as is shown in Figure 13b. It is depicted that the efficiency increase is 78.35-99.63%, which shows the algorithm has a positive effect on both strong and weak interferences.