## 4 Simulation and Result
### Computational Complexity Analysis
In particular, the real-time calculation of the HDE algorithm only requires complex multiplication and Fourier transform. Compared with the two-dimensional interpolation operation of the \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & **Jamming** & **Initialization** & **Real-Time** \\  & **Object** & **Stage** & **Stage** \\ \hline \multirow{2}{*}{SA} & nonlinear & & \\  & trajectory SAR & — & \((19 MN+3)N_{r}+10N_{r}\log_{2}(N_{r})\) \\ \hline \multirow{2}{*}{HDE} & nonlinear & & \\  & trajectory SAR & \(10N_{a}N_{r}\log_{2}(N_{a})+20N_{a}N_{r}\) & \(15N_{r}\log_{2}(N_{r})+15N_{r}+7\) \\ \hline \multirow{2}{*}{SFI} & linear & & \\  & trajectory SAR & \(5 MN\log_{2}(MN)+17N_{a}N_{r}+5\) & \(\big{(}4L^{2}+10L+21\big{)}N_{r}+10N_{r}\log_{2}(N_{r})\) \\ \hline \multirow{2}{*}{SM} & linear & & \\  & trajectory SAR & \((15 MN-2N)N_{r}\) & \(17 MN_{r}-2N_{r}+10N_{r}\log_{2}(N_{r})\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Basic operation amount comparison of different algorithms. SFI algorithm and SM algorithm, the calculation efficiency is higher, and the real-time operation amount is reduced by more than 70%. The average running time simulation experiment was carried out on a computer with AMD PRO 5975 WX CPU (main frequency: 3.6 GHz). In addition, the simulation parameters are shown in Table 1, \(N_{a}=1388\), \(N_{r}=2733\). We used Matlab2021a to simulate the two nonlinear-trajectory SAR deceptive jamming algorithms and calculated the average running times under different template sizes, as given in Table 4.  
It is further verified that the HDE algorithm has the characteristics of the deceptive jamming algorithm in the azimuth frequency domain, and its real-time calculation complexity has nothing to do with the template size, and is far superior to the SA algorithm. In addition, the simulation time results do not perfectly match the theoretical analysis, as MATLAB uses different degrees of optimization algorithms for different calculations. In addition, the MATLAB interpreter is less efficient, and simulation times are relatively long. If field-programmable gate arrays or digital signal processors are used, the processing speed can be increased by more than tens of times, and the real-time requirements are guaranteed. In the implementation of SAR jamming, the jammer must complete all operations within each PRI, and the calculation complexity of the real-time stage is particularly important. Based on the above analysis, the calculation complexity of the HDE algorithm is more advantageous than other algorithms, and it is more conducive to the deceptive jamming of large false scenes for nonlinear-trajectory SAR. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multirow{2}{*}{**Size**} & \multicolumn{2}{c}{**Preprocessing**} & \multicolumn{2}{c}{**Real-Time**} \\  & & **(ms)** & & **(ms)** \\ \hline
**M** & **N** & **HDE** & **HDE** & **SA** \\ \hline
100 & 100 & 126.26 & 3.12 & 916.66 \\
300 & 300 & 126.44 & 3.26 & 7718.07 \\
500 & 500 & 126.98 & 3.28 & 21,907.11 \\
1000 & 1000 & 126.78 & 3.27 & 89,696.28 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average Running Time of The Nonlinear Deceptive Jamming Algorithms  
Figure 16: The relationship between the operation amount and the total number of scatters in the template. (**a**) is the total operation amount and (**b**) is the operation amount in the real-time calculation stage.