# Flexible Null Broadening Robust Beamforming Based on JADE
## 4 Simulation  
**Simulation conditions:** ULA is composed of 16 sensors, the sensors spacing \(d=\lambda/2\), the sample snapshots \(K=200\), the desired signal angle \(\theta_{0}=0^{\circ}\), SNR \(=0\) dB and the interference angle \(\theta_{1}=-60^{\circ}\), \(\theta_{2}=50^{\circ}\). It is assumed that the interference with \(\theta_{1}\) incidence is dynamic interference, and the interference with \(\theta_{2}\) incidence is non-dynamic interference. The interference-to-noise ratio is INR1 \(=30\) dB and INR2 \(=25\) dB, respectively, and the broadening angle is 2 degrees. Under the above-mentioned simulation conditions, the proposed algorithm is compared with CMT [16], FCMT [17], INCM-RAB [20] and optimal beamformers in pattern, output SINR, output interference power and output SINR. **Experiment 1:** The flexibility and precision of null broadening verification (\(Pq=1\&\Delta\theta=2^{\circ}\)). It is assumed that the gain-phase errors obey Gaussian distribution \(N\big{(}1,0.05^{2}\big{)}\) and \(N\Big{(}0,\big{(}0.5^{\circ}\big{)}^{2}\Big{)}\), respectively. According to the simulation conditions above, the null broadening pattern is obtained as follows:  
Compared with the traditional CMT, the advantage of the proposed algorithm in this paper is that the algorithm can flexibly broaden the null. As shown in Figure 2, the proposed algorithm generates a narrow null at non-dynamic interference \(\theta_{2}=50^{\circ}\) and \begin{table}
\begin{tabular}{c l} \hline \hline
**Steps** & **Operation** \\ \hline
1 & Separate the signal steering vector from the observation data using (13); \\
2 & Match the signal steering vector by correlation coefficient method using (15,16); \\
3 & Reconstruct and taper the interference mismatch matrix using (20); \\
4 & Calculate the weight vector of proposed algorithm using (25). \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The detailed steps for implementing the proposed algorithm. a wide null at dynamic interference \(\theta_{1}=-60^{\circ}\). It can save the consumption of DOFs at non-dynamic interference \(\theta_{2}=50^{\circ}\). In addition, compared with similar flexible algorithms, FCM, the proposed algorithm, has a deeper null and a more precise widening angle at dynamic interference, resulting in a better interference suppression capability. **Experiment 2:** Influence of null deepening coefficient on null depth (\(Pq=1,10,100\&\Delta\theta=2^{\circ}\)). It is assumed that the gain-phase errors obey Gaussian distribution \(N\big{(}1,0.01^{2}\big{)}\) and \(N\Big{(}0,\big{(}0.5^{\circ}\big{)}^{2}\Big{)}\), respectively. The broadening angle is 2 degrees. Other simulation conditions are the same as the simulation Experiment 1. The pattern of the proposed algorithm is compared when Pq is 1,10 and 100. As shown in Figure 3, RAB is compared with the proposed algorithm under different null deepening coefficients. When the coefficient of null deepening Pq is 1, the depth of null is about \(-90\) dB. When Pq is set to 10, the depth of the null deepens from \(-90\) dB to \(-108\) dB, and the null deepens about 20 dB. When Pq is 100, the null is larger than \(-120\) dB and exceeds RAB. Therefore, the reasonable CMT can be designed by the suitable Pq, which can suppress the dynamic interference thoroughly. In general, we should set Pq = 10-100. However, we should set Pq > 100 in a strong interference environment. Figure 3: Comparison of null depth: (**a**) overall pattern, (**b**) local enlarged drawing. Figure 2: Null broadening pattern: (**a**) overall pattern, (**b**) local enlarged drawing. **Experiment 3:** Robustness verification--Performance under gain-phase error. This experiment considers the influence of gain-phase errors, and compares the changes of output SINR and input SNR of different algorithms. The experiment considers the gain-phase errors, and compares the output SINR of different algorithms with the change of input SNR.