## 3 Analysis
### Adaptive Null Steering Performance
We also obtain the simulated cross-polarization levels of the proposed antenna in _zx_- and _zy_-planes compared to those of the conventional two-element patch array antenna. The average cross-polarization levels over all elevation angles of both array antennas were less than \(-\)108 dBi, and the cross-polarization level of the proposed array is maximally 14.7 dB higher than that of the conventional patch array. From these results, although the proposed array shows higher cross-polarization levels and slightly lower array gains than the conventional patch array, the interelement spacing of the proposed array can be miniaturized to 0.08\(\lambda\). Such nulling performances of the proposed array are observed in comparisons with the conventional monopole and patch arrays. The interelement spacing for the monopole array is set to 0.1\(\lambda\), and for the patch array is 0.4\(\lambda\). They are the narrowest possible interelement spacings for the two array elements. For the simulations, the direction of the interference angle is varied from \(-\)60\({}^{\circ}\) to 60\({}^{\circ}\) with an interval of 1\({}^{\circ}\), and the jammer power to noise power ratio (JNR) is changed from 10 dB to 40 dB with the independent gaussian random noise created by 50 iterations. Figure 16 represents the comparisons of the root-mean-square (RMS) null depths in terms of JNR for the proposed, conventional monopole, and patch arrays. The proposed array with the very close interport spacing of 0.08\(\lambda\) can maintain the deepest null depth compared to those of the conventional monopole and patch arrays, and the null depth of \(-\)54.3 dB is observed at a JNR of 40 dB. Note that, in this interference mitigation, it is essential to not only have a deep null depth but also to consider other important factors such as low blind region for receiving wanted signals [47] and fast iteration time to form a null pattern [11; 47]. Figure 17 shows the RMS null widths versus JNR; the narrowest null width of 27.6\({}^{\circ}\) is obtained when the JNR increases above 15 dB. Figure 18 presents the RMSE comparisons of the null DOA. Although the proposed array has the higher RMSE under a JNR of 20 dB, the RMSE of less than 0.8\({}^{\circ}\) can be sustained above a JNR of 20 dB. To observe the null steering capability in a wide scan angle,the simulations of the null depths in accordance with \(\theta_{jam}\) varied from \(0^{\circ}\) to \(90^{\circ}\) at a JNR of 15 dB are also conducted, and the results of the proposed array are compared to the conventional patch arrays. The average null depth of the proposed array is 3.1 dB higher than that of the patch array in high elevation angle (\(0^{\circ}\leq\theta_{jam}\leq 12^{\circ}\)). On the other hand, in the low elevation angle (\(13^{\circ}\leq\theta_{jam}\leq 90^{\circ}\)), the proposed antenna has an 8.7 dB deeper average null depth than that of the patch array. The results demonstrate that the proposed two-element array is suitable for achieving the required null pattern characteristics with an extremely narrow array distance due to the modal difference, the low pattern correlation, and the high isolation between the array elements. Figure 16: Root-mean-square (RM) S null depth in terms of jammer power to noise power ratio (JNR) of the proposed array compared to the conventional patch and monopole arrays. Figure 15: 3D and 2D null steering patterns of the proposed array with the power spectrum: (**a**) 3D radiation pattern in UV domain; (**b**) power spectrum with initial and final weights; (**c**) null performance parameters.