## 4 Methods for Improving Scanning Performance
The maximum current amplitude is observed at both the left and right edges of the patch. In contrast to the surface current of Ant-1, Ant-2 displays a more concentrated distribution, which can be regarded as a reduction in the equivalent radiation aperture of the antenna. Consequently, according to antenna theory, this results in a broadened beamwidth. The phased array factor (AF) at any observation angle (\(\theta\), \(\varphi\)) when the PAA is scanned to angle (\(\theta\)s, \(\varphi\)s) is given by  
\[AF(\theta,\varphi)=\sum_{n=1}^{N_{x}}\sum_{m=1}^{N_{y}}I_{n,m}e^{j(k\sin\theta (nd_{x}\cos\varphi+md_{y}\sin\varphi)+\phi_{n,m})} \tag{4}\]  
Figure 5: Four-element (2 \(\times\) 2) subarrays of different types. where \(k\) is the free-space propagation constant, and \(\phi_{n,m}\) is a phase shift equal to the rotation angle. \(I_{n,m}=e^{-j\varphi_{n,m}}\) is the excitation applied to the nth and mth elements, \(n\) is the antenna column number (\(n\) = 0-8), \(m\) is the antenna row number (\(m\) = 0-8), and \(\varphi_{n,m}\) are the phases applied by  
\[\varphi_{n,m}=k\sin(\theta_{s})(nd_{x}\cos\varphi_{s}+md_{y}\sin\varphi_{s}) \tag{5}\]  
The normalized simulated scanning patterns of different types of PAA in the E-, H- and D-planes at \(f_{h}\) (\(1.03f_{0}\)) are illustrated in Figures 8-10, respectively. The cross-pol (X-pol) in each case is normalized to its corresponding co-pol. The cross-pol is calculated using [PERSON]'s third definition [PERSON] (1953). Array 1 exhibits a gain fluctuation of 3.8 dB in E-plane and 2.6 dB in H-plane with a scanning coverage of 45\({}^{\circ}\). After using the modify SIW cavity, Array 2 demonstrates the ability to scan to \(\pm 45^{\circ}\) with gain fluctuations of 2.1 dB and 2.6 dB in the E- and H-plane, respectively. Array 3 exhibits a roll-off with a 2.2 dB drop at E-plane and 2.1 dB drop at H-plane at \(\pm 45^{\circ}\). Notably, the cross-pol levels are less than \(-64\) dB when scanning \(\pm 45^{\circ}\) in E-plane. For both Array 1 and Array 2, the cross-pol levels are about \(-10\) dB when patterns are steered to \(45^{\circ}\) in H-plane. However, after applying SQR, the normalized cross-pol levels of Array 3 are less than \(-60\) dB when patterns are steered to \(45^{\circ}\) in H-plane. The sidelobe level (SLL) is close to \(-13.3\) dB at broadside. Unfortunately, due to the element pattern and the mismatch of the ports, the SLL gradually increases with the steering angle. The worst simulated SLLs of Array 3 are \(-10.8\) dB and \(-10.5\) dB when scanning over all scan angles in E- and H-planes, respectively. As can be seen from the three figures, the cross-pol levels in the D-plane of the three arrays are almost same, so SQT cannot reduce the cross-polarization level on the D-plane. Figure 6: Comparison of the simulated patterns of the central element at \(f_{h}\). Figure 7: Simulated current distributions of the center element. Table 1 summarizes the pattern feature of the three PAAs. The peak gains of both Array 1 and Array 2 are 23.7 dBi, but they scanning radiation pattern is asymmetry, which bring different gain fluctuation when scanning the same angle in positive and negative in E-plane. This is mainly due to the embedded element pattern. The X-pol level of is relatively high. The X-pol levels of Array 1 and Array 2 in H-plane is \(-5.3\) dB, and \(-8.9\) dB, respectively. Although the peak gain of Array 3 is 23.6 dB, Array 3 has a symmetry scanning radiation pattern. Moreover, Array 3 exhibits low gain fluctuation of less than 2.3 dB. The X-pol levels of Array 3 are less than \(-74.5\) dB in E- and H-planes. Comparing these results, the scanning potential of proposed SIW patch array is significantly better. It should be noted that the proposed results are not optimal, it is just a demo case. Figure 8: Normalized patterns of Array 1 at \(f_{h}\): (**a**) E-plane, (**b**) H-plane, and (**c**) D-plane. Figure 10: _Cont._  
Figure 9: Normalized patterns of Array 2 at \(f_{h}\): (**a**) E-plane, (**b**) H-plane, and (**c**) D-plane.