## 4 Methods for Improving Scanning Performance  
Based on the two CBPAs, an 8 \(\times\) 8 PAA model with 16 four-element subarrays was constructed for comparison with the 2 \(\times\) 2-element subarray, as depicted in Figure 5. Array 1 consists of the Ant-1 unit, while Array 2 comprises the Ant-2 unit. As mentioned previously, Array 3 is composed of Ant-2 unit, which has undergone sequential rotation. As we know, sequential rotation is often used in designing circular polarized antennas with element angular orientation and feed phase arranged in a 0\({}^{\circ}\), 90\({}^{\circ}\), 0\({}^{\circ}\), 90\({}^{\circ}\) fashion or 0\({}^{\circ}\), 90\({}^{\circ}\), 180\({}^{\circ}\), 270\({}^{\circ}\) fashion. In this paper, the Array 3 has its elements arranged in 2 \(\times\) 2 square grid configurations with element angular orientation and feed phase arranged in a 0\({}^{\circ}\), 180\({}^{\circ}\), 180\({}^{\circ}\), 0\({}^{\circ}\) fashion. As shown in Figure 4, Array 3 becomes the image arrangement, so it can be said that image arrangement can be called a special case of sequential rotation [27; 28]. Figure 4: Simulated active VSWR in an infinite array. Figure 3: Simulated 1S\({}_{11}\) 1 of antennas 1 and 2. The mechanism of the 2 \(\times\) 2-element subarray can also be explained theoretically. From Figure 4, the far-field patterns in the two principal planes, the X-Z plane or the Y-Z plane, can be obtained via a direct summation of the fields from all four patches. We let the total far field in the X-Z plane be denoted by \(Fxz\), the vertical field vector from patch 1 by \(H_{1}\), the vertical field vector from patch 2 by \(H_{2}\), etc. The total far field can then be written as follows:  
\[ \begin{array}{l}F_{yz}=H_{1}e^{-jk_{0}d\sin\theta}e^{j0^{\circ}}+H_{2}e^{jk_ {0}d\sin\theta}e^{j180^{\circ}}+H_{3}e^{jk_{0}d\sin\theta}e^{j180^{\circ}}+H_{ 4}e^{-jk_{0}d\sin\theta}e^{j0^{\circ}}\\ =(H_{1}e^{j0^{\circ}}+H_{4}e^{j0^{\circ}})e^{-jk_{0}d\sin\theta}+(H_{2}e^{j180 ^{\circ}}+H_{3}e^{j180^{\circ}})e^{jk_{0}d\sin\theta}\end{array}  \tag{2}\]  
Since this is a uniformly excited array, \(H_{1}=H_{2}=H_{3}=H_{4}=H\); therefore  
\[ \begin{array}{l}F_{yz}=2H\left(e^{j0^{\circ}}e^{-jb_{0}d\sin\theta}+e^{j180 ^{\circ}}e^{jb_{0}d\sin\theta}\right)\\ =-j4H\sin(k_{0}d\sin\theta)\end{array}  \tag{3}\]  
where \(k_{0}\) is the free-space propagation constant, \(d\) is the interelement spacing, and \(\theta\) is the scanning angle. The \(H\) terms represent a pure linearly polarized wave, and the sine term is an element array factor. This total field \(Fyz\) is, thus, equivalent to that generated from four linearly polarized elements. In this fashion, the cross-pol level of the array can decrease substantially. This phenomenon can be explained in Figure 5. The solid arrows are edge field due to fundamental \(TM_{10}\) mode, which generates the co-pol radiation. The dashed arrows are edge field due to \(TM_{02}\) mode, which is shown here only as an example and is one of the many modes that contribute to cross-pol. It demonstrates that only the co-pols are reinforced but the cross-pols canceled. It is this cancellation of the cross-pols that permits the low cross-pol in H-plane. The active element patterns of center element are presented in Figure 6. The observed asymmetry in E-plane is a direct consequence of the strong coupling that exists between the surface waves and the currents present on adjacent planes. This coupling is primarily attributed to the physical discontinuities caused by the probe feed structure [24]. The blind spot has been shifted from 60\({}^{\circ}\) in Ant-1 to over 70\({}^{\circ}\) in Ant-2. The zeros in the pattern align perfectly with the blind spots identified in the active VSWR. When compared with the radiation pattern of Ant-1, Ant-2 exhibits a broadened beamwidth. Figure 7 depicts the simulated surface current distribution of the radiating patch at \(f_{h}\) and serves to elucidate the operational mechanism of the wide-beam antenna.