# Optimization Design for Sparse Planar Array in Satellite Communications
## 3 Sparse Surface Array and Material Design  
### Planar Array Geometry  
The geometry of the array is an important aspect of the optimized design of the array. Different array geometry configurations result in different antenna patterns. Commonly used planar array geometric configurations mainly include rectangular arrays, circular arrays, polygonal arrays, concentric circle arrays, cross arrays, and spiral arrays. From the perspective of the antenna pattern, the main lobe generally determines the resolution of the array, and the sidelobe determines the anti-interference performance of the array, which is why the peak sidelobe level and control main lobe width should be reduced in array optimization design. Figure 6 shows the four typical arrays that are most frequently used in sparse area array optimization designs.  
In order to investigate the influence of array geometry on the antenna pattern, Figures 7-9 depict the antenna pattern with equiamplitude distribution and omnidirectional characteristics of the uniform rectangular array (URA), uniform circle array (UCA) and concentric circle array (CCAA). For all arrays, the amplitude weighting \(w_{mn}=1\) and the single-element pattern \(T_{n}(\theta,\varphi)=1\). The arrays considered are uniformly configured with 256 elements and an element spacing of \(\lambda/2\). The beam pointing angle is \((0^{\circ},0^{\circ})\). Rectangular arrays have a good resolution in the evenly distributed range of elements and are preferred in the radar field, but they exhibit a disadvantage that the other side of the main lobe contains an additional main lobe of the same strength [12]. The uniform circular array arrangement does not have any  
Figure 6: Basic types of planar arrays: (**a**) rectangular arrays; (**b**) circular arrays; (**c**) hexagonal arrays; (**d**) concentric circle arrays.  
edge elements, and the main sidelobes of the antenna pattern are evenly distributed, which can decompose the excitation into symmetric spatial components to reduce the coupling; thus, the circular array has lower coupling and better robustness than the rectangular array [1], but the sidelobes are higher than the rectangular array. Circular arrays are often used for wireless communications, especially in smart antenna designs. The concentric circle array and the uniform circle array are significantly lower than the sidelobes, but the concentric circle pattern still shows a high grating lobe close to the level of the main lobe. For instance, [PERSON] utilized spaceborne isophoric sparse concentric circle arrays to achieve global coverage of GEO orbit while limiting sidelobe effects [13]. Furthermore, another study [14] comparing the antenna pattern of uniform hexagonal arrays with uniform circle arrays revealed that the uniform hexagonal array has superior gain and has lower sidelobes than the uniform circle array [14].  
Figure 8: Uniform circular array antenna pattern. (**b**) illustrates a vertical view of the configuration presented in (**a**). They are all antenna patterns of the same array, but from different perspectives.  
Figure 7: Uniform rectangular array antenna pattern. (**b**) illustrates a vertical view of the configuration presented in (**a**). They are all antenna patterns of the same array, but from different perspectives.  
Figure 9: Concentric circle array antenna pattern. (**b**) illustrates a vertical view of the configuration presented in (**a**). They are all antenna patterns of the same array, but from different perspectives.