## 3 Results and Verification  
Based on the previous mathematical modeling and algorithm, the thinned array with a desired radiation pattern is achieved. In this section, the achieved array structure is first presented. Then, the array performance is shown for verification.  
In accordance with the mathematical modeling and algorithm in Section 2, the optimized array structure of the large-scale 64 \(\times\) 64 thinned array with 2400 elements is shown in Figure 2. As illustrated in Figure 2a, the full array is a 64 \(\times\) 64 array with 4096 elements. The presence of a \"red box\" indicates an active element, while the presence of a \"white box\" means that there is no element. The total number of \"red boxes\" is 2400, which means that the thinned array has 2400 elements. Also, Figure 2a shows that every 2 \(\times\) 2 element in the thinned array is a subarray.  
To construct a thinned array, the array element was built first. The element was designed on three PCBs. The centers of the three PCBs are aligned. The substrate for the Sub1 and Sub 2 was Rogers RT5880 with a relative permittivity of 2.2 and a thickness of 0.381 mm. The substrate of the feeding structure was Rogers RT4003, with a relative permittivity of 3.5 and a thickness of 0.203 mm. Two rectangle patches, sized Lp1 = 2.4 mm and Lp2 = 2.6 mm, respectively, serving as the radiator, were etched onto the top layer of the Sub1 and Sub2, respectively. The Sub1 and Sub2 are bonded together using glue (prepreg layer). The glue was Rogers RO4350F with a relative permittivity of 3.52, a loss tangent of 0.004, and a thickness of h3 = 0.1 mm.  
Based on the thinned array structure in Figure 2a and the array element in Figure 2b, a thinned array with 2400 elements was constructed, as shown in Figure 2c. The element  
Figure 2: Array structure and array element of the proposed thinned array. **(a)** Structure of the thinned array with 2400 elements (the “red box” represents the active element, and the “white box” represents no elements). **(b)** Structure of the array element: **(b1)** side view, **(b2)** top view of Sub1, and **(b3)** top view of Sub2; \(h1=0.381\), \(h2=0.381\), \(h3=0.1\) mm, \(h4=0.203\), \(Lp1=2.4\), \(Lp2=2.6\), \(lg=5\), units: mm. **(c)** Model of the proposed thinned array with 2400 elements and an element spacing of 5 mm. **(d)** Fabricated prototype of the proposed thinned array with 2400 elements. **(e)** Top-down view of the bottom-right quarter of the array. **(f)** Bottom-up view of bottom-right quarter of the array.  
spacings between each element were set to 5 mm. The proposed thinned array shown in Figure 2c was fabricated and is shown in Figure 2d. Several metal screws were used to align and fix the large-scale array. To better show the array, Figure 2d depicts the top-down view of the bottom-right quarter of the array. The array elements are on this layer. Figure 2e shows the back view of the bottom-right quarter of the array. The TR-modules are on this layer. Every 2 \(\times\) 2 element of the array that is a subarray is directly fed by a TR module. Also, the TR modules have four output ports, which connect to the four ports of the 2 \(\times\) 2 elements of the subarray directly.