## 4 Parameter-Identification-Based Configuration Design
### Effectiveness in Algorithm  
In order to verify the effectiveness of the CPI algorithm in Algorithm 1, a concrete antenna configuration is investigated in this section. Thereinto, the initial aperture diameter \(D_{\text{a}}\) is \(2000\,\text{mm}\), the focus/diameter ratio \(\eta\) is \(0.5\), the number of panels is 18, the interference distance \(s\) is \(5\,\text{mm}\), the vertical displacement \(h\) is \(10\,\text{mm}\), the fairing diameter \(D_{\text{f}}\) is \(740\,\text{mm}\) and the deviation parameter \(k_{\text{d}}\) is \(0.6\). All values of the structural parameters are listed in the left-side column of Table 2. After executing the CPI algorithm, the relevant results are reported in the right-side column of Table 2, and the corresponding antenna configuration is shown in Figure 9. (The antenna configuration is represented in the same manner as that in Figure 7 for a visual and clear demonstration, which is generated in a precise way--programming in _Wolfram Mathematica_). ```
1:Focus/diameter ratio \(\eta\), number of panels \(n\), fairing envelope diameter \(D_{t}\), deviation parameter \(k_{\text{d}}\), vertical displacement \(h\), interference parameter \(s\); Output: Maximum aperture diameter \(D_{a}^{*}\), transformation matrix \(\mathbf{T^{*}}\), residual \(E^{*}\), compensation parameters \(k_{1}^{*},k_{2}^{*}\) and \(\beta^{*}\);
2:function\(E(k_{1},k_{2})\)\(\triangleright\) Definition of residual function \(E\)
3: Give point sets \(\{A_{1},B_{1},P\}\) and \(\{A_{1},B_{1},P\}^{\prime}\) by solving Equation (10) using [PERSON]'s method;
4: Give transformation matrix \(\mathbf{T}\) from \(\{A_{1},B_{1},P\}\) to \(\{A_{1},B_{1},P\}^{\prime}\) by rigid-body registration algorithms;
5: Calculate the right-hand expression in Equation (12);
6:return\(E\);
7:endfunction
8:function\(g_{1}(\beta)\)\(\triangleright\) Definition of distance function \(g_{1}\)
9: Calculate the right-hand expression in Equation (14); \(\triangleright\) This step will repeatedly call function \(E\)
10:return\(g_{1}\);
11:endfunction
12:function\(g_{2}(D_{a})\)\(\triangleright\) Definition of maximum distance function \(g_{2}\)
13: Solve the optimization model in Equation (15); \(\triangleright\) This step will repeatedly call functions \(E\) and \(g_{1}\)
14:return\(g_{2}\);
15:endfunction
16:Solve Equation (16); \(\triangleright\) This step will repeatedly call function \(E,g_{1}\) and \(g_{2}\)
17:return\(D_{a}^{*}\), \(\mathbf{T^{*}}\), \(E^{*},k_{1}^{*},k_{2}^{*}\) and \(\beta^{*}\); \(\triangleright\) The expected axis can be obtained by \(T^{*}\), as elaborated below. ```  
**Algorithm 1** Configuration parameter identification (CPI)  
If the CPI algorithm is effective for the configuration, all of the four GCs in Section 4.1 must be satisfied first when the antenna is in its folded state. The following verification is performed by observation and measurement in _Mathematica_. Foremost, all of the GCs are confirmed. The bimetric, front and top views demonstrating the above antenna folded configuration are presented in Figure 9, from which it can be observed in Figure 9a that points \(A_{1}\) and \(D_{1}\) are precisely located on the envelope, thereby satisfying GCs 1 and 2.