# Planar Array Failed Element(s) Radiation Pattern Correction: A Comparison
## 3 Results & Discussion
### Optimization Algorithm Results  
Then, the failed radiation pattern was restored by optimizing the remaining active elements of the array. The optimization methods described in Section 2.2 were applied to the failed radiation pattern following the optimization flow. New weights for the remaining working element were assigned to calculate SNR for the current radiation pattern. The objective function is evaluated as in (10). The objective function minimizes the error between the current radiation pattern and the reference radiation pattern without any  
Figure 5: (**a**) 25 Failed Elements at \(8\times 8\) planar array. (**b**) Failed Radiation Pattern of an \(8\times 8\) planar array with 25 failed elements in the array. failed elements in the array. The iteration continues until the optimization meets the exit condition where the optimization stops. An example of results from applying the PS optimization method to 25 failed element radiation patterns is shown in Figure 6 and the optimized weights are shown in Table 1.  
Next, the optimization methods were implemented for eight different types of failure as listed in Table 2 to analyze the efficiency of the methods towards different types of failure in 8 \(\times\) 8 and 6 \(\times\) 6 planar arrays, respectively. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
0.8769 & 0 & 0 & 0.6770 & 0 & 0.9038 & 0 & 0.2347 \\
0.0653 & 0.6605 & 0.6178 & 0 & 0 & 0 & 0.5568 \\
0.2086 & 0.3900 & 0.1778 & 0.1778 & 0.5316 & 0 & 0 & 0.6393 \\
0 & 0.5631 & 0.3279 & 0.3279 & 0 & 0.2687 & 0 & 0 \\
0.4582 & 0 & 0 & 0 & 0.3085 & 0.3196 & 0.0361 & 0.5067 \\
0 & 0 & 0.2741 & 0.0241 & 0.4068 & 0.6483 & 0.7023 & 0.8944 \\
0.1980 & 0.5388 & 0.9444 & 0.9444 & 0 & 0.7895 & 0.7164 & 0 \\
0 & 0 & 0 & 0 & 0.4538 & 0.8857 & 0.8857 & 0.6541 \\ \hline \end{tabular}
\end{table} 
Table 1: Optimized weights for random 25 element failure with the PS method. Figure 6: Optimized radiation pattern with the PS method. The results of the 8 \(\times\) 8 planar array in Rows 4 and 7 that failed for all four optimization methods are shown. Figure 7a-c represents the initial, failed, and optimized radiation patterns of the SA method. The corresponding optimized weights are shown in Table 3. In this case, the optimized radiation pattern has a higher SNR value compared to failed radiation pattern. This method could not meet the objective where optimized weights in a planar array should generate an optimized radiation pattern that matches the reference radiation pattern with a lower SNR value than the failed radiation pattern SNR. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Failure** & **Details** & **Array Size** \\ \hline Type 1 & Rows 4 and 7 & \\ Type 2 & Columns 3 and 5 & 8 \(\times\) 8 planar array \\ Type 3 & Rows 4, 7 and Columns 3, 5 & (64 elements) \\ Type 4 & Random 25 location failures & \\ \hline Type 5 & Rows 4 and 5 & \\ Type 6 & Columns 3 and 5 & 6 \(\times\) 6 planar array \\ Type 7 & Rows 4, 5 and Columns 3, 5 & (36 elements) \\ Type 8 & Random 12 location failures & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Failure types for 8 \(\times\) 8 and 6 \(\times\) 6 planar arrays. Figure 7: \(Cont.\)  
Figure 7: (a) Initial Radiation Pattern for the SA Method. (b) Failed Radiation Pattern for the SA Method. (c) Optimized Radiation Pattern for the SA Method. Figure 8: (a) Initial Radiation Pattern for the GA method. (b) Failed Radiation Pattern for the GA method. (c) Optimized Radiation Pattern for the GA method. The PSO method results for the same type of failure are shown in Figure 9a-c. The optimized weights using this method are shown in Table 5. Here, the method has matched the SNR value of the optimized radiation pattern with the reference radiation pattern. The main lobe level is also maintained. From an SNR value of 19 in the failed radiation pattern, the method has successfully reduced the value to 15 in the optimized radiation pattern.