# Optimization Design for Sparse Planar Array in Satellite Communications
## 4 Sparse Planar Array Optimization Design Method
### Intelligent Optimization Methods
#### 4.2.4 Sparse Array Optimization Design Based on Hybrid Algorithm
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Subject**} & \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Number of**} & \multicolumn{2}{c}{**Number of**} & \multirow{2}{*}{**Reference**} & \multirow{2}{*}{**PSLL (dB)**} & \multirow{2}{*}{**PSLL (dB)**} & \multirow{2}{*}{**Filling**} & \multirow{2}{*}{**Directivity**} \\  & & **Referenced** & & & & & & \\  & & **Array Elements** & & & & & & \\ \hline  & & 49 & 35 & \(-\)17.6 dB & \(-\)17.64 dB & 0.71 & \\ Synthesis of linear and planar & & 121 & 77 & \(-\)24.33 dB & \(-\)24.35 dB & 0.64 & \\ arrays via sequential convex & & 121 & 89 & \(-\)24.33 dB & \(-\)24.37 dB & 0.74 & / \\ optimizations [74] & & 121 & 102 & \(-\)24.33 dB & \(-\)24.32 dB & 0.84 & \\  & & 121 & 105 & \(-\)24.33 dB & \(-\)24.34 dB & 0.87 & \\ \hline Synthesis of Concentric Circular & & 60 & 33 & \(-\)18.09 dB & \(-\)24.15 dB & 0.55 & \\ Antenna Array Using Whale & & 90 & 58 & \(-\)21.89 dB & \(-\)26.71 dB & 0.64 & \\ Optimization Algorithm [54] & & 126 & 73 & \(-\)20.88 dB & \(-\)25.46 dB & 0.58 & / \\ \hline Pattern design of 2D antenna & & & & & & & \\ arrays using & & 49 & 49 & \(-\)12.65 dB & \(-\)20.96 dB & \multirow{2}{*}{1} & 17.14 dB \\ biogeography-based & & 100 & 100 & \(-\)12.96 dB & \(-\)20.82 dB & & 20.27 dB \\ optimization [51] & & & & & & & \\ \hline Effective minimization of side & & & & & & & \\ lobe level of sparse thinned & & & & & & & \\ planar array antenna in & & 108 & 84 & \(-\)26.35 dB & \(-\)22.27 dB & 0.78 & / \\ multiple planes with & & & & & & & \\ constraints [52] & & & & & & & \\ \hline Planar Thinned Antenna Array & & & & & & & \\ Synthesis Using Modified Brain & & 200 & 100 & \(-\)20.0 dB & \(-\)19.9 dB & 0.50 & / \\ Storm Optimization [103] & & & & & & & \\ \hline Concentric circular antenna & & & & & & & \\ array synthesis for side lobe & & 18 & 18 & \(-\)11.23 dB & \(-\)36.84 dB & \multirow{2}{*}{1} & 12.15 dB \\ suppression using moth flame & & 30 & 30 & \(-\)9.55 dB & \(-\)27.92 dB & & 10.76 dB \\ optimization [55] & & & & & & & \\ \hline Design of planar concentric & & & & & & & \\ circular antenna arrays with & & & & & & & \\ reduced side lobe level using & & 105 & 51 & \(-\)18.26 dB & \(-\)18.19 dB & 0.48 & / \\ symbiotic organism’s search & & & & & & & \\ \hline A hybrid approach based on & & & & & & & \\ PSO and Hadamard difference & & 36 & 21 & \(-\)13.06 dB & \(-\)13.57 dB & 0.58 & \\ sets for the synthesis of square & & 144 & 75 & \(-\)16.74 dB & \(-\)18.01 dB & 0.52 & / \\ thinned arrays [46] & & & 576 & 323 & \(-\)18.97 dB & \(-\)22.22 dB & 0.56 & \\ \hline Adaptive Learning of & & & & & & & \\ Probability Density Taper for & & & & & & & \\ Large Planar Array Thinning [37] & & & & & & & \\ \hline Synthesis of large planar & & & & & & & \\ thinned arrays using IWO-IFT & 1928 & 772 & \(-\)23.0 dB & \(-\)27.13 dB & 0.40 & 32.92 dB \\ algorithm [93] & & & 578 & \(-\)22.4 dB & \(-\)25.93 dB & 0.30 & 31.79 dB \\ \hline A two-step method for the & & & & & & & \\ low-sidelobe synthesis of & & & & & & \\ uniform amplitude planar & & & & & & \\ sparse arrays [94] & & & & & & \\ \hline Multiple-constraint synthesis of & & & & & & \\ rotationally symmetric sparse & & & & & & \\ circular arrays using a hybrid & & & & & & \\ algorithm [95] & & & & & & \\ \hline Low-sidelobe pattern synthesis & & & & & & & \\ for sparse conformal arrays & PSO- & & & & & \\ based on PSO-SOCP & & & & & & & \\ optimization [104] & & & & & & \\ \hline A Hybrid Approach for the & & & & & & & \\ Synthesis of Planar Thinned Arrays with Sidelobes & & & & & & \\ Reduction [99] & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(Cont.\)