# Optimization Design for Sparse Planar Array in Satellite Communications
## 4 Sparse Planar Array Optimization Design Method
### Intelligent Optimization Methods
#### 4.2.1 Sparse Area Array Optimization Based on Traditional Intelligent Methods
The authors of [44] adopted a mirror operation, took the first lobe level as the optimization function, introduced the control coefficient of the number of elements, used the simulated annealing method to obtain a sparse array with an excellent low sidelobe pattern, and reduced the calculation amount of the algorithm. The advantage of using simulated annealing is that the position and weight of the array elements can be optimized at the same time. Although this method cannot guarantee that the global optimal solution will be obtained, it can greatly increase the probability of searching for the optimal solution; it is necessary to debug and compare the initial temperature, decay rate, and other parameter combinations to find the optimal solution suitable for specific scenarios. The disadvantage is that the searchability is not enough, whereby it is sometimes impossible to obtain a good solution, and it is not easy to reduce the peak sidelobe level. The particle swarm algorithm is a swarm intelligence algorithm obtained by simulating the behavior of flocks of birds foraging for food in coordination with each other. Aiming at the problem of reducing peak sidelobe level, the improved binary Boolean particle swarm optimization (BPSO) is applied to the design of sparse planar arrays [45], which obtains lower sidelobes and better reliability. Although the principle of the BPSO algorithm is simpler, it only considers itself and does not consider the characteristics of sparse area array, which can cause huge computational problems in practical applications. The authors of [46] proposed a hybrid synthesis particle swarm optimization (HSPSO) algorithm based on the Hadamard set, which is more in line with the design characteristics of a sparse area array, and reduces the peak sidelobes while limiting the number of elements. This study presents a comparison between the proposed HSPSO method and the SPSO method. The _PSLL_ results obtained using the HSPSO and SPSO methods were evaluated for different scenarios with varying array element numbers and filling factors. Specifically, for an array element turned ON number of 21 and a filling factor of 0.58, the _PSLL_ obtained using the HSPSO method was found to be 0.51 dB lower than that achieved using the SPSO method. Similarly, for an array element turned ON number of 75 and a filling factor of 0.52, the _PSLL_ obtained using the HSPSO method was 1.27 dB lower than that obtained using the SPSO method. Lastly, for an array element turned ON number of 323 and a filling factor of 0.56, the _PSLL_ obtained using the HSPSO method was 3.25 dB lower than that obtained using the SPSO method. In order to solve the problem that particle swarm optimization converges quickly and easily falls into the local optimal solution, the authors of [47] proposed an improved PSO algorithm, which adopts the analytic initial value in the initialization process and analyzes the element weight through matrix operation, specifies the weight as the random initial value of any particle, and uses the PSO algorithm to iterate. This algorithm can improve the convergence characteristics of the algorithm. The advantage of using this algorithm to optimize the sparse area array is that the algorithm complexity is low and the parameters are few, but it faces the problem of fast convergence and falling into local extremes. Ant colony algorithms benefit from the natural phenomenon of ants looking for food. The ant colony algorithm was applied to the sparse area array design for the first time in [48], and a low sidelobe was obtained, but other factors affecting the antenna pattern, such as amplitude phase, were not limited. Aiming at the problem of peak sidelobe level reduction, the authors of [49] used the ant colony optimization method to adjust the position of the elements in the uniform sparse circle array, obtaining a lower peak sidelobe level and providing the maximum directivity in the opposite direction.