# 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 traditional intelligent method is the earliest intelligent method applied to the optimization design of sparse area arrays; these methods are adapted functions of the target optimization. In the optimization design of sparse plane arrays, we generally define the fitness function as some array parameters, where the goal is to solve the optimization of fitness. The traditional intelligent optimization method is suitable for optimizing planar arrays with small array scale, and it can achieve good results. However, as the array's scale increases, this method needs to break through the bottleneck of computational efficiency. When the amount of computation is large, this type of algorithm faces convergence deterioration and easily falls into the problem of local optimization. As the scale of the array expands, the CPU consumption increases, which reduces the efficiency of the algorithm. Among the many traditional intelligent optimization methods, the genetic algorithm, simulated annealing method, particle swarm algorithm, and ant colony algorithm are most frequently used. For the sake of easier understanding, we summarize the flowchart of these four types of methods for designing sparse area arrays in Figure 13.  
Traditional intelligent algorithms generally take the adaptation function as the optimization goal; the most typical approach is to take the peak sidelobe level as the fitness function of the population, where the output function is generally the antenna pattern, and the goal is to obtain the smallest peak sidelobe level. The number of elements and their arrangement also affect the output of the function. In 1994, [PERSON] [40] and [PERSON] [41] applied genetic algorithms to sparse array optimization design problems for the first time. In order to reduce the peak sidelobe level, [PERSON] used a genetic algorithm to optimize an array of 20 \(\times\) 10 sparse planes, obtaining a lower peak sidelobe level than the statistical method with a filling rate of 58%. However, due to the above document element position limitations, it can only be located in an equidistant grid, which can neither optimize the excitation weight nor minimize the number of elements. The authors of [42] divided the planar array into several subarrays, and used genetic algorithms to weight the subarrays by amplitude and phase excitation. Another study [35] was aimed at large sparse planar arrays, where the excitation amplitude phase  
Figure 13: Flowchart of four traditional intelligent algorithms. weights of the array elements were optimized, the weak excitation was removed, and a comprehensive method of planar antenna array cosecant square radiation pattern based on genetic algorithm was proposed to optimize the peak sidelobe level and small ripple deviation. The genetic algorithm is suitable for processing sparse planar arrays of small and medium scale, whereby it can obtain the global optimal solution. However, as the aperture of the array becomes larger, the calculation complexity is high, the convergence is slow, it easily falls into local optimization, and the number of elements cannot be minimized. In order to solve the problem of the minimum number of elements, [PERSON] [43] applied the simulated annealing method to the synthesis of sparse planar arrays, where the position and weight were optimized. The method was applied to a small planar array composed of 112 array elements and a large planar array composed of 3228 elements under the full array condition, while the small array was optimized with a filling rate of 55% and 60%, and the large array was thinned by 88.9%. All results obtained the peak sidelobe level equivalent to the full array situation, but the effect of this method on the reduction in peak sidelobe level was not obvious.