# 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
The authors of [96] integrated the FFT method into the PSO algorithm to improve the generation efficiency of the antenna pattern, and proposed a particle swarm algorithm based on CUDA, which is a parallel particle swarm method that integrates the FFT algorithm and intelligence method to realize the synthesis of large-scale reflection arrays. The combination of intelligent optimization methods and analysis methods can realize multiparameter joint optimization with strong adaptability. The hybrid method proposed in [97] combines CO technology and the SA method to successfully realize the joint optimization of counter-element excitation and position. This hybrid optimization approach is highly adaptable to various array synthesis problems. A hybrid method using the density cone (DT) method to initialize genetic algorithms was applied to synthesize thinning arrays [98], enhancing the ability of global optimization methods to synthesize large aperture sparse areal arrays. The authors of [99] proposed a hybrid method combining convex programming (CP) and the genetic algorithm (GA) to minimize peak sidelobes of sparse surface arrays and optimize the position and excitation of arrays. The authors explored the sparse division of an array with a size of \(16\lambda\times 13\lambda\) and 891 elements into a sparse array consisting of only 265 elements. The fill factor was set at a mere 29.7%. The results were nothing short of astonishing. The \(PSLL\) obtained from this novel approach proved to be significantly lower than the expected value of \(-20\) dB. Combining the analysis method with the local optimization method can realize multi-parameter joint optimization, taking into account the method's calculation speed and strong pertinence. The Fourier transform of the model designed by the Elliott-Stern method is used to obtain the initial element excitation [100], and IFT is applied to iteratively optimize the element excitation, which synthesizes a large torus sparse array, improving the algorithm's speed and robustness. The authors of [34] combined the density cone (DT) method and iterative Fourier method; the IFTDT algorithm was proposed to perform ring partition of the array aperture and determine the number of zonal array elements through the Taylor aperture distribution model, which significantly improved the convergence ability and convergence stability of the IFTDT algorithm. Aiming at beamforming problems, a hybrid method combining IFT and quadratic programming was proposed in [101], which could obtain better radiation performance while reducing the number of elements. The authors of [102] combined the fast Fourier transform method and generalized the analytic equation, proposing a uniformly distributed circular array synthesis method with quantitative weights to reduce the peak sidelobe level and the narrowest half-power beamwidth. Ultimately, to facilitate a more intuitive comparison of the synthesis results yielded by the four optimization techniques, for the benefit of our readers, Table 1 furnishes the quantitative indications for element quantity, fill factor, \(PSLL\), and directionality drawn from key references pertaining to the four optimization methods expounded upon in this chapter.