Extreme Sparse-Array Synthesis via Iterative Convex Optimization and Simulated-Annealing Expanded Array

Sparse-array synthesis can considerably reduce the number of sensor elements while optimizing the beam-pattern response performance. The sparsity of an array is related to the degrees of freedom of the array elements. A sparse-array method based on iterative convex optimization and a simulated-annealing expanded array is proposed in this paper. This method transforms the sparse-array problem into a minimum l1 norm problem and obtains the sparse array by solving the convex optimization problem using the primal-dual algorithm. Meanwhile, to improve the degree of freedom, array elements are expanded using stochastic perturbation. According to the simulated-annealing algorithm, the closed array elements are reopened with a specific probability, which is iteratively thinned and expanded. The results show that the proposed method can obtain an extremely sparse array, which is better than that obtained using the existing methods.