Design and Optimization of Sparse Planar Antenna Arrays Based on Special Matrices

As sparse arrays can cover a large space with relatively few elements, their low cost and undegraded radiation patterns have attracted more and more interest. And also due to the randomness of antenna locations, sparse arrays can avoid the generation of grating lobes while the spacing between adjacent antenna is greater than half a wavelength. However, the locations of the antenna need to be carefully considered to ensure its acceptable level of performance. And Formally, the design of sparse arrays can be expressed as a constrained multidimensional nonlinear optimization problem. However, due to the lack of convexity, using deterministic optimization methods to solve this kind of multi-extremity problem is very tricky, and non-deterministic optimization methods (such as iterative methods) that are very time-consuming and wasteful of resources are always used to solve the problem. In this work, a simple and time-saving method for designing a two-dimensional planar antenna array using a deterministic method based on special matrices (including, Magic square, Latin square, and triangular matrix) are proposed. And the detailed design process, MATLAB simulation verification and comparative analysis are presented in the paper.