Optimization of Sparse synthesis aperture imaging array on hexagonal grids with difference basis

Design and Optimization of Sparse MMW synthesis aperture imaging array on hexagonal grids are researched in this paper. The arrangement of sparse array can be represented by configuration matrix. Using auto correlation matrix and cross correlation matrix of configuration matrix, distribution of sampling points in UV plane of hexagonal array is analyzed, and conditions for sampling points covering the whole UV plane are deduced. Then, the question is converted to design and optimization of a sparse rectangular array. With the virtue of full coverage and low redundancy, difference basis series are used to design hexagonal array, and a method to construct a optimized sparse hexagonal array is presented. Theoretical analysis and simulation show that the sampling points of the optimized hexagonal array can cover the UV plane without holes, and its redundancy is lower than that of a typical X style array.