Two-dimensional unitary matrix pencil method for synthesizing sparse planar arrays

An innovative approach based on the two-dimensional unitary matrix pencil (2-D UMP) is proposed for the synthesis of arbitrary sparse planar arrays. In this study, the estimation of array parameters is recast as a 2-D poles extraction problem, and the number of antenna elements is minimized by the reduced rank processing. Firstly, the 2-D element positions including horizontal and vertical coordinates are directly found as the generalized eigenvalues of the equivalent matrix pencils without solving poles. Then the element excitations can be computed with the least-squares estimator once the real positions are obtained by the correct pairing procedure. The pattern matching accuracy and the array sparseness are further improved owing to the utilization of a unitary transformation, which converts a complex matrix to a real one along with its eigenvectors. A set of representative numerical experiments is provided to assess the effectiveness and advantages of the proposed method.