Reducing the Number of Elements in Multiple-Pattern Linear Arrays by the Extended Matrix Pencil Methods

Previously, the matrix pencil method (MPM) and the forward-backward MPM (FBMPM) were used to effectively reduce the number of antenna elements in the single-pattern linear arrays. This work extends the MPM and FBMPM-based synthesis methods to the synthesis of multiple-pattern linear arrays with a smaller number of elements. The extended MPM (resp., the extended FBMPM) method organizes all the multiple pattern data into a composite Hankel (resp., composite Hankel-Toeplitz) matrix from which the minimum number of elements and the common poles corresponding to element positions can be obtained with similar processing used in the original MPM or FBMPM synthesis method. In particular, the extended FBMPM inherits the advantage of the original FBMPM that a useful restriction is put on the distribution of poles, which makes the element positions obtained much more accurate and robust. Numerical experiments are conducted to validate the effectiveness and robustness of the proposed methods. For the tested cases, the element saving is about 20% ~ 25% for reconfigurable shaped patterns, and can be even more for electrically large linear arrays with scanned pencil-beams.