An Extended Generalized Matrix Pencil Method to Synthesize Multiple-Pattern Frequency-Invariant Linear Arrays

This letter develops an extended generalized matrix pencil method (EGMPM) for the synthesis of multiple-pattern frequency-invariant linear arrays. In this method, all the pattern data sampled from different frequencies and different patterns are organized into a Hankel matrix. The problem of estimating the best common excitations and locations is converted into solving a singular value decomposition and some least-square problems. The previously proposed generalized matrix pencil method and extended matrix pencil method are both special cases of the EGMPM. A set of numerical experiments on Chebyshev pattern, shaped pattern, Taylor pattern, pencil-beam pattern, and flat-beam pattern is shown to validate the proposed method.