Synthesis of Nonuniformly Spaced Linear Arrays With Frequency-Invariant Patterns by the Generalized Matrix Pencil Methods

This work extends the matrix pencil method (MPM)-based synthesis technique to the case of nonuniformly spaced linear arrays with wideband frequency-invariant (FI) patterns. A new sampling strategy is proposed to obtain multiple pattern data of different frequencies having the same poles that correspond to the FI element positions. The obtained multiple pattern sequences have the same shape for the FI pattern requirement, but with different lengths. The generalized MPM (GMPM) and its forward-backward version (GFBMPM) are developed to estimate the best common element positions for different frequencies, which can significantly reduce the number of elements required for the specified wideband pattern shape. The element excitations are solved by the regularized least-square (LS) method at each frequency. Then, an efficient method by utilizing the FFT is presented to obtain real-coefficient finite-impulse-response (FIR) filters for implementing the frequency-varying excitations. A set of numerical examples for the FI synthesis of pencil-beams, shaped patterns, scannable patterns, and Taylor patterns with low SLLs are presented to validate the effectiveness and advantages of the proposed methods. The element saving is about 11.2%-49.4% for usual cases.