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

Abstract

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 sidelobe levels, are presented to validate the effectiveness and advantages of the proposed methods. The element saving is about 11.2% − 49.4% for usual cases.Index Terms-Nonuniformly spaced array, wideband array, frequency-invariant pattern, generalized matrix pencil method.

Synthesis of frequency‐invariant patterns by the fast multitask compressive sensing

“…This pattern was synthesized in using 21 uniform sensors with the spacing of 1.42 cm. In , the GMPM was used to synthesize the pattern with 11 elements. The frequency range for the FI pattern is 3.33–12 kHz , which is uniformly distributed to K = 32 tested frequencies.…”

“…The focus of this research is to detect the realization and evaluate the effectiveness of this fast scheme. Detailed steps are presented, and comparable results are obtained as those of the generalized matrix pencil method (GMPM) , which is one of the state‐of‐the‐art non‐iterative techniques for the same object as the proposed method.…”

Power Gain Pattern Synthesis via Successive Convex Approximation Technique

“…A RRAY antenna has been widely used in many fields such as sonar, radar, speech processing, and navigation to wireless communications because of its flexible beamforming ability [1]- [6]. Pattern synthesis is a process to obtain the required antenna radiation pattern and could improve the performance of the array antenna.…”

Quantum Particle Swarm Optimization for Synthesis of Non-uniformly Spaced Linear Arrays with Broadband Frequency Invariant Pattern

“…Many methods have been proposed for the synthesis of nonuniformly spaced arrays [7][8][9][10]. Some techniques like genetic algorithm and neural-network based methodology and performance of raised power series arrays have been described in [7][8] for synthesizing wideband non-uniformly spaced arrays.…”

“…The method described in [9] uses the asymptotic theory of unequally spaced arrays to produce ultra-wideband pattern with invariant main beam, but generates higher SLL. Another method for synthesis of nonuniformly spaced linear arrays with wide band frequency-invariant patterns using the generalized matrix pencil methods has been described in [10]. In this paper, a simple method is presented for broadband frequency invariant pattern using Quantum Particle Swarm Optimization (QPSO) algorithm for synthesis of nonuniformly spaced linear array antenna [11][12][13].…”