A Compressive-Sensing Inspired Alternate Projection Algorithm for Sparse Array Synthesis

Daniele Pinchera,Mario Lucido,Fulvio Schettino,Gaetano Panariello,Marco Migliore

doi:10.3390/electronics6010003

Abstract

In this paper, we propose a simple approach for sparse array synthesis. We employ a modified generalized alternate projection algorithm using ℓ 1 -norm constrained minimization in order to achieve the excitation and the position of the elements of a sparse array. The proposed approach is very flexible, since it deals with power pattern masks and allows the inclusion of the effects of element pattern and mutual coupling. Its implementation is relatively simple, thanks to the possibility to use well-known convex programming techniques. The presented method is particularly suitable for the synthesis of patterns commonly employed in radar systems; the numerical results provided show good performances with respect to concurrent methods available in open literature.

Highlights

Array pattern synthesis is of paramount importance for designing modern radar systems, and it is an important and active area of research
To validate the proposed approach, we will show the results of some synthesis examples; in particular, we will discuss two sparse arrays, capable of radiating a flat-top beam to be employed—for instance, in a virtual subarray radar architecture [23]
By means of the Sparse-Forcing Generalized Alternate Projection (SFGAP) we are able to find a sparse array with 10 elements, radiating a pattern satisfying the mask constraints, but without seeking a preliminarily calculated solution, as in the methods employed by other researchers

Summary

Introduction

Array pattern synthesis is of paramount importance for designing modern radar systems, and it is an important and active area of research. Many efficient synthesis strategies are available in the case of fixed positions of the radiating elements [1,2]. These algorithms take advantage of the linear relationship between the far-field and the unknown (i.e., the excitations of the radiating elements), and, with proper constraints, require the use of fast and efficient local minimizing algorithms. The efficient synthesis of non-equispaced (or sparse) arrays is an open problem. The strong nonlinearity of the radiation operator with respect to the array elements’ positions prevents the effectiveness of local minimization algorithms. The use of global minimizing approaches, like evolutionary algorithms, allows to asymptotically obtain an optimal solution of the problem

Results

Discussion

Conclusion