Synthesis of Sparse Arrays With Focused or Shaped Beampattern via Sequential Convex Optimizations

Abstract

Abstract-An iterative procedure for the synthesis of sparse arrays radiating focused or shaped beampattern is presented. The algorithm consists in solving a sequence of weighted convex optimization problems. The method can thus be readily implemented and efficiently solved. In the optimization procedure, the objective is the minimization of the number of radiating elements and the constraints correspond to the pattern requirements. The method can be applied to synthesize either focused or shaped beampattern and there is no restriction regarding the array geometry and individual element patterns. Numerical comparisons with standard benchmark problems assess the efficiency of the proposed approach, whose computation time is several orders of magnitude below those of so-called global optimization algorithms.

Synthesis of Sparse or Thinned Linear and Planar Arrays Generating Reconfigurable Multiple Real Patterns by Iterative Linear Programming

“…Recently, the iterative reweighted 1 -norm optimization was presented in [30] to approach as closely as possible to 0 -norm for enhanced sparsity. This method has been successfully applied to the sensors selection for single-pattern arrays in [31][32][33]. Now, we extend the idea to enhance the sparsity of the multiple-pattern array synthesis.…”

“…The iterative reweighted 1 optimization was presented in [30], and recently this idea was used to reduce the number of elements for a single focused beam or shaped pattern, by developing the iterative second-order cone programming (SOCP) in [31][32][33] or sequential compressive sensing (CS) approach in [34]. We now apply this idea to reduce the number of elements for multiple-pattern arrays by selecting the best common elements, each with multiple optimized excitations, under multiple power pattern requirements that are all given by upper and lower bounds.…”

Comparison Guidelines and Benchmark Procedure for Sparse Array Synthesis

“…We will perform first the benchmarking of the 22 element array provided in [7]; this pencil beam array has a non-symmetrical power pattern defined in the range u ∈ [−22] in order to allow the beam scanning, without the appearance of grating lobes, in the whole visible range (so u s = 1). In particular the side lobe level for the achieved pattern § is below −21.356 dB for u ≤ −0.1261 and it is below −30.328 dB for u ≥ 0.1238.…”

“…Due to their advantages, several methods have been developed: evolutionary techniques [1][2][3][4], compressive sensing inspired approaches [5][6][7][8], and many others [9][10][11][12][13]. In spite of the importance of the problem, no specific comparison procedures among synthesis methods have been developed up to date.…”

An Iterative Approach for the Synthesis of Optimized Sparse Time-Modulated Linear Arrays

“…Let us consider as representative examples, the matrix pencil method [24], compressive sensing-based techniques [25][26][27], and convex optimization-based techniques [28,29]. In principle, such strategies could be applied to also deal with sparse TMAs, but they are not naturally conceived to handle SRs.…”