A Two-Step Method for the Low-Sidelobe Synthesis of Uniform Amplitude Planar Sparse Arrays

Abstract

A two-step method combining the algorithms of iterative Fourier transform (IFT) and differential evolution (DE), called IFT-DE, is proposed in this paper for the low sidelobe synthesis of a uniform amplitude planar sparse array (PSA). Firstly, the entire aperture of the array is divided into a set of square lattices that are spaced at half wavelength. Then the elements are forced to be located on the lattices through performing IFT, so that a planar thinned array (PTA) is formed across the aperture. Undoubtedly the interval between adjacent elements of the PTA is an integer multiple of half wavelength. In the second step, for each column of PTA the elements spaced greater than or equal to a wavelength are selected as the candidates whose locations need to be optimized by DE procedure, as long as the renewed inter-element spacing is not less than half wavelength. Consequently, a PSA with reduced sidelobe level may be obtained. According to the aforementioned selection rule, only a small part of elements that account for the total number need to be relocated, which denotes that the number of individual parameters waiting for optimizing by DE is decreased considerably, and thereby greatly accelerates the convergence speed of the algorithm. A set of synthesis experiments for PSA ranging from small to moderate size are presented to validate the effectiveness of the proposed method.

Synthesis of Uniformly Excited Concentric Ring Arrays by the Strategy of Partial Density Tapering and the Algorithm of Differential Evolution

“…In addition, for the case when N � 201, the best array after 50 runs of the PDT-DE has a PSL equal to −30.34 dB. e performance of the array shows a PSL suppression of 1.21 dB compared to the value obtained by the MGA [11] and a PSL suppression of 6.13 dB compared to that demonstrated by the IFT-DE [18]. More detailed results, including the ring radii and the number of elements in each ring, are given in Table 1.…”

Optimization Design for Sparse Planar Array in Satellite Communications

“…Nevertheless, despite these substantial variations, the directivity of the synthesized consequences via both the IWO-IFT strategy and the IFT approach was not found to possess any significant differences. The authors of [94] used the IFT method to form a sparse plane array first; then, the DE algorithm was used to optimize the position, and a two-step IFT-DE method was proposed by combining the iterative Fourier transform method and the differential evolution method to reduce the number of elements and the peak sidelobe level and accelerate the convergence speed of the algorithm. The authors explored the synthesized outcomes of rectangular arrays in [94].…”

“…The authors of [94] used the IFT method to form a sparse plane array first; then, the DE algorithm was used to optimize the position, and a two-step IFT-DE method was proposed by combining the iterative Fourier transform method and the differential evolution method to reduce the number of elements and the peak sidelobe level and accelerate the convergence speed of the algorithm. The authors explored the synthesized outcomes of rectangular arrays in [94]. Each array possessed diverse aperture dimensions with 36, 64, and 100 array elements, and the fill factor of the array was set at 50%.…”