Abstract
Sparse arrays have grating lobes in the far field pattern due to the large spacing of elements residing in a rectangular or triangular grid. Random element spacing removes the grating lobes but produces large variations in element density across the aperture. In fact, some areas are so dense that the elements overlap. This paper introduces a low discrepancy sequence (LDS) for generating the element locations in sparse planar arrays without grating lobes. This nonrandom alternative finds an element layout that reduces the grating lobes while keeping the elements far enough apart for practical construction. Our studies consider uniform sparse LDS arrays with 86% less elements than a fully populated array, and numerical results are presented that show these sampling techniques are capable of completely removing the grating lobes of sparse arrays. We present the mathematical formulation for implementing an LDS generated element lattice for sparse planar arrays, and present numerical results on their performance. Multiple array configurations are studied, and we show that these LDS techniques are not impacted by the type/shape of the planar array. Moreover, in comparison between the LDS techniques, we show that the Poisson disk sampling technique outperforms all other approaches and is the recommended LDS technique for sparse arrays.
Highlights
Sensing applications, such as radio telescopes, satellite communications, sonars, and defense radars, require large antenna arrays
We study sparse low discrepancy sequence (LDS) arrays with 86% less elements than a fully populated array, and present numerical results that demonstrate these sampling techniques are capable of completely removing the grating lobes of sparse arrays
Sparse arrays have a significantly smaller number of elements compared to traditional dense arrays which minimizes their cost and complexity
Summary
Sensing applications, such as radio telescopes, satellite communications, sonars, and defense radars, require large antenna arrays. Interelement spacings stantially fewer driven radiating elements than a conventional uniformly spaced array with in the sparse array can be chosen such that no large grating lobes are formed and sidelobes the same beamwidth having identical elements. The advantages of LDS for sparse phased array design demonstrated that the Hammersley sequence maintains the large separation between the elements, while reducing the grating lobes compared to element spacings derived from random, pseudo-random, and uniform plus jitter sequences [35]. In this paper we use low discrepancy sequences to distribute elements in a sparse planar array aperture while maintaining the following properties:. We study sparse LDS arrays with 86% less elements than a fully populated array, and present numerical results that demonstrate these sampling techniques are capable of completely removing the grating lobes of sparse arrays.
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