Uniform amplitude sparse arrays have recently gained a renewed interest and a number of synthesis techniques, mainly based on global optimization algorithms, have been presented. In this paper, after a discussion about the expected characteristics of such arrays, a simple deterministic approach for the case of pencil beams patterns is proposed and discussed. The approach, which outperforms previous synthesis techniques, takes inspiration from existing (not well-known) density taper procedures to develop a two stages synthesis where the first step is solved in a new closed analytical form, while the second one just requires local refinements or fast 1-D optimizations. As a consequence, the proposed approach avoids the need of multidimensional global optimization procedures and the inherent possibly prohibitive computational costs. Notably the first step, which also exhibits an improved flexibility with respect to other analytical techniques, already outperforms previous approaches in a number of cases of interest. Several numerical results confirm the effectiveness and usefulness of the proposed tools.

Deterministic Synthesis of Uniform Amplitude Sparse Arrays via New Density Taper Techniques

A deterministic procedure to design a nonperiodic planar array radiating a rotationally symmetric pencil beam pattern with an adjustable sidelobe level is proposed. The elements positions are derived by modifying the peculiar locations of the sunflower seeds in such a way that the corresponding spatial density fits a Taylor amplitude tapering law which guarantees the pattern requirements in terms of beamwidth and sidelobe level. Different configurations, based on a Voronoi cell spatial tessellation of the radiative aperture, are presented, having as a benchmark the requirements for a typical multibeam satellite antenna.

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Sunflower Array Antenna with Adjustable Density Taper

The paper describes a deterministic algorithm based on simple analytical equations for designing planar circular sparse array antennas where the positions and the dimensions of the radiating elements are jointly exploited and optimized. The proposed solution permits addressing one of the main limitations associated to sparse arrays, i.e., their poor aperture efficiency especially when patterns with low sidelobe levels are obtained using only the density of the elements avoiding any amplitude tapering. The accuracy of the method is guaranteed by the fact that the achieved directivity differs from the target value, associated to a continuous reference aperture distribution, by a quantity asymptotically equal to the factor π/4 (corresponding to about -1.05 dB) representing the filling factor of a circular planar array organized in concentric rings populated by circular apertures. As required for several applications, the method includes the possibility to add a constraint on the maximum scanning angle with respect to the boresight direction.

Array Antennas With Jointly Optimized Elements Positions and Dimensions Part II: Planar Circular Arrays

The synthesis of electrically large, aperiodic planar arrays with equi-amplitude excitations plays an increasingly relevant role in satellite applications. Unfortunately, for such a kind of synthesis problems, local optimization procedures may be ineffective, whereas global optimization procedures involve a severe computational effort. To circumvent these problems, a new deterministic approach for fast design of aperiodic concentric ring arrays is proposed. The method exploits easily obtained optimal continuous planar solutions, accounts for the geometric properties of the array element and allows, once the central geometry of the array (that is, at least the most internal ring) is fixed, to compute in a deterministic, iterative, very fast way the whole geometry of the density-tapered concentric ring array. Numerical examples show the effectiveness of the method, which provides in a few seconds layouts of hundreds of elements able to produce directivity patterns that satisfy realistic satellite project requirements.

A Deterministic Two Dimensional Density Taper Approach for Fast Design of Uniform Amplitude Pencil Beams Arrays

A novel analytical approach to the synthesis of linear sparse arrays with non-uniform amplitude excitation is presented and thoroughly discussed in this paper. The proposed technique, based on the concept of auxiliary array factor, is aimed at the deterministic determination of the optimal array element density and excitation tapering distributions useful to mimic a desired radiation pattern. In particular, the developed antenna placement method does not require any iterative or stochastic optimization procedure, resulting in a dramatic reduction of antenna design times. Selected examples are included in order to assess the effectiveness and versatility of the proposed approach in the framework of aperiodic array synthesis problems.

A Novel Deterministic Synthesis Technique for Constrained Sparse Array Design Problems

This Memorandum considers least-mean-square comparison of directivity patterns of line sources having different illumination distributions.

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Worthie Doyle

Papers

On approximating linear array factors