Unequally Spaced Arrays Based on the Poisson Sum Formula

Abstract

It has been recognized that unequally spaced arrays can offer some advantages over equally spaced arrays, mainly in the following areas: 1) thinned array by reducing the number of elements to achieve the high resolution without producing grating lobes; 2) broadbanding or wide scanning without grating lobes; 3) reducing sidelobes for the array of uniform amplitude; and 4) unequally spaced arrays on a curved surface. Historical accounts and a basic theory of unequally spaced arrays based on Poisson Sum Formula are given. Most of the analytical approach can be obtained by numerical computation. Analytical methods may show additional physical mechanisms and offer alternative approaches. This paper also discusses some additional applications on circular arrays, active impedance and arrays on a curved surface.

Generalized Array Factor Approach to the Assessment of Discrete Tapered Nonuniform Leaky-Wave Antenna

“…The obtained values are indicated by black circles on Fig. 9 and are compared with the ones given by the analytical equations (19)(20). Arbitrarily, differences of -values obtained from both calculations less than 20 % were considered acceptable, see Fig.…”

“…This approach used in combination with design procedures for unequally spaced array [20] could lead to new kinds of designs. However, special attention should be paid to the fact that, for LWAs, the UCs are fed through the propagation of the wave inside the waveguide.…”

A Hybrid Algorithm for Synthesizing Linear Sparse Arrays

“…Therefore, sparse arrays have more freedom degrees of optimization to achieve lower PSLL than thin arrays have. Recently, several approaches, such as analytical methods [3][4][5], modified genetic algorithm (MGA) [6], differential evolution algorithm (DEA) [7], vector mapping and simultaneous perturbation stochastic approximation [8], and invasive weed optimization (IWO) [9] have been developed for synthesizing sparse arrays. The performances of those techniques on achieving low PSLL are quite limited as a result of position-only optimization.…”

Hybrid Approach for the Synthesis of Unequally Spaced Array Antennas With Sidelobes Reduction

“…Representative works providing the theoretical rules for determining the elements' relative positions for low sidelobes are described in [5], [6], [7], [8], where the rules are developed based on Floquet mode [9] behaviors in the antenna radiations. In particular, [5] and [7] attempt to optimize the aperture current distribution for the fundamental mode to resemble the radiation patterns analogous to that of Taylor's line sources.…”

“…In particular, [5] and [7] attempt to optimize the aperture current distribution for the fundamental mode to resemble the radiation patterns analogous to that of Taylor's line sources. On the other hand, [6] and [8] focus on efforts to suppress the grating lobes near the main lobe that result from the second Floquet modes.…”