A Stochastic Study of Large Arrays Related to the Number of Electrically Large Aperture Radiators

Abstract

A study of the maximally sparse large planar arrays with electrically large elements is presented. The conditional probabilities of the element placements and their resulting auxiliary radiation integrals are derived. Through them the average and the directivity pattern formulas are also derived. Employing these formulas, we present a convex method that provides a solution to the maximally sparse problem when main lobe constraints are imposed on the directivity pattern. In particular, by taking the possible types of elements into account, we manage to obtain the lower bound of the directivity that an array should exhibit. This lower bound is analytically derived in the form of a Pareto (sub-) set that classifies the possible arrays into feasible and nonfeasible ones. This Pareto set can also enable tradeoff studies to be conducted without the need to consider the full range of every parameter. From the procedure, several acceptable combinations of elements are obtained. Simulation results, which confirm the methodology, are presented.Index Terms-Aperiodic arrays, maximally sparse arrays.

Multibeam antennas for global satellite coverage: theory and design

“…In this section, the broadside multibeam design theory is reviewed. After the problem statement, the implications of average power pattern formula (including Pareto-front theory and deterministic sampling) which were recently provided by the authors [18] are stated. The section ends with a solid presentation of the resulted algorithm.…”

“…The Pareto-front formula is extracted as follows: for large arrays assembled by large aperture radiators, it is proved that the average directivity pattern for small angles of θ can be written as [18]…”

“…Indeed there are promising and innovative methods limited to one-dimension arrays and others that are based on iterative techniques and/or complex optimisation methods for planar arrays. Recently, the authors following a rigorous theoretical approach have introduced a clear and solid mathematical framework that provides closed-form analytical Pareto-front results for the synthesis of planar arrays [18,19]. Adopting this strategy various estimations on possible array layout solutions can be obtained.…”

“…Assuming a priori that the array is constituted by an assigned number of element types (for instance small, medium and large radiators), the identification of the most appropriate number and position of elements per type is not trivial and implies the implementation of new design algorithms. In [18,19] both the appropriate number and the element position/orientation have been provided. Indeed, in these publications various examples were given, but the achieved result was limited to sub-continental coverages.…”

Tx/Rx multibeam satellite antenna array design assesment on a single aperture

“…We assume that we use one type of elements. This means that the maximum directivity determines the minimum number of elements, [7].…”