Existence and Uniqueness of Hyperhelical Array Manifold Curves

A number of significant problems, arising frequently in array signal processing, have been successfully tackled using methods based on the concept of the array manifold. These approaches take advantage of the inherent information about the array system which is encapsulated in the geometry of the array manifold. Array ambiguities, array uncertainties, array design and performance characterization are just some of the areas that have benefited from this approach. However, the investigation of the geometry of the array manifold itself for most array geometries has been proven to be a complex problem, especially when higher order geometric properties need to be calculated. Nevertheless, special array geometries have been identified, for which the array manifold curve assumes a specific “hyperhelical” shape. This property of the array manifold greatly simplifies its geometric analysis and, consequently, the analysis of the associated array geometries. Hence, the goal of this paper is twofold; to provide the necessary and sufficient conditions for the existence of array manifold curves of hyperhelical shape; and to determine which array geometries can actually give rise to manifold curves of this shape.