Antenna array manifold: A simplified representation

The array manifold vector is one of the most important parameters of an array system. For a general non-linear array of sensors. (i.e. a two or thrice dimensional array geometry), the locus of dir manifold vectors is a hypersurface embedded in a multidimensional complex space, with parameters of interest the azimuth and elevation angles. in this paper, a simplified representation of this complex hypersurface on a real two-dimensional plane is presented. This simplification/mapping, using concepts from differential geometry, maintains the main characteristics of the original array manifold surface and has the potential of providing new grounds for design and analysis of array systems. In this study, both planar and three-dimensional :arrays of omnidirectional sensors will be considered.