Extended Array Manifolds: Functions of Array Manifolds

The response of an array processing system has been widely modelled using the concept of the array manifold. The conventional array manifold is a function of the geometry of the array, the carrier frequency and the directions of arrival (DOAs) of the sources only. However, the emergence of more sophisticated array systems, for instance antenna array communication systems, dictates the extension of this array manifold into various new types of manifolds that incorporate additional system and channel parameters, such as the code-division multiple access (CDMA) (spreading and scrambling) codes, the lack of synchronization, Doppler effects, polarization parameters, subcarriers, etc. This paper is concerned with the definition and geometric investigation of a generic model for these new manifolds that can be expressed as functions of the conventional array manifolds and, hence, are defined herein as extended array manifolds. Thus, initially, the concept of the extended array manifold is introduced and is shown to accommodate both existing and newly defined extensions of the widely employed in the literature conventional (or spatial) array manifold. Next, the geometric properties and parameters of the extended array manifold are studied and linked with the properties of the associated spatial array manifold in an attempt to facilitate the geometric study of the former by taking advantage of the well understood study of the latter.