Investigation of the spatio-temporal array manifold of linear arrays using differential geometry

This paper is concerned with the study of linear array systems, operating in an asynchronous, multipath/multiple-access environment. In the modeling and analysis of array systems, the array manifold vector is being widely used, providing the spatial information of the signal environment. Recently, because of the inherent limitations of the array manifold to accurately model a multiple-access/multipath signal environment, the concept of the Spatio-Temporal ARay (STAR) manifold has been introduced, which extends the conventional - spatial array manifold by, incorporating both temporal information and the distinct "signature" of each user/target/path. The properties of the array manifold have already been extensively studied and the aim of this paper is to examine the corresponding properties of the STAR manifold. It is shown that there is a direct relationship between these two manifolds and that the characteristics of the STAR manifold of linear arrays can be derived from those of the array manifold. Finally, this technique is generalised to handle not only the STAR manifold, but, also, a wide class of linear mappings of the array manifold.