Manikas A. Differential Geometry in Array Processing

Imperial College Press, 2004.Array processing has an enormous set of applications and has recently experienced an explosive interest due to the realization that arrays have a major role to play in the development of future communication systems, wireless computing, biomedicine (bio-array processing) and environmental
monitoring.
The heart of any application is the structure of the employed array of sensors and this is completely characterized by the array manifold. The array manifold is a fundamental concept and is defined as the locus of all the response vectors of the array over the feasible set of source/signal
parameters. In view of the nature of the array manifold and its significance in the area of array processing and array communications, the role of differential geometry as the most particularly appropriate analysis tool, cannot be over-emphasized.
The array manifolds are embedded not in real, but in N-dimensional complex space (where N is the number of sensors). Therefore, by extending the theoretical framework of R3 to complex spaces, the underlying and under-pinning objective of this book is to present a summary of those results of differential geometry which are exploitable and of practical interest in the study of linear, planar and three-dimensional array geometries.