Array geometry optimization for ambiguity resolution in direction finding

The array response in the presence of a single signal is given by the array manifold. The manifold should be different for different directions of arrival (DOA). If for a given set of widely separated DOAs the manifold is similar, large errors, usually referred to as ambiguity errors, are likely to occur. We introduce a measure of similarity between array response vectors. A tight lower bound of the similarity measure can be easily derived. The array geometry associated with the highest lower bound performs better than other arrays with the same aperture and the same number of sensors. Therefore, this bound can be used for selecting the best array configuration from a given set of candidate geometries. It is shown that for wideband arrays, the optimal array selection should be performed only once, at the highest frequency of operation. Unlike most of the results in the literature, our approach is not limited to linear arrays, and it can be applied successfully to any array configuration.