Modeling and estimation of ambiguities in linear arrays

In this paper, the problem of ambiguities inherent in the manifold of any linear array structure is investigated. Ambiguities, which can be classified into trivial and nontrivial, depending on the ease of their identification, arise when an array cannot distinguish between two different sets of directional sources. Initially, the new concept of an ambiguous generator set is introduced; it represents/generates an infinite number of ambiguous sets of directions. Then, by uniformly/nonuniformly partitioning the array manifold curve of a linear array, different ambiguous generator sets can be calculated, and as a direct result, a sufficient condition for the presence of ambiguities is obtained. The theoretical aspects of the investigation are followed by the proposal of an innovative approach that calculates not only all such ambiguities existing in a linear array of arbitrary geometry but the rank of ambiguity in each case as well. The main results presented in the paper are supported by a number of representative examples.