A construction of arrays free of rank ambiguities

Schmidt [1981] has established that ambiguity in steering vectors would lead to ambiguous direction-of-arrival (DOA) estimates. In the literature, arrays free of upto rank-k ambiguities, where k⩾3, have not been identified. The present authors construct a class of cross arrays which are free of upto rank-k ambiguities, where k∈{1, 2...}. Through the study, they derive a theorem for characterizing inherent ambiguities associated with a class of cross and circular arrays. They also provide a counterexample to the conjecture for characterizing higher rank ambiguity, proposed by Lo and Marple [1992]