A dual isometric transformation for the determination of ambiguities in bearing estimation

Abstract

Linear dependence in the array antenna manifold (“steering vectors”) leads to a failure of subspace-based methods (e.g. “MUSIC”) in identifying source locations. These manifold ambiguities provide parasitic peaks in the spatial spectrum. In this paper, we present a method for determining the manifold ambiguities for a linear array based on isometric polygon transformations in the complex plane. For rank-two ambiguities, we demonstrate that the array can be split into two subarrays. This step reduces the problem to a determination of rank-one ambiguities for just one of these subarrays. We then generalize these results for rank- n ambiguities. The geometrical construct presented enables an exhaustive determination of any-rank ambiguity for the array under consideration. Examples are used to illustrate the proposed method.