Study of ambiguities in array manifold: a general framework

In the performance evaluation of sources localisation methods, resolution is not the only criterion. Degradations may occur, due to parasite peaks in the spectrum, which may be connected to high sidelobes in the beam pattern or to ambiguities themselves. The paper studies the presence of ambiguities in an array of given planar geometry. The ambiguity problem for an arbitrary array is examined and ambiguous situations are identified. We propose a general framework for the analysis and obtain a generalisation of the results given in previous publications for rank one and two ambiguities. For rank k⩾3 ambiguities, the results focus on linear arrays, for which we derive original and synthetic results. Some interesting results are driven for non-uniform linear arrays, including sparse linear arrays