A geometrical framework for the determination of ambiguous directions in subspace methods

In signal subspace parameter estimation techniques, like MUSIC, 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. This paper studies the presence of ambiguities in an array of given planar geometry. We propose a general framework for the analysis and thus we obtain a generalisation of results published by Lo and Marple (1992) and by Proukakis and Manikas (see Proc. ICASSP´94, vol.4, p.549-52, 1994) for rank one and two ambiguities. For rank k⩾3 ambiguities the study is restricted to linear arrays, for which we derive original and synthetic results. We present a geometrical construction that is able to determine all the ambiguous directions which can appear for a given linear array. The method allows determination of any rank ambiguities and for each ambiguous direction set, the rank of ambiguity is obtained. The search is exhaustive. Application of the method requires no assumption for the linear array and is easy to implement. An example is detailed for a non-uniform linear array