Stability of manifold ambiguity resolution in DOA estimation with nonuniform linear antenna arrays

We investigate the stability of direction-of-arrival (DOA) manifold ambiguity resolution for uncorrelated Gaussian sources. Such ambiguity is associated with linear dependence amongst the points on the antenna array manifold (in the “conventional” case, where the number of sources is less than the number of sensors), or amongst the points on the antenna co-array manifold otherwise (in the “superior” case). We previously introduced identifiability conditions for manifoldly ambiguous scenarios and described a new diagonal-fitting algorithm for ambiguity resolution. Simulations revealed the existence of superior scenarios that are extremely sensitive to estimation errors, typical of the DOA estimation techniques applied. This phenomenon gives rise to the notion of “stable” and “unstable” identifiability, which we discuss here