Identifiability and manifold ambiguity in DOA estimation for nonuniform linear antenna arrays

This paper considers the direction-of-arrival (DOA) estimation identifiability problem for uncorrelated Gaussian sources and nonuniform antenna arrays. It is now known that sparse arrays always suffer from manifold ambiguity, which arises due to linear dependence amongst the columns of the array manifold matrix (the “steering vectors”). While the standard subspace DOA estimation algorithms such as MUSIC fail to provide proper unambiguous estimates under these conditions, we demonstrate that in most cases involving uncorrelated Gaussian sources, manifold ambiguity does not necessarily imply nonidentifiability. An effective manifold ambiguity resolution algorithm is introduced. A superior number of uncorrelated Gaussian sources (more than sensors) may also be unambiguously localised by sparse arrays under specified identifiability conditions. While manifold ambiguity does not apply to superior scenarios, a similar “co-array manifold ambiguity” phenomenon may compromise DOA estimation. The proposed algorithm can also resolve such ambiguity in all identifiable cases.