Positive-definite Toeplitz completion in DOA estimation for fully-augmentable nonuniform linear antenna arrays

This paper considers the problem of DOA (direction-of-arrival) estimation for multiple uncorrelated plane waves incident upon so-called “fully-augmentable” sparse linear arrays. When the number of waves, m, is less than the number of antenna sensors, M, a new approach is presented which constructs a full-sized positive definite (p.d.) Toeplitz matrix from the M×M direct data covariance matrix Rˆ. Alternating projections are then applied to find a p.d. Toeplitz matrix with truncated signal subspace. When m⩾M, direct augmentation is used to form an initial Toeplitz estimate which is then treated as in the previous case. Results on simulated data demonstrate that this new approach has superior DOA-estimation performance compared with existing methods