Positive-definite Toeplitz completion in DOA estimation for nonuniform linear antenna arrays : Part I: Fully augmentable arrays

• Published in: IEEE transactions on signal processing Vol. 46; no. 9; pp. 2458 - 2471
• Main Authors: ABRAMOVICH, Y. I, GRAY, D. A, GOROKHOV, A. Y, SPENCER, N. K
• Format: Journal Article
• Language: English
• Published: New York, NY Institute of Electrical and Electronics Engineers 01.09.1998
• Subjects: Applied sciences; Exact sciences and technology; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Linear antenna; Completion; Maximum likelihood receiver; Positive definite matrix; Plane wave; Covariance matrix; Toeplitz matrix; Cramer Rao inequality
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/78.709534

This paper considers the problem of direction-of-arrival (DOA) estimation for multiple uncorrelated plane waves incident on so-called `fully augmentable' sparse linear arrays. In situations where a decision is made on the number of existing signal sources (m) prior to the estimation stage, we investigate the conditions under which DOA estimation accuracy is effective (in the maximum-likelihood sense). In the case where m is less than the number of antenna sensors (M), a new approach called `MUSIC-maximum-entropy equalization' is proposed to improve DOA estimation performance in the `preasymptotic region' of finite sample size (N) and signal-to-noise ratio. A full-sized positive definite (p.d.) Toeplitz matrix is constructed from the MxM direct data covariance matrix, and then, alternating projections are applied to find a p.d. Toeplitz matrix with m-variate signal eigensubspace (`signal subspace truncation'). When m greater than or equal to M, Cramer-Rao bound analysis suggests that the minimal useful sample size N is rather large, even for arbitrarily strong signals. It is demonstrated that the well-known direct augmentation approach (DAA) cannot approach the accuracy of the corresponding Cramer-Rao bound, even asymptotically (as N arrow right infinity ) and, therefore, needs to he improved. We present a new estimation method whereby signal subspace truncation of the DAA augmented matrix is used for initialization and is followed by a local maximum-likelihood optimization routine. The accuracy of this method is demonstrated to be asymptotically optimal for the various superior scenarios (m greater than or equal to M) presented.