POSITIVE-DEFINITE TOEPLITZ COMPLETION IN DOA ESTIMATION FOR NONUNIFORM LINEAR ANTENNA-ARRAYS - PART I - FULLY AUGMENTABLE ARRAYS

This paper considers the problem of direction-of-arrival (DOA) estimat ion for multiple uncorrelated plane waves incident on so-called ''full y augmentable'' sparse linear arrays, In situations where a decision i s made on the number of existing signal sources (m) prior to the estim ation stage, we investigate the conditions under which DOA estimation accuracy is effective (in the maximum-likelihood sense). In the case w here m is less than the number of antenna sensors (M), a new approach called ''MUSIC-maximum-entropy equalization'' is proposed to improve D OA estimation performance in the ''preasymptotic region'' of finite sa mple size (N) and signal-to-noise ratio. A full-sized positive definit e (p.d.) Toeplitx matrix is constructed from the M x M direct data cov ariance matrix, and then, alternating projections are applied to find a p.d. Toeplitz matrix with m-variate signal eigensubspace (''signal s ubspace truncation''). When m greater than or equal to M, Cramer-Rao b ound analysis suggests that the minimal useful sample size N is rather large, even for arbitrarily strong signals. It is demonstrated that t he well-known direct augmentation approach (DAA) cannot approach the a ccuracy of the corresponding Cramer-Rao bound, even asymptotically (as N --> infinity) and, therefore, needs to be improved. We present a ne w estimation method whereby signal subspace truncation of the DAA augm ented matrix is used for initialization and is followed by a local max imum-likelihood optimization routine. The accuracy of this method is d emonstrated to be asymptotically optimal for the various superior scen arios (m greater than or equal to M) presented.