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

TLDR

Let's aggregate. Background sentences: 1. "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." 2. So background sentence: "DOA estimation for multiple uncorrelated plane waves on fully augmentable sparse linear arrays requires large sample sizes, as indicated by Cramer‑Rao bound analysis." That covers both.

Abstract

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 M/spl times/M direct data covariance matrix, and then, alternating projections are applied to find a p.d. Toeplitz matrix with m-variate signal eigensubspace ("signal subspace truncations"). When m/spl ges/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/spl rarr//spl infin/) and, therefore, needs to be 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/spl ges/M) presented.