Optimal Utilization of Signal-Free Samples for Array Processing in Unknown Colored Noise Fields

Many algorithms for direction-of-arrival (DOA) estimation require the noise covariance matrix to be known or to possess a known structure. In many cases, the noise covariance is, in fact, estimated from separate measurements. This paper addresses the combined effects of finite sample sizes, both in the estimated noise covariance matrix and in the data with signals present. It is assumed that a batch of signal-free samples is available in addition to the signal-containing samples. No assumption is made on the structure of the noise covariance. In this paper, the asymptotic covariance of the weighted subspace fitting (WSF) algorithm is derived for the case in which the data are whitened using an estimated noise covariance. The expression obtained suggests an optimal weighting that improves performance compared to the standard choice. In addition, a new method based on covariance matching is proposed. Both methods are asymptotically statistically efficient. The Cramer-Rao lower bound (CRB) on the covariance of the estimate for the data model is also derived. Monte Carlo simulations show promising small sample performance for the two new methods and confirm the asymptotic results