Improved Capon Estimator for High-Resolution DOA Estimation and Its Statistical Analysis

Despite some efforts and attempts have been made to improve the direction-of-arrival (DOA) estimation performance of the standard Capon beamformer (SCB) in array processing, rigorous statistical performance analyses of these modified Capon estimators are still lacking. This paper studies an improved Capon estimator (ICE) for estimating the DOAs of multiple uncorrelated narrowband signals, where the higher-order inverse (sample) array covariance matrix is used in the Capon-like cost function. By establishing the relationship between this nonparametric estimator and the parametric and classic subspace-based MUSIC (multiple signal classification), it is clarified that as long as the power order of the inverse covariance matrix is increased to reduce the influence of signal subspace components in the ICE, the estimation performance of the ICE becomes equivalent to that of the MUSIC regardless of the signal-to-noise ratio (SNR). Furthermore the statistical performance of the ICE is analyzed, and the large-sample mean-squared-error (MSE) expression of the estimated DOA is derived. Finally the effectiveness and the theoretical analysis of the ICE are substantiated through numerical examples, where the Cramer-Rao lower bound (CRB) is used to evaluate the validity of the derived asymptotic MSE expression.